Two-sigmaish CMS multilepton excesses with a \(\tau\)

A possible hint of third-generation superpartners

Matt Strassler mentioned an interesting anomaly reported by CMS at a SUSY conference this week:

A Discrepancy to Keep an Eye On (Prof Dr RNDr Matt Strassler PhD CSc DrSc Dot COM)

It's small enough so that you may assume that it's just another example of a fluctuation that will go away with more data. But it's large enough for many of us to gain the right to be intrigued. ;-)



The excesses have something to do with multileptons. If you search this blog for multileptons, you find many articles, mostly from late year 2011 and early year 2012. The words "year" were inserted for you to notice that there were many hyperlinks in the previous sentence. It's plausible that those flukes have gone way during the 1.5-2.0 years.

What are the overrepresented events this time?




The CMS folks have performed a search for some signatures – at this point, it's not quite clear what comprehensive theory beyond the Standard Model they are testing but multileptons of course do naturally appear in long enough decay chains of supersymmetric particles (they are a strong hint that at least a pair of new particles was produced because they're almost absent in the Standard Model and in the decay of one new particle) – for events with four leptons and some of the subsets of these events exhibit modest but tantalizing excesses.




We're talking about events with four leptons including

• at least one \(\tau^\pm\) that decays to hadrons; I start with that to point out that the signal could have something to do with the third generation of fermions and their partners
• one light (\(e^\pm\) or \(\mu^\pm\)) lepton-antilepton pair (this is what OSSF1, opposite-sign-same-flavor-one, stands for) that seems not to originate from a Z-boson decay (because the Z-boson is assumed to be understood and boring; the condition is called "off-Z")
• the total energy in the lepton pair plus a few other jets quantified by a variabled called \(H_T\) should be surprisingly small relatively to expected LHC energies; this condition indicates a threshold above which a new massive particle was barely created
• another charged lepton, \(e^\pm\), \(\mu^\pm\), or \(\tau^\pm\)
• some missing momentum – which surely gets a contribution from the neutrino(s) that is (are) produced along with the \(\tau\) lepton but may also include the LSP etc.

A table that Matt reproduces for us has about 48 entries and 3 of them contain noticeable excesses. All of them are in the OSSF1, \(H_T\lt 200\GeV\), off-Z, \(N(\tau_h)=1\), \(N_{b\rm -jets}=0\) – bins with other options for these variables are really consistent with the Standard Model predictions.

The three bins with an excess only differ in the missing transverse energy:\[

\begin{array}{|c|c|c|}
\hline
E_T^{\rm miss} & {\rm predicted} & \text{observed}\\
& \text{events}& \text{events}\\
\hline
(0,50) & 7.5\pm 2 & 15\\
\hline
(50,100) & 2.1\pm 0.5& 4 \\
\hline
(100,\infty)& 0.6\pm 0.24 & 3\\
\hline
{\rm total} & 10.2\pm 2.1 & 22\\
\hline
\end{array}

\] Sorry if the error margins shouldn't have been added in quadrature; even if it is roughly correct, it's not the totally accurate way to account for the error margins. I guess that the right error should be between 3 and 4 events. I suspect that the errors in the table are just the systematic ones and the Poisson-type statistical ones \(\sqrt{N}\) must be added in quadrature manually. If you can clarify these issues, it would be appreciated.

At any rate, when you combine these three similar channels – naturally ignoring the magnitude of the transverse energy – you get something that may look like a greater than (or at least approximately equal to) \(3\sigma\) excess (because \(10.2\) and \(22\) are really far from each other). I don't want to say \(5\sigma\) which the sloppy calculation above could hint at because I don't believe this can be the right result.

I would say that the missing energy may be arbitrarily low in the events above so if an LSP is created, it should be a light one, safely below \(50\GeV\) – possibly the \(8.6\GeV\) dark matter particle suggested by CDMS II-silicon and others. And the superpartners created at the beginning of the reaction are likely to have something to do with the third generation – like staus. Or sbottoms...

This is not an excess you should think about every night at 3 a.m. so far. But it's an excess that you may return to at some point in the future and describe by the words that you already knew about it on August 29th, 2013, before the revolution got started.

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Tohoku, JP wins the International Linear Collider

The project may still be cancelled...

In June 2013, I discussed the contest between the Sefuri mountains and the Kitakami mountains who will build the International Linear Collider if any collider will be built. Recall that the former offered a sexy 4-minute musical video; the latter offered a somewhat boring, 21-minute-long educational video.

The "boring" video guys won! ;-) Congratulations to Hitoshi Murayama et al.

Tohoku pitched for ¥1 trillion [$10 billion] collider (JP Times)

---

Miyagi, Iwate prefecture mountains picked as possible site for int'l particle accelerator (The Mainichi)

The Japan Times tell us that 50% of the cost should be paid for by the host country and there seems to be some degree of skepticism in the newspaper and in the ministry of education etc.



83% of the overall expenses are construction costs; the rest is paid for land acquisition, salaries, and the production of the equipment.




I am convinced that $5 billion is a small amount for Japan that would earn a special status for the Land of the Rising Sun. Whether you like it or not, the state-of-the-art particle physics collider is still the #1 science project that turns the host country into a natural candidate for the headquarters of the world's pure scientific research. Even among non-friends of physics, I believe that the LHC contributes to the feeling that Europe is perhaps not quite entering the process of irreversible decay (in some respects, it's perhaps ahead of the U.S. and China etc.) and Japan could get revived in a similar way.




Incidentally, I want to mention that CDF and DZERO published a new paper on the top quark-antiquark forward-backward asymmetry,

Differential cross section \(\dd \sigma/\dd(\cos \theta t)\) for top-quark-pair-production in \(p\bar p\) collisions at \(\sqrt{s} = 1.96\TeV\),

where they insist on the existence of the strange effect and claim that the whole effect may be attributed to the first, "linear" spherical harmonic \(Y_{10}\). The other coefficients (up to something like \(\ell=7\)) of the spherical harmonics seem to be OK.

Thanks to Joseph S. for the links.

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Promoting HEP physics in the U.S.: a poll

Listen now: I disabled the Odiogo's "listen now" buttons because the company found out that there's insufficient demand for audio ads on the web and the service has to be a paid one, from $129 a year (since September 1st), which seems like too much to me. It's plausible that this blog could be free as a "personal" one but I don't want to investigate.

Joseph S. sent me a link to the Symmetry Magazine, Why Particle Physics Matters, that offers you four 1-minute-or-so videos explaining the Americans why HEP physics is worth their money. You may vote for your favorite.



I decided not to hide my preferences. This guy from Mississippi is my winner. His passion for learning and his particle physics built on Columbus' shoulders sound appropriate to me.




He's arguably a particle physicist from the only not-clearly-left-wing state (or city) and I think you can see it in his style and presentation. It has much more energy. He's been trained to proselytize and convince other people about things that aren't obviously true and important according to their culture.




In comparison, the remaining three people seem slightly bored and their videos seem somewhat boring to me, offering some PC-style theses about people who are ill, colored, or female. They seem to be used to preach to the converted, colleagues in a partly intellectually sterile environment that suffers from group think.

Now, the Champions League theme song came to Pilsen for the first time (when Pilsen played in the Champions League for the first time, it had to play in Prague because our municipal stadium wasn't great yet). Tonight, I simply have to watch the first match of FC Viktoria Pilsen against the Slovenian champion, Maribor. It's aired on Prima Cool, the channel that airs The Big Bang Theory and similar programs.



The winner of the double match will play in the basic group of the UEFA Champions League; the loser will fall down to the Europa League of Losers. ;-)

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In defense of five standard deviations

Originally posted on August 12th. The second part was added at the end. The third part. Last, fourth part.

Five standard deviations are cute.



However, Tommaso Dorigo wrote the first part of his two-part "tirade against the five sigma",

Demistifying The Five-Sigma Criterion

I mostly disagree with his views. The disagreement begins with the first word of the title ;-) that I would personally write as "demystifying" because what we're removing is mystery rather than mist (although the two are related words for "fog").

He "regrets" that the popular science writers tried to explain the five-sigma criterion to the public – I think they should be praised for this particular thing because the very idea that the experimental data are uncertain and scientists must work hard and quantitatively to find out when the certainty is really sufficient is one of the most universal insights that people should know about the real-world science.




When I was a high school kid, I mostly disliked all this science about error margins, uncertainties, standard deviations, noise. This sentiment of mine must have been a rather general symptom of a theorist. Error margins are messy. They're the cup of tea of the sloppy experimenters while the pure and saint theorist only works with perfect theories making perfect predictions about the perfectly behaving Universe.

Of course, sometimes early in the college, I was forced to get dirty a little bit, too. You can't really do any empirical research without some attention paid to error margins and probabilities that the disagreements are coincidental. As far as I know, the calculations of standard deviations was one of the things that I did not learn from any self-studies – these topics just didn't previously look beautiful and important to me – and the official institutionalized education system had to improve my views. The introduction to error margins and probabilistic distributions in physics was a theoretical introduction to our experimental lab courses. It was taught by experimenters and I suppose that it was no accident because they were more competent in this business than most of the typical theorists.

At any rate, I found out that the manipulations with the probability distributions were a nice and exact piece of maths by themselves – even though they were developed to describe other, real things, that were not certain or sharp – and I enjoyed finding my own derivations of the formulae (the standard deviations for the coefficients resulting from linear regression were the most complex outcomes of this fun research).




At any rate, hypotheses predict that a quantity \(X\) should be equal to \(\bar X\pm \Delta X\) if I use simplified semi-laymen's conventions. The error margin – well, the standard deviation – \(\Delta X\) is never zero because our knowledge of the theory, its implications, or the values of the parameters we have to insert to the theory are never perfect.

Similarly, the experimenters measure the value to be \(X_{\rm obs}\) where the subscript stands for "observed". The measurement also has its error margin. The error margin has two main components, the "statistical error" and the "systematic error". The "total error" for a single experiment may always be calculated (using the Pythagorean theorem) as the hypotenuse of the triangle whose legs are the statistical error and the systematic error, respectively.

The difference between the statistical error and the systematic error is that the statistical error contains all the contributions to the error that tend to "average out" when you're repeating the measurement many times. They're averaging out because they're not correlated with each other so about one-half of the situations are higher than the mean and one-half of them are lower than the mean etc. and most of the errors cancel. In particular, if you repeat the same dose of experiments \(N\) times, the statistical error decreases \(\sqrt{N}\) times. For example, the LHC has to collect many collisions because the certainty of its conclusions and discoveries is usually limited by the "statistics" – by their having an insufficient number of events that can only draw a noisy caricature of the exact graphs – so it has to keep on collecting new data. If you want the relative accuracy (or the number of sigmas) to be improved \(K\) times, you have to collect \(K^2\) times more collisions. It's that simple.

On the other hand, the systematic error is an error that always stays the same if you repeat the experiment. If the CERN folks had incorrectly measured the circumference of the LHC to be 27 kilometers rather than 24.5 kilometers, this will influence most of the calculations and the 10% error doesn't go away even after you perform quadrillions of collisions. All of them are affected in the same way. Averaging over many collisions doesn't help you. Even the opinions of two independent teams – ATLAS and CMS – are incapable of fixing the bug because the teams aren't really independent in this respect as both of them use the wrong circumference of the LHC. (This example is a joke, of course: the circumference of the LHC is known much much more accurately; but the universal message holds.)

When you're adding error margins from two "independent" experiments, like from the ATLAS collisions and the CMS collisions, you may add the statistical errors for "extensive" quantities (e.g. the total number of all collisions or collisions of some kind by both detectors) by the Pythagorean theorem. It means that the statistical errors in "intensive quantities" (like fractions of the events that have a property) decreases as \(1/\sqrt{N}\) where \(N\) is the number of "equal detectors". However, the systematic errors have to be added linearly, so the systematic errors of "intensive" quantities don't really drop and stay constant when you add more detectors. Only once you calculate the total systematic and statistical errors in this non-uniform way, you may add them (total statistical and total systematic) via the Pythagorean theorem (physicists say "add them in quadrature").

So far, all the mean values and standard deviations are given by universal formulae that don't depend at all on the character or shape of the probabilistic distribution. For a distribution \(\rho(X)\), the normalization condition, the mean value, and the standard deviation are given by\[

\eq{
1 & = \int dX\,\rho(X) \\
\bar X &= \int dX\,X\cdot \rho(X) \\
(\Delta X)^2 &= \int dX\,(X-\bar X)^2\cdot\rho (X)
}

\] Note that the integral \(\int dX\,\rho(X)\) with the extra insertion of any quadratic function of \(X\) is a combination of these three quantities. The Pythagorean rules for the standard deviations may be shown to hold independently of the shape of \(\rho(X)\) – it doesn't have to be Gaussian.

However, we often want to calculate the probability that the difference between the theory and the experiment was "this high" (whether the probability is high enough so that it could appear by chance) – this is the ultimate reason why we talk about the standard deviations at all. And to translate the "number of sigmas" to "probabilities" or vice versa is something that requires us to know the shape of \(\rho(X)\) – e.g. whether it is Gaussian.



There's 32% risk that the deviation from the central value exceeds 1 standard deviation (in either direction), 5% risk that it exceeds 2 standard deviations, 0.27% that it exceeds 3 standard deviations, 0.0063% that it exceeds 4 standard deviations, and 0.000057% which is about 1 part in 1.7 million that it exceeds five standard deviation.

So far, Dorigo wrote roughly four criticisms against the five-sigma criterion:

• five sigma is a pure convention
• the systematic errors may be underestimated which results in a dramatic exaggeration of our certainty (we shouldn't be this sure!)
• the distributions are often non-Gaussian which also means that we should be less sure than we are
• systematic errors don't drop when datasets are combined and some people think that they do

You see that this set of complaints is a mixed bag, indeed.

Concerning the first one, yes, five sigma is a pure convention but an important point is that it is damn sensible to have a fixed convention. Particle physics and a few other hardcore hard disciplines of (usually) physical sciences require 5 sigma, i.e. the risk 1 in 1.7 million that we have a false positive, and that's a reasonably small risk that allows us to build on previous experimental insights.

The key point is that it's healthy to have the same standards for discoveries of anything (e.g. 1 in 1.7 million) so that we don't lower the requirements in the case of potential discoveries we would be happy about; the certainty can't be too small because the science would be flooded with wrong results obtained from noise and subsequent scientific work building on such wrong results would be ever more rotten; and the certainty can't ever be "quite" 100% because that would require an infinite number of infinitely large and accurate experiments and that's impossible in the Universe, too.

We're gradually getting certain that a claim is right but this "getting certain" is a vague subjective process. Science in the sociological or institutionalized sense has formalized it so that particle physics allows you to claim a discovery once your certainty surpasses a particular thresholds. It's a sensible choice. If the convention were six sigma, many experiments would have to run for a time longer by 35% or so before they would reach the discovery levels but the qualitative character of the scientific research wouldn't be too different. However, if the standard in high-energy physics were 30 sigma, we would still be waiting for the Higgs discovery today (even though almost everyone would know that we're waiting for a silly formality). If the standard were 2 sigma, particle physics would start to resemble soft sciences such as medical research or climatology and particle physicists would melt into stinky decaying jellyfish, too. (This isn't meant to be an insulting comparison of climatology to other scientific disciplines because this comparison can't be made at all; a more relevant comparison is the comparison of AGW to other religions and psychiatric diseases.)

Concerning Tommaso's second objection, namely that some people underestimate systematic errors, well, he is right and this blunder may shoot their certainty about a proposition through the roof even though the proposition is wrong. But you can't really blame this bad outcome – whenever it occurs – on the statistical methods and conventions themselves because you need some statistical methods and conventions. You must only blame it on the incorrect quantification of the systematic error.

The related point is the third one, namely that the systematic errors don't have to be normally distributed (i.e. with a distribution looking like the Gaussian). When the distribution have thick tails and you have several ways to calculate the standard deviations, you should better choose the largest one.

However, I need to say that Tommaso heavily underestimates the Gaussian, normal distribution. While he says that it has "some merit", he thinks that it is "just a guess". Well, this sentence of his is inconsistent and I will explain a part of the merit below – the central limit theorem that says that pretty much any sufficiently complicated quantity influenced by many factors will be normally distributed.

Concerning Tommaso's last point, well, yes, some people don't understand that the systematic errors don't become any better when many more events or datasets are merged. However, the right solution is to make them learn how to deal with the systematic errors; the right solution is not to abandon the essential statistical methods just because someone didn't learn them properly. Empirical science can't really be done without them. Moreover, while one may err on the side of hype – one may underestimate the error margins and overestimate his certainty – he may err on the opposite, cautious side, too. He may overstate the error margins and \(p\)-values and deny the evidence that is actually already available. Both errors may turn one into a bad scientist.

Now, let me return to the Gaussian, normal distribution. What I want to tell you about – if you haven't heard of it – is the central limit theorem. It says that if a quantity \(X\) is a sum of many (\(M\to\infty\)) terms whose distribution is arbitrary (the distributions for individual terms may actually differ but I will only demonstrate a weaker theorem that assumes that the distributions coincide), then the distribution of \(X\) is Gaussian i.e. normal i.e. \[

\rho(X) = C\exp\zav{ - \frac{(X-\bar X)^2}{2(\Delta X)^2} }

\] i.e. the exponential of a quadratic function of \(X\). If you need to know, the normalization factor is \(C=1/(\Delta X)\sqrt{2\pi}\). Why is this central limit theorem true?

Recall that we are assuming\[

X = \sum_{i=1}^M S_i.

\] You may just add some bars (i.e. integrate both sides of the equation over \(X\) with the measure \(dX\,\rho(X)\): the integration is a linear operation) to see that \[

\bar X = \sum_{i=1}^M \bar S_i.

\] It's almost equally straightforward (trivial manipulations with integrals whose measure is still \(dX\,\rho(X)\) or similarly for \(S_i\) and that have some extra insertions that are quadratic in \(S_i\) or \(X\)) to prove that\[

(\Delta X)^2 = \sum_{i=1}^M (\Delta S_i)^2

\] assuming that \(S_i,S_j\) are independent of each other for \(i\neq j\) i.e. that the probability distribution for all \(S_i\) factorizes to the product of probability distributions for individual \(S_i\) terms. Here we're assuming that the error included in \(S_i\) is a "statistical error" in character.

So the mean value and the standard deviation of \(X\), the sum, are easily determined from the mean values and the standard deviations of the terms \(S_i\). These identities don't require any distribution to be Gaussian, I have to emphasize again.

Without a loss of generality, we may linearly redefine all variables \(S_i\) and \(X\) so that their mean values are zero and the standard deviations of each \(S_i\) are one. Recall that we are assuming that all \(S_i\) have the same distribution that doesn't have to be Gaussian. We want to know the shape of the distribution of \(X\).

An important fact to realize is that the probabilistic distribution for a sum is given by the convolution of the probability distributions of individual terms. Imagine that \(X=S_1+S_2\); the arguments below hold for many terms, too. Then the probability that \(X\) is between \(X_K\) and \(X_K+dX\) is given by the integral over \(S_1\) of the probability that \(S_1\) is in an infinitesimal interval and \(S_2\) is in some other corresponding interval for which \(S_1+S_2\) belongs to the desired interval for \(X\). The overall probability distribution is given by \[

\rho(X_K) = \int dS_1 \rho_S(S_1) \rho_S(X_K-S_1).

\] You should think why it's the case. At any rate, the integral on the right hand side is called the convolution. If you know some maths, you must have heard that there's a nice identity involving convolutions and the Fourier transform: the Fourier transform of a convolution is the product of the Fourier transforms!

So instead of \(\rho(X_K)\), we may calculate its Fourier transform and it will be given by a simple product (we return to the general case of \(M\) terms immediately)\[

\tilde \rho(P) = \prod_{i=1}^M \tilde\rho(T_i).

\] Here, \(P\) and \(T_i\) are the Fourier momentum-like dual variables to \(X\) and \(S_i\). However, now we're almost finished because the products of many (\(M\)) equal factors may be rewritten in terms of an exponential. If \(\rho(T_i)=\exp(W_i)\), then the product of \(M\) equal factors is just \(\exp(MW_i)\) and the funny thing is that this becomes totally negligible if \(MW_i\gg 1\). So we only need to know how the right hand side behaves in the vicinity of the maximum of \(T_i\) or \(W_i\). A generic function \(W_i\) may be approximated by a quadratic function over there which means that both sides of the equation above will be well approximated by \(C_1\exp(-MC_2 T_i^2)\) for \(M\to\infty\).

It's the Gaussian and if you make the full calculation, the Gaussian will inevitably come out as shifted, stretched or shrunk, and renormalized so that \(X\), the sum, has the previously determined mean value, the standard deviation, and the probability distribution for \(X\) is normalized. Just to be sure, the Fourier transform of a Gaussian is another Gaussian so the Gaussian shape rules regardless of the variables (or dual variables) we use.

So there's a very important – especially in the real world – class of situations in which the quantity \(X\) may be assumed to be normally distributed. The normal distribution isn't just a random distribution chosen by some people who liked its bell-like shape or wanted to praise Gauss. It's the result of normal operations we experience in the real world – that's why it's called normal. The more complicated factors influencing \(X\) you consider, and they may be theoretical or experimental factors of many kinds, the more likely it is that the Gaussian distribution becomes a rather accurate approximation for the distribution for \(X\).

Whenever \(X\) may be written as the sum of many terms with their error margin (even though the inner structure of these terms may have a different, nonlinear character etc.; and the sum itself may be replaced by a more general function because if it has many variables and the relevant vicinity of \(X\) is narrow, the linearization becomes OK and the function may be well approximated by a linear combination i.e. effectively a sum, anyway), the normal distribution is probably legitimate. Only if the last operation to get \(X\) is "nonlinear" – if \(X\) is a nonlinear function of a sum of many terms etc. or if you have another specific reason to think that \(X\) is not normally distributed, you should point this fact out and take it into account.

But Tommaso's fight against the normal distribution as the "default reaction" is completely misguided because pretty much no confidence levels in science could be calculated without the – mostly justifiable – assumption that the distribution is normal. Tommaso decided to throw the baby out with the bathwater. He doesn't want an essential technique to be used. He pretty much wants to discard some key methodology but as a typical whining leftist, he has nothing constructive or sensible to offer for the science he wants to ban.

Second part

Dorigo's second part of the article is insightful and less controversial.

He reviews a nice 1968 Arthur Rosenfeld paper showing that the number of fake discoveries pretty much agrees with the expectations – some false positives are bound to happen due to the number of histograms that people are looking at. Sometimes experimenters tend to improve their evidence by ad hoc cuts if they get excited by the idea that they have made a discovery. Too bad.

Dorigo argues that the five-sigma criterion should be replaced by a floating requirement. This has various arguments backing it. One of them is that people have differing prior subjective probabilities quantifying how much plausible or almost inevitable they consider a possible result. Of course that extraordinary claims require extraordinary evidence while almost robustly known and predicted ones require a weaker one. It's clear that people get convinced by some experimental claims at a lower number of sigmas than for other claims. But I wouldn't institutionalize this variability because due to the priors' intrinsically subjective character, it's extremely hard to agree on the "right priors".

He also mentions OPERA that made the ludicrous claim about the superluminal neutrinos that was called bogus on this blog from the very beginning. It was a six-sigma result (60 nanoseconds with a 10 nanoseconds error), we were told. Dorigo blames it on the five-sigma standards. But this is just silly. Whatever statistical criterion you will introduce for a "discovery", you will never fully protect physics against a silly human error that may introduce an arbitrary large discrepancy to the results – against stupid errors such as the loosened cable. I wouldn't even count it as a systematic error; it's just a stupid human error that can't really be quantified because nothing guarantees that it remains smaller than a bound. So I think it's irrational to mix the debate about the statistical standards with the debate about loosened cables and similar blunders that cripple the quality of an experimental work "qualitatively" – they have nothing to do with one another!

Third part

In the third part, Dorigo discusses three extra classes of effects and tricks that may lead to fake discoveries. I agree with everything he writes but none of these things implies that the 5-sigma standard is bad or that it could be replaced by something better.

The first effect is mismodeling (well, a systematic error on the theoretical side); the second effect is aposterioriness, the search for bumps in places where we originally didn't want to look (which is OK for discovering new physics but such unplanned situations may heavily and uncontrollably increase the number of discrepancies i.e. false positives we observe, and we shouldn't forget about it when we're getting excited about such a discrepancy); and dishonest manipulation of the data (there's no protection here, except to shoot the culprit; if someone wants to spit on the rules, he will be willing to spit on any rules).

Fourth, last part

In this fourth and final part, Dorigo continues in a discussion of a bump near \(150\GeV\). At the very end, he proposes ad hoc modifications of the five-sigma rule – from 3 sigmas for the B decay to two muons to 8 sigmas for gravitational waves. One could assign ad hoc requirements that differ for different phenomena but it's not clear how it would be determined for many other phenomena for which the holy oracle Dorigo hasn't specified his miraculous numbers. Moreover, the patterns in his numbers don't seem to make any sense. It is very bizarre why a certain exotic, not-guaranteed-to-exist decay of the B-mesons is OK with 3 sigmas while the gravitational waves that have to exist must pass 8 sigmas. Moreover, some other observed signatures, like "SUSY", aren't really signatures but whole frameworks that may manifest themselves in many experiments and each of them clearly requires a different assignment of the confidence levels if we decide that confidence levels should be variable. There would be some path from being sure that there's new physics to being reasonably sure that it's a SUSY effect – Dorigo seems to confuse these totally different levels of knowledge.

If this table with the variable confidence levels were the goal of Dorigo's series, then I must say that the key thesis of his soap opera is crap.

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LIGO: improving sensitivity by squeezed states

Gravitational waves could become visible next year

On Friday, SciTechDaily wrote about an interesting recent article in Nature:

Improvements to LIGO Detector Will Allow Scientists to ‘Listen’ to Black Holes Forming (SciTechDaily, Daily Galaxy)

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Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light by J. Aasi and 24 co-authors (Nature Photonics: full PDF paper here)

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LIGO.org press release

LIGO, the Laser Interferometer Gravitational-Wave Observatory, a large L-shaped instrument to detect the gravitational waves, hasn't seen anything yet but it may change soon and dramatically.



The authors of the new Nature paper – the whole LIGO collaboration – is sending special packets of light, the squeezed states, to one of the LIGO detectors and this modification is improving the sensitivity.




Sometimes it sounds like they are claiming that they are circumventing the Heisenberg uncertainty principle but I hope that they're not being completely silly. They're apparently improving a suboptimal technique that has been used so far.




With the upgrade, the facility could become able to observe black holes that are just being born. The gravitational waves could provide us with completely new "eyes" to see many phenomena in the Universe.

LIGO is now being upgraded to Advanced LIGO, scheduled to be operational in 2014. Correct me if I am wrong but I think that the current usage of the squeezed states isn't completely new but what's new is that the squeezed states are being used for the frequency range 150-300 Hz.

Also, my understanding is that this improvement should be ready when Advanced LIGO begins its operations. That's why another article in The Daily Galaxy claims that the direct detection of the gravitational waves is imminent. It sounds pretty exciting.

Just to be sure, state-of-the-art theorists don't have any realistic doubts about the existence of gravitational waves as predicted by GR. It seems impossible for GR to work in all the situations where it has been tested while failing in the case of the gravitational waves. Also, the discovery of a binary pulsar that generated the 1993 Physics Nobel Prize allowed one to verify that the celestial system is losing the same energy each second (the loss is measured from the accelerating frequency of the orbits) that is carried away by the GR-calculable gravitational waves. This consistency check has actually been repeated using independent celestial objects (which have different parameters) so it's almost certainly not a coincidence. We're only waiting for a direct detection of the waves and the applications of these new "eyes".

Hat tip: Bahamas

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Some physics links

Carroll's QM, NYT's firewalls, Jester's whining on scales

Sean Carroll has unlocked the quantum chapter from his "Eternity" book,

Quantum Mechanics Made Easy,

which I found better than expected despite its misleading comments about the "collapse", "its" relationships with the "arrow of time", the meaning of the "Copenhagen Interpretation", the "many worlds" as the "leading alternative contender", and many other things (he omits Bohm etc.). Carroll's text is flawed in different ways than e.g. Brian Greene's musings about the interpretation of quantum mechanics but I wouldn't say it's "more flawed". I am still not aware of any popular presentation of the foundations of quantum mechanics that is done right.




Now, Dennis Overbye wrote quite an informative and long The New York Times article about the black hole firewalls and the ER-EPR correspondence,

A Black Hole Mystery Wrapped in a Firewall Paradox.

Overbye confirms his status as one of the world's best popular science writers who focuses on theoretical physics. As a reader, you are reminded about some of the intellectual stories of Einstein and Hawking as well as the interactions that made various people confuse each other about the firewall fallacy on the West Coast. Susskind whose opinions resembled a yo-yo hasn't changed his views for several months, we're told.

Incidentally, Bousso has a new paper about the firewalls and if I judged the situation according to everything that is written in these still equally confusing if not crazy papers (Bousso claims that there's a firewall even when the black hole is very young – a brutal violation of locality), I would have to agree that they're as confused as 40 years ago – something written in Overbye's article. In the real world, the claim that things haven't become much clearer in the last 40 years is an outrageously crazy lie. At least my understanding of all these questions is much better than even 15 years ago – perhaps because I don't change my mind whenever someone writes some new bullshit.



Most frequent surnames. Click for all 40 informative and funny maps that you will ever need. Via the Pirate of Prague.

There will be a workshop in Santa Barbara about these matters. It's organized by Don Marolf. He also posted his own new paper arguing that holography doesn't depend on strings. As far as I can see, it's a sloppy tirade full of unsubstantiated claims – well, the claims are supported at most by a vague analysis of something that has been analyzed very accurately since late 1997. We know pretty much exactly what the bulk stringy objects – strings and branes and black holes etc. – mean in the boundary CFT, when they matter, when they can be neglected, which properties of string theory are important and unimportant for various derivations (e.g. of black hole entropy), and so on. It's hard to imagine how a superficial paper such as Marolf's could be considered as anything else than a redundant, outdated, not quite competent, low-quality addition to the literature.




Finally, Jester at Resonaances published a new blog entry after 4 months or so (delay caused by "work, travel, frustration, depression, and sloth").

I agree with all of his "matter of fact" claims but I don't share his emotional reaction at all.

Jester says that since the 1930s, physicists – we would say phenomenologists – would be looking towards a holy grail, a high-energy scale, which always happened to be the electroweak scale. New physics had to be added to make the theory work. Now, the theory at the electroweak scale (the Standard Model) seems to be completed and consistent as a renormalizable quantum field theory so there's nothing else to "inevitably expect" at that scale – and the LHC confirms that except for the Higgs, this scale isn't "overflowing" with tons of new physics. So even though it's still likely but not certain that there's new physics such as SUSY at a nearby scale, the physicists have to look at another scale to achieve a certainty about new physics but he doesn't know which one.



So this is how the situation looks to Jester – and Savas. No clear direction for progress, they think.

Jester's claims about the physics are true but his reasons for frustration are inappropriate. What he dislikes is that regardless of the energy of the next (realistic) collider, \(30\TeV\), \(100\TeV\), or \(1,000\TeV\), we can't be quite sure that the collider finds new physics. I agree with that but I am not shocked by it in any way.

It has been clear to me that the Standard Model was a complete renormalizable theory – a theory that can be extrapolated to really, really high energy scales – since I was a college sophomore. (In the following year, I began to attend QFT courses: buy the book on the electroweak theory by my major undergraduate QFT instructor.) So of course that once all the necessary pieces of this Standard Model are established, there is no other new physics testable at the accelerators that is "inevitable" in an energy range that is "guaranteed".

One could say that I was solving similar questions as Jester but it was 20 years ago. Is that the first time when Jester realizes that the Standard Model is a complete renormalizable QFT that doesn't need extra additions? We know about some likely additions linked to the Higgs stability, hierarchy problem, dark matter, inflation etc. (Jester discusses them as well) but we're not guaranteed that they're accessible by any particular realistic collider.

Well, I have always even shared Jester's strategy to find an energy scale below which new physics is guaranteed. And I found it (so did Max Planck 100 years earlier although he didn't quite understand the physics of the scale). It's the Planck scale. New phenomena have to occur at the scale \(10^{19}\GeV\) or lower (it may be much lower in models with large or warped extra dimensions but the true fundamental scale can't be higher).

It would be fun if the scale could be accessed by direct experiments except that it seems unlikely and we have always thought it was unlikely. So why should we be "negatively surprised" now? I, for one, don't care much (and have never cared much) that Nature has made the scale so high that it's not accessible by our particle physics experiments. (Of course, the gap between the scales has to be this high because it's ultimately needed for the existence of life. Evolution of life requires lots of sunny days. Stars are long-lived because they contain many nuclei that may be burned and the number of nuclei ends up large because gravity is so much weaker than other forces and pressures so lots of nuclei are needed for the gravity to become significant and compensate the repulsive pressures.)

The Planck scale is the scale where my thinking about fundamental physics – and the thinking of any top-down theorist – begins. From this inaccessible scale, one may dig deeper perhaps down to the experimenters' scales but it has always been clear that the true fundamental scale where important things have to exist is the Planck scale. (Stringy and grand unified theories make it likely but not guaranteed that there are some interesting additional phenomena at scales slightly, perhaps 10-100 times, lower than the Planck scale, too.) Everything else are just optional islands alternating with optional deserts. You may demand that there is some land in the ocean at each 100 miles (and even claim that gaps in the ocean that are longer than 100 miles prove that geography is no science because you can't swim there) except that the rules of geography don't have to respect your demands. The existence and inner workings of Eurasia is mostly independent of America so – even though Jester may find it surprising – no one is guaranteed that there has to be an America at most 100 miles from Spain.

So what the confused headless hens show is just a minor thing – that the dogmatic bottom-up, direct-experiments-based view on fundamental physics isn't a sustainable strategy to keep the research going. All the people claiming that physicists are only allowed to think about things that must have consequences for particular near-future experiments have always been as deeply misguided as the Spanish Catholics who wanted to prevent Columbus from trying to sail to another continent around the round globe.

One has to think about topics that are behind the currently observable horizons if he wants to make real progress! We could say that the bottom-up paradigm is complete and dead and it's time for every single phenomenologist to learn some string/M-theory because this is the new physics that is guaranteed at a certain well-defined scale. Otherwise one will be stuck with increasingly bizarre speculations based on a wishful thinking. The hen cartoon is right: if you're chasing a new visible island of new physics that has to be visible from your place, you will lose the sense of direction and your search will be chaotic and unguided. Look at Jester's words:

So, while pushing up the energy frontier in accelerators will continue, I think that currently searching high and low for a new scale is the top priority. ...

He wants to guess the kingdom of the new scale and its princess from some higher-dimension operators such as\[

\frac{1}{\Lambda^2}(\bar s\gamma_\rho b) (\bar \mu \gamma^\rho \mu).

\] It's a fact that you're not guaranteed to find anything at any particular scale. It's like looking at the Atlantic Ocean with your binoculars. Are you guaranteed to see hints of a new continent, America? Isn't it better to be more courageous and abandon the totally unjustified assumption that your left leg should permanently stand on the Iberian peninsula? Columbus did so. His group was sailing for a few thousand kilometers – he didn't exactly know how much was needed – and he discovered a new continent. Chances are that you can't discover a new important land without getting wet!

Just to be sure, I think it's slightly more likely than not that SUSY will be discovered at the LHC in 2015 and the probability is comparable to one-half that the dark matter underground experiments will agree about a dark matter particle. But none of these probabilities is "well above 99 percent", for example. Indeed, we're not guaranteed that any particular experiment will discover these new things. There's no scientific or rational reason why we should be guaranteed that. And there's no reason for science to stop just because we're not guaranteed such things.

Again, it's time for HEP non-experimenters to (at least partially) switch to the top-down thinking unless they want to increasingly resemble the headless hens.

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Both neutralino, sbottom may weigh less than \(20\GeV\)

Dark matter searches and LHC rumors may converge in a light sbottom-photino point

I decided that the most exciting hep-ph preprint today is

Supersymmetry with Light Dark Matter confronting the recent CDMS and LHC Results

by Alexandre Arbey, Marco Battaglia, and Farvah Mahmoudi. An interesting detail about the list of the authors is that all of them are partially affiliated with the CERN theory division. Why is it interesting? Because the LHC top squark rumor from February 2012 was later rumored to have arrived from the CERN theory division so these three physicists might know much more about the superpartners accessible to the LHC than the rest of us.



They are inspired by the "positive side" of the dark matter wars and investigate whether the MSSM (Minimal Supersymmetric Standard Model) may predict the LSPs (Lightest Superpartners: the supersymmetric theories' candidates for the WIMP dark matter particle, in most cases) that are as light as \(10\GeV\) or so. Note that the most accurate figure suggested by the "coalition of the willing" is \(8.6\GeV\) by CDMS II Silicon.




At any rate, the new CERN theoretical paper argues that in contrast with the unproven assumption in the bulk of the MSSM literature (that superpartner masses are above \(100\GeV\)), this very light new particle that the dark matter direct search experiments are perhaps seeing could be the ordinary neutralino from the MSSM, the simplest and most widely studied supersymmetric model of particle physics.

The late LEP collider that used to work in the LHC tunnel until 2000 (LHC's song) has measured the invisible width of the Z-bosons – the number of times when this boson decays to invisible final products – and it hasn't found anything. It means that such a light hypothetical LSP can't be interacting with the Z-boson too strongly. Consequently, it must be mostly photino, a state that is perpendicular to the zino.




This is my wording which, I believe, reflects a more appropriate choice of the basis than the bino/wino dichotomy. The usual 2-dimensional basis in the space of the neutral colorless gauge bosons consists of the photon and the Z-boson and you may consider their superpartners, the photino and the zino. It's perhaps more natural because the fermionic superpartners get contributions to their masses from the Higgs mechanism, too (and not just from SUSY breaking). Because the \(Z\to \tilde\chi^0_1\tilde\chi^0_1\) must be suppressed (the superscript zero is the electric charge; the subscript labels particles of a similar kind from the lightest so 1 means the lightest one in the group), it follows that \(\tilde\chi^0_1\), the lightest neutralino (which happens to be the LSP), must be nearly a photino.

Because the photon is "mostly" the \(U(1)_Y\) B-boson while the Z-boson is "mostly" the \(W_3\) neutral W-boson, we may also say (and they do say) that the LSP in their scenario is mostly the bino. In the popular MSSM scenarios, the LSP is on the contrary mostly a neutral wino. As I said, I think that we could be shown that it's more natural to keep the basis photino/zino for the superpartners as well and the LSP discussed in the paper could be almost exactly a photino.

Such a light LSP would lead to various contradictions in the generic case but all of them will be solved with the extra assumption stated in the next paragraph. Moreover, the very light LSP would generically have a too tiny cross section with the nucleons which would make it impossible for these photinos to show up in the dark matter direct search experiments.

Both problems are solved if the NLSP (Next to Lightest Superpartner i.e. the second lightest supersymmetric partner) is the mostly right-handed sbottom, \(\tilde b_R\), with the near-maximal mixing angle around \(\pi/2\). If the mass splitting is\[

M_{\tilde b_R} - M_{\tilde \chi^0_1} \lt 7\GeV,

\] then the nucleon-WIMP cross section is pleasantly increased, some unwanted processes are suppressed, and everything seems OK. For the light sbottom, they mention their preferred mass range \(15\)-\(25\GeV\). But if you assume that the LSP sits near \(8.6\GeV\), the CDMS II Silicon figure, then you may see that the light sbottom should be lighter than \(16\GeV\) or so.

The lighter top squark should be between \(600\GeV\) and \(700\GeV\) in this picture. The lower bound follows from the stop's absence in some LHC searches; the (less certainly known) upper bound is required to preserve the stability of the Higgs potential. The heavier, mostly left-handed sbottom is another \(100\GeV\) or so above the top (or at least not far). The second lightest neutralino and the lightest charginos are between \(150\) and \(1,000\GeV\).

I think it would be lots and lots of fun if the LHC began to discover the superpartners starting from the very light photino and bottom squark. Such a possibility seems to be consistent with all LHC constraints, with the positive hints suggested by the dark matter direct search experiments, and perhaps even with the rumors that the LHC may have been seeing some hints of third-generation squarks for some time and that the CERN theory division is the environment that may be ahead of us in the knowledge of this breakthrough. ;-)

To parameterize the possibilities, the paper is employing the pMSSM, the 1999 phenomenological MSSM i.e. the MSSM's bottom-up phenomenology-inspired (19 masses of superpartners quantifying) subspace of the parameter space, that is more viable than the nearly excluded, top-down-inspired (but equally dimensional) CMSSM ("C" for "constrained") / mSUGRA (Minimal Super Gravity) subset and that is likely to spread in the SUSY model building literature in the foreseeable future.

In most of the typical MSSM literature, the superpartners were always reorganized to charginos, neutralinos etc. and treated independently of their known superpartners. I increasingly feel that this may have led to an unnecessarily generalized choice of the bases.

Instead, it's plausible that the simple superpartners of the known particles, including the photon and the Z-boson, could produce a more realistic basis. It seems very natural to me to believe that the photino isn't too heavy i.e. isn't too far from the (vanishing) mass of the photon; the zino isn't "too" (more than a factor of 4 heavier) far from \(90\GeV\); and the sbottom and the stop aren't too far from the masses of the third-generation quarks, either. In fact, the Wildlife Supply Company already offers you a $47 plastic tool to replace all bottom quarks in an object by comparably light sbottoms (see the amazon.com link). With this logic taken seriously, I would also expect the stau[s] (tau slepton) and the tau sneutrino to be relatively light; the assumption is that the particle-superpartner mass proximity doesn't apply to the first two generations and gluons-gluinos.

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Detonation of the Sun

A frequent source of links has sent me the coordinates of a page

Explosion of Sun

introducing a paper by Alexander Bolonkin and Joseph Friedlander urging all the physicists to think about the possibility that a malicious regime will send a thermonuclear weapon into the Sun and speed up the reactions inside the Sun – effectively converting all of our beloved star to a giant H-bomb long before our main source of useful energy is expected to go red giant around the year 7.5 billion AD.



This picture contains just a real-world eruption! Via IO9.

In the authors' opinion, physicists and others have a moral duty to either exclude the possibility, or look for security measures that would protect us against such a rogue regime, or prove that such a protection is impossible.

First of all, is such an explosion possible?




I don't think so. Note that the concern isn't much different from the old concern that some fathers of the H-bomb had to think about – namely whether the H-bomb would start to devour the whole atmosphere and the rest of the Earth as it realized that it's a thermonuclear fuel that may be burned.

Why is it similar?




It's similar because the present authors are afraid of the increase of the Sun's temperature from the current 9-17 million Celsius degrees in the Sun core to temperatures that are at least an order of magnitude higher and allow the reactions to be exponentially sped up. Consequently, the present temperature is negligible relatively to the desired one. In that respect, the comparison of real and "desired" temperatures is analogous to the situation on Earth where the atmosphere is also much cooler than the temperature needed to change the atmosphere to thermonuclear fuel. In both cases, the initial temperature may be neglected and approximated by zero.

Moreover, the Sun density is about 1.4 times the maximum density of water so it is surprisingly comparable to the densities encountered on our blue, not green planet, too.

The arguments showing that such a risk isn't there are somewhat subtle – the "proof" that we're safe is in no way trivial from a beginner's viewpoint. But I am confident it may be formulated. It seems to me that the "detonating Sun alarmists", much like the "detonating Earth's atmosphere alarmists", are neglecting various other quantities describing the environment that go beyond the temperature and density.

It's plausible that you may create much higher temperatures in a cubic meter of the Sun – probably only on the surface because it's implausible that any material will be able to penetrate through the solar matter whose temperature starts at 6000 Celsius degrees or so (all conventional materials melt and/or evaporate around that point). But if you create such huge temperatures in a small region, it doesn't imply that they will spread.

It seems clear to me that the rate of cooling of the "detonatingly hot" region will be too high when the size of the region grows. More importantly, you just never obtain a high density in this way. The density of the Sun is what it is, dictated by the overall solar mass and the solar volume, and an extra bomb doesn't change this counting much. Because the density of the bulk of the Sun will remain fixed, the ultimate near-equilibrium temperature of fusion is pretty much dictated by this density, and this temperature is what we observed in the Sun today.

See also my answer Why Jupiter isn't a star, whether Jupiter may be blown up and what it would mean, how to stop or blow apart a star, why asteroids around us don't have relativistic velocities, or many other questions and answers about related dramatically catastrophic cosmic (im)possibilities. ;-)

For these reasons and others, I am not really afraid of a Khamenei who would like to turn the ancient Egyptian God, the Sun, into an unhinged Allah. ;-)

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Skyrmions could make hard disks 100 times smaller

Remotely related: sci-fi gets real: tech junkies should look at 27 science-fiction concepts that morphed into reality in 2012.

Nature's Ron Cowen reviewed a technical paper in Nature that is one month old,

Writing and Deleting Single Magnetic Skyrmions (Niklas Romming and 7 co-authors from Hamburg).

See also reviews in Gizmodo and those via Google News. Thanks to Viktor K. for the link.



Skyrmions, some topologically non-trivial solutions of non-linear sigma-models first described by Tony Skyrme in the 1960s, may be thought of as tiny vortices of atoms. Because in this very recent breakthrough, Romming et al. became able to create and destroy them at will, it's plausible that they may be used in future magnetic information storage technologies.

I've been in love with skyrmions decades before I knew their name.




It really began when I was 15. I was obsessively reading Albert Einstein's book "My World View" ("Mein Weltbild", in a Czech translation) that I had found somewhere in the bookshelves (I guess that it would originally belong to my paternal grandfather, a professional painter/artist and geometry teacher).




In this book, one that probably overlaps with "Ideas and Opinions" heavily, Einstein popularly presents his views and insights about relativity, religion, socialism, Jewish questions, Nazism, meanders, Max Planck, alleged incompleteness of quantum mechanics, and other things.

Einstein wrote many inspiring things, many things that looked deeply ethical, many political ideas I would later find myself in disagreement with, many ideas about physics that were right, and some ideas about physics that were wrong.

Those nearly 25 years ago, I was only beginning to be exposed to quantum mechanics and for a year, I was an employee of Einstein's dream to construct the unified field theory de facto as a classical field theory, if you allow me to use the standard terminology. After some months, I had to begin to steal ideas from proper quantum mechanics to explain the hydrogen atom, before I was forced to steal all of quantum mechanics, of course, but let me avoid the hydrogen atom here.

While its quantum dynamics implies that some quantum numbers are discrete, there are also other observables that have to be discrete in the real world (because they were observed as discrete!) although such a quantization rule seems hard to get in a classical field theory. In one of the essays, Einstein wrote something like (using a modernized terminology):

Quantum mechanics is probably incomplete and a complete description should still be looked for. There is no proof that an old-fashioned, realist, classical theory may not account for the quantum phenomena. For example, the quantization of the electric charge could follow from a classical field theory. There could be a classical field theory that allows us to derive that whenever the charge density vanishes on the boundary of a region, the region contains a charge that is an integral multiple of the elementary charge.

I took that as a homework and apparently found a solution. Imagine that in each point of the spacetime, there is a field that takes values on a three-sphere. If \(\vartheta(x,y,z,t)=0\) corresponds to a conventionally preferred point of the sphere (the North Pole) in the same way that we know from the two-sphere, we may add a potential energy term to our action such as\[

S_{\rm pot}\sim - C \int \dd^4 x\,\vartheta^2

\] that will place the value of \(\vartheta\) in the majority of the spacetime close to the value zero. However, in a limited three-dimensional region, the field \(\vartheta\) may probe all points of the target three-sphere. We may figure out that in those regions, the real space may be "wrapped" on the target space three-sphere.

The charge density may be calculated as the "solid angle" spanned by the infinitesimal region of space in the three-sphere. That means that the charge current is proportional to the Hodge dual of a Jacobian of a sort,\[

j^\kappa = \frac{e}{6}\cdot\frac{1}{2\pi^2} \varepsilon^{\kappa\lambda\mu\nu} \partial_\lambda V^a \partial_\mu V^b \partial_\nu V^c \varepsilon_{abcd} V^d

\] where \(V^a\) is the four-vector embedding the three-sphere pointer into a four-dimensional Euclidean space of a sort; we always have \(V^a V_a=1\). I hope that I inserted the right normalization factor above; \(1/6\) avoids the multiple counting over the permutations of \(a,b,c\) while the other factor divides by the "full solid hyperangle" i.e. the surface/volume of the unit three-sphere \(2\pi^2\) for the integral of \(j^0\) over the regions where something happens to be an integer multiple of \(e\).

This seemed like a cute idea. Later, I learned that the magnetic (monopole) charge density actually is represented by a similar topological trick. However, the electric charge is quantized for purely quantum mechanical reasons. Due to the quantization of energy in the quantum harmonic oscillators, one may only add energy to charged fields by creation operators whose electric charges are quantized. There's nothing wrong about this intrinsically quantum explanation for the electric charge.

In the 1990s, the discovery of dualities (and S-duality in particular) showed that these two constructions or explanations for the charge quantization are equivalent although the proof is in no way obvious.

In 1998, I still didn't know the word "skyrmion" although my adviser Tom Banks was telling me that I should have found out what the word meant. ;-) But when I and Ori Ganor asked how the cylindrical M2-branes stretched between pairs of M5-branes are represented at the Coulomb branch of the 6-dimensional (2,0) theory, they are represented by skyrmions, too. The fivebranes become knitted.

This 6-dimensional construction differs from the 4-dimensional construction above by some changes to the dimension only. First, the pointer field isn't labeling a three-sphere but a four-sphere. You may obtain the corresponding vector \(V^a\) from the 5-dimensional transverse Euclidean space as the separation of the corresponding points of the two M5-branes normalized so that it is a unit vector, i.e. as\[

V^a = \frac{\Phi^a_M - \Phi^a_N}{|\Phi_M -\Phi_N|}

\] where the index \(a=1,2,3,4,5\) labels the transverse dimensions to the M5-branes and \(M,N\) label the M5-branes themselves (Chan-Paton indices of a sort).

There's one more difference between the six-dimensional and four-dimensional case. The six-dimensional theory has five and not just four spatial dimensions. So the four-sphere may only be wrapped by four spatial dimensions and the solution remains constant in 1 remaining spatial dimension (plus 1 temporal dimension). That's why the resulting skyrmionic objects are strings rather than point-like objects. They become tensionless strings ("the" tensionless strings known in this theory) in the \(\Phi_M-\Phi_N\to 0\) limit where the Coulomb-branch-based description of the theory breaks down.

In 2000, Ken Intriligator used some nice anomaly considerations to derive structurally similar terms in the six-dimensional theory. I've tried to see that the equations are equivalent to the skyrmion-based ones but the two papers always seemed slightly inequivalent at the end.

In various effective descriptions of nuclear physics, one encounters nonlinear sigma-models and the baryon number seems to be exactly given by the skyrmionic wrapping number. I guess that the detailed implementation of the nonlinear sigma-models is inequivalent in the condensed-matter-physics setup by Romming et al. but the mathematics is going to be analogous. In a foreseeable future, this 50-year-old piece of mathematical physics that has appeared at various places of real physics may dramatically improved magnetic information storage systems.

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SUSY, a scapegoat: different kinds of belief

...much of the anti-SUSY propaganda is unbelievable...

One week ago, I argued that it is totally inappropriate to use the adjective "speculative" for theoretical frameworks such as supersymmetry.

It's a topic that's being discussed at many places which is why now, one week later, I will reopen these issues. Two days ago, Alok Jha of the Guardian wrote his text

One year on from the Higgs boson find, has physics hit the buffers?

and it was discussed at a leading HEP crackpots' website where Giotis, Urs Schreiber, and others kindly debate some nasty and stupid physics haters. Incidentally, the subtitle in Jha's article calls SUSY "the elusive followup theory to the Higgs mechanism". First, it isn't the only or most accurate way to describe SUSY which is mostly independent of the Higgs issues. Second, it isn't "the" only followup theory to the Higgs mechanism. Third, if it were "the [right] followup", it shouldn't be shocking if we need more than 1 year after the discovery of the Higgs boson to discover SUSY. One year is a short time in the history of physics.

But the basic point that Giotis began to emphasize to these demagogues is that the existence of SUSY in Nature and the discovery of SUSY at the LHC are two completely different questions. The LHC is an accelerator that allows us to reach energies that are one order of magnitude greater than the energies accessible at the previous top collider, the Tevatron. But even at the logarithmic scale, you would need to make about 15 analogous steps to get close to the fundamental scale (or the string scale).

The LHC may look expensive to some people but it's just far from a tool allowing us to directly test the most fundamental questions about Nature. Whether this increase of the log(energy) by 1/15 of what we would like is enough to find groundbreaking discoveries isn't and couldn't be clear. The LHC has found the Higgs boson and it is not "impossible" that this is it.




Columbus may have seen no traces of a new (or old and exotic) continent 2,000 kilometers West from Spain but that didn't imply that there were no new continents in that direction.

In Spring 2007, I listed some probabilities of different ambitious propositions in high-energy physics. It's still about right but I would say that my numbers were slightly optimized to be acceptable for the bulk of high-energy physics theorists. At any rate, you see that the probability that string theory is right is closer to 100% than to 50% (I would insert a higher number today); the probability of SUSY at the GUT or lower scale was quoted as 70% (and yes, I would write the same number today, with most of the remaining 30% corresponding to SUSY that only gets restored between the GUT scale and the Planck scale); and the probability of SUSY at the LHC was 50%. Note that it has never been "guaranteed" that the LHC would see SUSY and almost none of the SUSY champions has ever claimed such a thing. I surely haven't. I have always viewed SUSY at the LHC as a "damn plausible" possibility which is worth thinking about because it's so exciting.

Science produces insights, people write new papers, they have time to think about the old ones, so the probabilities are evolving. But there has been no complete revolution since 2007 so the current numbers are qualitatively the same. Of course that the probability that the LHC will find SUSY has moderately decreased because the LHC has already depleted a fraction (but far from 100%) of its ability to find new physics. The claims that theorists are completely negating their logic and circumvent the rules are just lies.




Now, of course that it would be great fun if the LHC started to produce tons of new physics. But something's being "fun" is a totally different thing from its being true – and from its being a prediction of a theoretical framework. Individual models may predict SUSY at the LHC – and parameter spaces of these theories may at least claim that "SUSY at the LHC is very natural". But it is not really clear which of these parameter spaces of classes of theories is right so science in general isn't able to predict when the supersymmetry or any other example of new physics will be discovered with any certainty at this point – and whether it will be at the LHC.

Ben Allanach, a top SUSY phenomenologist, said the following to the Guardian:

If the worst happens, and supersymmetry does not show itself at the LHC, Allanach says it will be a wrench to have to go and work on something else. “I’ll feel a sense of loss over the excitement of the discovery. I still feel that excitement and I can imagine it, six months into the running at 14 TeV and then some bumps appearing in the data and getting very excited and getting stuck in. It’s the loss of that that would affect me, emotionally.”

It's obvious and right that folks like Allanach are excited according to the experimental data that are arriving. Again, excitement is something else than the truth, too. Truth may seem unexciting for quite some time but it's still the truth and to find a new great truth, one (and the mankind) often has to be very patient, clever, and hard-working. By the way, by "something else to work on", Ben Allanach surely doesn't mean "other kinds of new low-energy physics" because this will have been largely falsified, too.

At any rate, the supersymmetric model building isn't the only part of research of SUSY or the only body of knowledge we have about SUSY. SUSY is a much grander principle whose importance goes well beyond the LHC and its limits. It seems necessary to produce fermions, ban tachyons, and improve some hierarchy-like problems according to the only known (and, most likely, the only mathematically possible) unifying theory of quantum field theory and general relativity – an overarching theory we still call string theory. From this broader, top-down viewpoint that I prefer, phenomenologists are just "engineers" who are working on specific ways to discover SUSY (and questions what exactly will be seen) in the near (or not so near) future.

But the SUSY research doesn't really boil down to these phenomenologists' work and it didn't start with that.

In the early 1970s, SUSY began in the USSR when some mathematical physicists asked whether spacetime symmetries greater than the Poincaré symmetry may be compatible with everything we know; and it started in the West when Pierre Ramond decided to incorporate fermions to the (previously) bosonic string theory. The Soviet guys found exactly one possible extension of the known spacetime symmetries, a graded Lie algebra known as supersymmetry. And Ramond found out that the world sheet SUSY was needed to add the fermions to string theory. Later, Ramond's (and Neveu-Schwarz's) string theory was shown to predict spacetime supersymmetry, too (with GSO projections). Years before that GSO's development, people walking in the footprints of Wess and Zumino were already building 4D supersymmetric quantum field theories. In the early 1980s, other folks like Savas Dimopoulos and Howard Georgi – soon accompanied by folks like Gordon Kane and Howard Haber – were reconciling supersymmetry with the Standard Model and looking what new things result from this union.

Of course that the Standard-Model-like supersymmetric models are the most relevant ones for the interpretation of likely and plausible experimental signals in the near future. But they're far from being the most fundamental supersymmetric models. Even in our Nature, SUSY is almost certainly realized by a more comprehensive theory than the MSSM – at least if you want to include higher-energy phenomena.

In the more formal QFT and string theory research, SUSY has been essential for most of the important other developments in the last 30 years, too. It was needed to make grand unification really convincing (due to the coupling unification in MSSM). It was needed to calculate some quantities that established dualities (S-duality, U-duality, Seiberg-Witten analyses of gauge theories), it was essential for the twistor prescriptions for gauge theories, to calculate the correct black hole thermodynamics from a microscopic theory, to establish and study almost all specific theory pairs in AdS/CFT. Matrix theory requires SUSY as well and there are many more examples. SUSY cures or improves certain "systemic" inconsistencies and hierarchies and the modern research has simply shown that "Yes SUSY" is a better default assumption than "No SUSY". The progress leading to this paradigm shift was theoretical in character but it was totally scientific, anyway.

The continuing validity of the Standard Model is just another example of the wisdom that successful theorists often underestimate the range of validity of their own theories. This 1994 paper by David Gross summarizing the 1938 Warsaw conference showed lots of confusion that was around at that time. With the shining exception of the early de facto string theorist Oskar Klein, all top physicists were eager to falsify quantum mechanics and/or quantum electrodynamics at nearby scales, typically the Compton wavelength of the electron (distance in between the size of the atom and the nucleus). Of course that we know that the validity of QED goes much further than that. Those big shots should have taken their discoveries more seriously than they did. Sometimes old physicists who have already achieved enough want the younger theorists to share their relatively simple path to fame and wealth but Nature isn't obliged to obey. After some discoveries, it may often take a longer time for new discoveries to emerge. It's not necessarily the current physicists' fault; it's often just a fact about Nature's inner workings.

The case of the Standard Model may very well be analogous. People are obsessed by the wishful thinking that they will see lots of discoveries in the rest of their lives which is an assumption requiring that the discrepancies between the experiments and the established theories will be found rather soon. But it doesn't have to be the case. However, if the discrepancies aren't found quickly, it doesn't mean that there is no new physics or the search for new physics is futile. It just means that Nature eventually forces us to be more patient as She unmasks that some guesses about the speed of new discoveries were too optimistic. The "right amount of patience" is something that only Nature is allowed to determine and we ultimately learn what the amount was. It's totally dumb to impose any Stalinist or Smolinist five-year plans or five-year deadlines if we really don't know where (how far) Nature has hid the new treasures.

Phenomenologists who made bets on new physics around the corner shouldn't be surprised. If 1,000 phenomenologists propose 1,000 different, inequivalent models for new physics beneath a threshold, e.g. 1 TeV, then it's guaranteed that at least 99.9% of them would ultimately be shown wrong. We didn't need the LHC to arrive to this conclusion. High-energy physics was producing lots of hypothesized and competing models of new physics because the development of these ideas was still cheaper than the construction of the experimental gadgets (the price of the LHC equals 100,000 annual salaries of a phenomenologist – e.g. 1,000 phenomenologists funded for 100 years which is a lot of papers, of order 100,000 as well). This price comparison (the fact that relevant HEP experiments have become relatively expensive) is the reason why it's inevitable that model builders have probed many possibilities in advance, most of which are guaranteed to be excluded by the LHC, so the composition of the phenomenological literature was guaranteed to paint a "too optimistic" projection of the coming experimental discoveries of new physics. These comments seem sort of obvious to me, I have always kept them in mind, but it seems that many other people were not.

In each article of this sort, I have to emphasize that SUSY is just treated as a scapegoat. The LHC data are compatible with the Standard Model so far which reduces the probability that any theory of new physics that is too radical is right; the LHC razor cuts through the space of possibilities within each paradigm of new physics. SUSY is the most well-motivated principle of new physics but among the experimentally relevant proposals of physics Beyond the Standard Model, SUSY is not being hurt more than others. In fact, just the opposite is true: the relative weight of SUSY in the signals of new physics that have a chance to be found first is increasing as other theories are being excluded more "sharply" than SUSY. It's something we have known before the LHC began its operations, too.

John Ellis is quoted by the Guardian:

John Ellis, a particle theorist at Cern and King’s College London, has been working on supersymmetry for more than 30 years, and is optimistic that the collider will find the evidence he has been waiting for. But when would he give up? “After you’ve run the LHC for another 10 years or more and explored lots of parameter space and you still haven’t found supersymmetry at that stage, I’ll probably be retired. It’s often said that it’s not theories that die, it’s theorists that die.”

The claim that theorists die but theories do not is catchy and cute but I don't really think it's an accurate description of the real world. Physicists are sometimes right, sometimes wrong, sometimes they die, sometimes they are born, sometimes they share their opinions with similar physicists, sometimes they don't, sometimes they're more right than younger physicists, sometimes they're less right than younger physicists, and so on. There isn't any general rule that would say that older physicists have to be wrong or something like that.

Moreover, what the death of old theorists is good for in most cases isn't really the death of wrong theories. Instead, the death of old theorists is often needed for the new and better theories to be allowed to live. Physicists like Albert Einstein would decelerate the progress in quantum mechanics if they were around for too long and in too high numbers; physicists like Paul Dirac would discourage younger physicists from computing renormalized corrections in quantum field theories because they didn't "believe" renormalization; physicists I could name but I won't name would slow down or cripple the research of string theory if these old chaps weren't dying sufficiently quickly, and so on.

I have already mentioned that in some cases, the old theorists are too conservative in the sense that they're no longer able to absorb the new theories and their logic, so they just use their authority to "refuse" them and be loud about it. On the other hand, I have also mentioned that old theorists often tend to expect more speedy revolutions than what Nature actually recommends. So old theorists may err in both directions. It's silly to assume that they always err in the same way. If this were the case, they would have to be completely stupid not to learn anything from similar if not "always the same" mistakes by their predecessors.

What I need to point out about Ellis' indication that he won't say that SUSY is wrong in his lifetime is that as far as I see the reality, he simply has very good scientific reasons to keep his opinions. It's something I have explicitly said many times myself. Long before the LHC began its operation, I was saying that the LHC may find no new physics but I would still be confident that string theory and SUSY are right in Nature.

It's pathetic for the aggressive cranks to interpret Ellis' words as a sign of dishonesty. The data coming from the LHC show that the proponents of any new physics have to be more patient than the (strongest) optimists were expecting. The data don't selectively imply that SUSY is wrong simply because SUSY models compatible with all the data exist. They just imply that the Standard Model is useful and accurate enough in a larger class of contexts but we know it's not quite accurate so it's a matter of when and what, and not if, the new physics starts to emerge. You can't rule out a well-defined theory such as a class of SUSY models differently than by falsifying it, by showing it's wrong, by finding a contradiction. Vague demagogic slogans about their "not even wrong" aren't enough for well-defined theories. Wolfgang Pauli has used the "not even wrong" slogan for largely ill-defined (and also fundamentally misguided because postulates-of-QM-denying) musings by David Bohm, not for a Pauli-style well-defined physics ideas such as SUSY. It's really an example of chutzpah to use Pauli's dismissive anti-Bohm slogan against a theory of the very kind that he would love (or discover!) if he hadn't died in 1958 (symmetries depending on the spin in new ways – which other physicist in the 1920s would have loved that?).

The Baltic American counterpart of Alexander Unzicker has not only offered this nasty and unfair criticism against Ellis. He also wrote:

The LHC will be in operation until 2030 or so, and you can always start arguing that 100 TeV will be needed to see SUSY (see here), ensuring that giving up won’t ever be necessary except for those now still wet behind the ears.

You see that it's a disgusting and dishonest demagogy, the kind of demagogy that the scum that keeps on reading that blog likes to hear. The single word that is most dishonest about the quote above is "start". People won't start to claim that 100 TeV is needed to (almost reliably) see SUSY. They have always claimed so. Some relatively recent phenomenological advances made the sub-100-TeV scale even more attractive. There are numerous reasons to think that something should be happening over there.

After all, the Superconducting Supercollider that was canceled almost 20 years ago was supposed to have the center of mass energy equal to 40 TeV which is pretty much of the same order as 100 TeV. So it's completely unfair to suggest that it would be a sign of the theorists' arrogance and their changing of the rules during the game if they wanted a 100 TeV collider in 2015. They – we – have always wanted one. It was the default energy scale for the accelerators that the theorists were actually planning. Political reasons forced the theorists to be satisfied with a 13 TeV collider more than 20 years later and many theorists would say that it could be enough to see new physics, too. But no doubt about that, at 13 TeV (or even 7-8 TeV), the risk that no new physics is found is of course higher than it is at 40 TeV.

I want to say that the suggestions by Shmoits and many similar people that the theorists are moving the lamp posts towards high energies is partly a lie, partly a tautology. It's partly a tautology because high-energy physics is about the research of high-energy phenomena and the more it knows, the more it moves towards higher energies. So some trend towards higher energies is inevitable as we're learning more. On the other hand, the "next big step" that the theorists were contemplating (and they were already building the collider) was always close to the vicinity of a TeV or dozens of TeV and if something has changed about this energy scale, it went down since the early 1990s or so, not up. Of course that there are also particular models that predicted new physics at low enough scales that would have shown up at the LHC by now but it didn't. They're excluded or their parameters have to be shifted towards less natural, heavier values. This is an inseparable part of learning: it's inevitable that there have to be periods in which the old theories just work so some specific enough scenarios with new physics have to be ruled out. But there are many classes of theories for which this hasn't really taken place.

People have been telling me about some advantages of precision machines, not too high-energy colliders and factories, and I have never bought into them. The energy frontier is still the most important place for progress. To increase the colliders' energy is the most natural way to increase the probability of new discoveries. This will probably be the case after the LHC, too. I am totally confident that the bulk of good phenomenologists agrees with me (I think that e.g. Nima Arkani-Hamed surely does).

Once the SSC was canceled, phenomenologists were sort of externally forced not to talk about "truly" high-energy colliders and these high energies themselves. But I don't really care. The cancellation of the SSC is an item in the history books and it doesn't mean that the mankind won't ever be allowed to build a super-20-TeV collider again. I don't find the old story too important today. The politicians don't have the power or the moral right to eternally constrain the scientists. They only decide about things at the timescale of their term. At longer timescales, things may be different. Of course that I want a 100 TeV or so collider. I have always wanted one but in the near future, due to some progress in the technologies, a real-world-priced collider that is this strong will become feasible again.

The ideas that one should "give up" this and similar research are really recommendations to abolish high-energy physics as a scientific discipline. There isn't any scientific evidence that this is sensible. Instead, the scientific evidence is overwhelming that the people proposing such things are dishonest stinky scumbags.

What I find unbelievably irritating are P.R.-like proclamations by individuals such as the crackpot-in-chief:

Urs, The problem is more your use of language, since if you made it clear to people that when you said “supersymmetry”, you meant something that can’t ever be tested, they wouldn’t take you very seriously. I think you’re right that some string theory/SUSY enthusiasts post-LHC will argue that nothing has shown them to be wrong, and nothing in their lifetime ever possibly can, but to the extent that they make this situation clear they will have a serious credibility problem.

What this jerk doesn't understand – or understands but doesn't want to admit – is that scientific theories aren't judged by their being taken seriously by brainwashed violent imbeciles among the laymen, the kind of low-brow primates who keep on devouring "Not Even Wrong" and similar feces and happily smack their lips at the same moment. Science is accepting or eliminating hypotheses according to the best scientific evaluation of the available evidence.

The available evidence makes it more reasonable to be convinced that SUSY is a part of Nature and unless a clear discovery occurs in the near future, a few years of extra experiments only have a modest ability to change the scientific opinions about this question because the experiments we can pay for today are simply not and cannot be machines that directly and "reliably" touch God's face. SUSY may turn out to be experimentally inaccessible by the LHC but the same would clearly be true about the non-existence of SUSY. So the evil people's belief that SUSY isn't out there is equally "unscientific" according to their own criteria – of course that these malicious kibitzers never apply their own rules to themselves.

Much of the science as we know it is about effects that we're certain or reasonably confident about but we can't directly experimentally test them. The closer we move towards the cutting edge, the higher percentage these "untestable" insights and hypotheses represent. Their being "untestable" in the most naive sense doesn't mean that they're not valuable. Many of them, including SUSY, are precious. One can be a completely uneducated, uncultural, brainwashed person who isn't able to understand these facts but these idiosyncrasies can't invalidate the facts. Columbia University's copy of Alexander Unzicker has been saying for years that in this sense, "[practically, now] untestable" ideas can't be an essential (or even legitimate) part of science. But what he has been saying has always been a lie, it is still a lie, and the people who haven't been able to figure out that this main thesis sold by the populist is rubbish have always been severely limited morons, they are still severely limited morons, and they will remain severely limited morons. Science has never worked according to their primitive recipes and to make things worse for them, science's distance from these recipes is increasing with time because our deepening understanding of the space of ideas allows scientists to separate credible theories and hypotheses from the raw experimental data by ever longer chains of derivations and implications.

Similarly, it is not the scientists' job to avoid a "credibility problem" with stupid and dishonest people who have no idea, especially with people who haven't even been capable of figuring out that Shmoits' rants are pure trash. Science is something completely different than P.R. This mediocre scum has gotten used to the situation in which their dirty buttocks are being licked by the populist politicians and media every day and everything must be according to the random desires of these degenerated spoiled brats. But as long as science remains science, it will carefully avoid this kind of external control. You don't find SUSY theorists "credible enough", stupid and nasty "Not Even Wrong" reader? Why don't you eat your own excrements to get some relief? The people who are telling you that science proceeds according to its looking "credible" to your random mood swings and vitriolic fads are not scientists even though sometimes they love to fraudulently create the impression. They are hardcore demagogues of the Shmoit kind – garbage like you. Thank you.

As a bonus, to expose the characteristic "quality" of the science by the anti-SUSY kibitzers, let me quote a comical crackpot called "N. Takanishi" at "Not Even Wrong":

Giotis, Three decades ago, I proved that SUSY cannot be the fundamental symmetry of physics. The reasoning is as follows. Evidently, SUSY, if it exists, must be spontaneously broken, but there is no Nambu-Goldstone fermion. Hence, one must assume that super-Higgs mechanism works. That is, supergravity must be encountered. However, quantum supergravity cannot be consistent with SUSY. This is because the global super-charge generators have no space-time index, while the translation generator P_mu does have a space-time index in contradiction with the SUSY anticommutation relation.

And it goes on and on and on. You see that he (or she) says that the supercharges have no spacetime indices. If he had asked his high school teacher, he would have known that supercharges have a spacetime index, a spinorial one. That's indeed needed for the SUSY algebra to be OK under the Lorentz symmetry and to have a spacetime vector (the momentum) on the right hand side. Completely rudimentary misunderstandings and ignorance – and I would say stupidity at a totally hopeless level – is what underlies the sand castle built by the anti-SUSY Mujahideens.

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