Friday, April 05, 2013

AMS: the steep drop is very likely there

Reconstructing the dark matter particle from sloppily censored data

On Wednesday, Sam Ting gave the talk about AMS-02 at CERN. If you missed the talk, you may watch the 85-minute recorded video here:
Recent results from the AMS experiment (CERN web, thanks to Joseph S.)
What I want to focus on are the slides 82-85, and especially 85, around 0:48:00-0:49:00. They show some particular events they have seen. The first three slides show a \(1\GeV\) electron and a positron with the same energy; a \(10\GeV\) electron and a positron of the same energy; a \(100\GeV\) electron and a positron of the same energy.

It could be a foolish IQ test – checking whether you know the geometric series – to ask you what is the next slide. Well, it could be a \(1\TeV\) electron and a positron of the same energy. Except that it's not. ;-)

Instead, the slide shows a \(982\GeV\) electron and a \(636\GeV\) positron; the latter figure is significantly lower than \(1\TeV\). Clearly, the number of electrons and positrons with similarly high energies that they could see was already pretty low. It seems extraordinarily natural to me to assume that \(982\GeV\) and \(636\GeV\) are the highest-energy electron and the highest-energy positron they have recorded so far: why wouldn't they boast about their biggest fish?

The text below is based on this assumption.

Sam Ting only showed the bins and the numbers of electron and positron events up to the highest \(260-350\GeV\) bin but we were not told the key information what was seen above this cutoff. Ting justified this silence by the data's not having a high enough confidence level, and so on. Still, there must exist some particular electron and positron events and it must be possible to count them.

We could have been told this raw data. We were not. I am convinced that he is trying to save some gunpowder for the AMS briefings in the following years – the spectrometer should operate for decades. At the same time, I have many reasons to think that if we were told something about the events above \(350\GeV\), we would see that their case for dark matter is much stronger than it looks from the officially published data.

Now, you should look at Figure 2a of the Cholis, Finkbeiner, Goodenough, Weiner 2008 paper. It shows how the positron fraction should behave for various neutralino masses in the most convincing models of WIMP, those based on neutralinos in supersymmetric theories.

The graph shows that if the known backgrounds were the only thing that contributes, the positron fraction should steadily decrease from \(0.05\) to \(0.01\) as you go from energies \(10\GeV\) to \(1,000\GeV\) on the log scale. Instead, AMS (and previously PAMELA and Fermi) saw the positron fraction increasing from \(0.05\) to \(0.15\) as you go from \(10\GeV\), a local minimum of the positron fraction, to \(350\GeV\).

This observed positron fraction is already much higher than the background – it's the "positron excess" that suggests new physics. However, pulsars could still be the mundane explanation of this excess. If the origin of this excess is truly new particle physics such as WIMPs, the drop of the positron fraction above \(350\GeV\) that we haven't seen should be steep.

The only new information I will use are the energies of the highest-energy events. The number of events of these high energies is pretty low. I was thinking how to approach the problem: Monte Carlo tests of various adjusted background-only and background-plus-signal distributions etc. Well, I would have to define lots of contrived fitting functions and do lots of complicated operations with them which would be a lot of work, especially given the fact that the final conclusions are very fuzzy and have an unimpressive statistical significance. At the end, I decided for a very simple strategy: to reasonably extend Table 1 of the AMS paper to the higher energies.

In the table below, I took the number of positrons in various bins and the positron fraction from Table 1 of the AMS paper. The total number of positrons+electrons in the first data column was calculated by a simple division. Now, the extra bins above \(350\GeV\) were added and the last bin in the electron+positron and positron columns that contained the highest-energy events of the two types was marked as \(1\). It could have been higher but both numbers have a comparable chance to be higher and the conclusions wouldn't dramatically change.

With the bins I chose, I interpolated the numbers in both columns (electron+positron, positron) by geometric series. And then I could calculate the positron fractions in the missing columns. The result looks like this:

Energy/\({\rm GeV}\) \(N(e^\pm)\) \(N(e^+)\) fraction
100-115 2719 304 0.11
116-132 1953 223 0.11
133-151 1284 156 0.11
152-173 1056 144 0.12
174-206 902 134 0.14
207-260 660 101 0.15
261-350 465 72 0.15
351-450 194 17 0.09
451-550 81 4 0.05
551-650 34 1 0.03
651-750 14 0 0
751-850 6 0 0
851-950 2-3 0 0
951+ 1 0 0

To make the story even shorter, my point is that the positron fraction must decrease to a very small value such as \(0.03\) in the bin around \(636\GeV\), the highest observed energy of a positron, because the number of electrons+positrons in that bin is still very high over there. It has to drop from the known value \(465\) in the \(260-350\GeV\) bin to \(1\) in the bin above \(950\GeV\). Because the number of electrons is behaving rather smoothly, I interpolated by some kind of geometric series to get \(34\) electrons+positrons in the \(551-650\GeV\) bin. I surely don't claim this number to be precise but I do think it is a good estimate and the number of positrons must be significantly larger than \(10\) in that bin, otherwise the graph of the number of electrons would be too bumpy which is unlikely.

The decrease from \(0.15\) below \(350\GeV\) to less than \(0.03\) above \(650\GeV\) may surely be classified as abrupt and it does suggest a WIMP (neutralino) mass of order \(350-650\GeV\). In fact, I think that there is a reason why AMS hasn't added another column above \(350\GeV\): the number of positron events was already very low over there, producing a positron fraction significantly smaller than \(0.15\). If the positron fraction were still close to \(0.15\) e.g. in \(350-500\GeV\), I am inclined to believe that they would still have added this extra bin.

If this extra reasoning is on the right track, the neutralino mass could be closer to the lower value, \(m_{\tilde \chi}\sim 350\GeV\). In fact, because all values between \(260\) and \(350\GeV\) were clumped together by AMS, it's equally plausible that the neutralino mass could be between \(260-350\GeV\) but closer to \(350\GeV\) because it seems that this "whole" bin is still behaving in the way that maximizes the positron fraction. Well, because the maximum of the positron fraction could actually be a bit higher than \(0.15\), perhaps close to \(0.20\), the \(260-350\GeV\) bin could be close to \(0.15\) because of the average of \(0.20\) in the lower half and \(0.10\) in the upper half. By these fuzzy ideas, I want to suggest that \(300\GeV\) is still plausible.

Again, I totally agree that even if AMS has the data sketched above, the data only support the conclusions I am trying to make at a rather low confidence level and it is very correct that AMS aren't trying to make bombshell announcements yet because they can't have the sufficient certainty.

On the other hand, it seems extraordinarily likely to me that Sam Ting must feel a bit strange because the picture he is presenting is significantly different from – weaker than – the picture he actually believes to be most likely based on the complete data he hasn't shown to us. I've tried to fill the gap above. The numbers above should make it a bit more explicit why I think that all the bloggers who say that AMS doesn't possess any hints are wrong: Katie Mack, Matthew Francis, Matthew Strassler, and probably many others.

If you look at the 2008 paper by Hooper, Blasi, Serpico, Table 1 shows you some positron fractions predicted by the pulsars, too. The decrease of the positron fraction is also rather steep, although not as steep as for WIMPs (a drop of the positron fraction to 1/5 of the maximum value just by doubling energy above the value producing the maximum seems unlikely with pulsars), but note that the positron fraction seems to be maximized for \(E\sim 100\GeV\), well below the apparent maximum near \(350\GeV\) suggested by the AMS data (with some extra reading in between the lines). That could be the real reasons why the pulsar explanation may suck although some people tried to argue that the models of pulsars could be adjusted and put on steroids to increase the maximum energy, too.

Note that in my "average" estimate of the high-energy particles, there were about \(310-311\) electrons and \(22\) positrons censored, producing \(0.07\) for the fraction above \(350\GeV\). The actual number of positrons and the fraction could be higher or lower. If the drop is truly steep, then the actual number of censored positrons is much lower than \(22\).


  1. One thing you didn't mention is that it gets harder to know whether something was an electron or a positron at higher energies. Obviously there's no sharp cutoff at 350 GeV, but the error bars might get really wide beyond that.

    Couldn't one flat out ask someone working on AMS what the data looks like beyond 350? Will that simply be kept a secret until the next time AMS releases data to the public? Just saying the uncertainty is high while refusing to say how high would be weird.

    On another note; assuming the entire positron excess is due to DM neutralinos annihilating, this gives us some info on the DM fraction in the early universe compared to now, right? Would this be compatible with CMB observations vs gravitational microlensing (or whatever is the best way to see how much DM there currently is)?

  2. There is a tendency by CERN to avoid to publish important results. This can be possibly traced back to the OPERA case where prudence would have helped. And this is true also for Higgs-like particles where they should have evidence for four more states of this kind but are carefully avoiding to made the information public.

  3. Dear Lubos, how many sigmas would you place on your conclusions assuming your guess about the undisclosed data is accurate?

  4. Hi Luke, two sigma - that's actually why I used the wording "very likely", it means 95% confidence level in my "IPCC-inspired" dictionary.

  5. "Obviously there's no sharp cutoff at 350 GeV"

    Well, it depends what you mean by "sharp" but a rather sharp cutoff near 350 GeV is indeed what I was trying to present as the most likely feature that their whole dataset shows.

  6. Hi Lubos, with a WIMP of about 300 GeV is not it likely that we can confirmate the same with the LHC data collected by, let's say, 2015?

  7. One can also fit the result to arxive:0810.5344 charts. An knowing that they do not have much statistics above 350 GeV, and apparently only one value above 650 GeV, one obtain more or less the same estimation as you, a neutralino slightly below 400 GeV...

  8. And that contradicts LHC results, and as a consequence the underlying neutralino model, so our conclusion is quite wrong maybe.

  9. What LHC results are contradicted? From what I see neutralino limits at 95% confidence are in ( CMS paper) 220GeV, quite consistent

  10. Perhaps one can formally request raw data under the protection of law :
    That would prevent it?

  11. Okay that he does not consider the data of sufficient quality for inclusion in their paper.
    But it is wrong not to consider the other people of sufficient quality to know and interpret them as they wish.
    The Fermi data have error bars quadruple big, and there will be no one complained about it.

  12. It may be that they are not sure of the errors for higher energies, for positron identification and even electron identification, and do not want to put points with huge errors on their plots. It is obviously a disagreement of physicists on data handling because Ting had been cryptic on the side of "we have remarkable information" some time before. Raw data are useless for the public, what you are asking is processed data through some analysis, and if the people doing the analysis are not confident it is correct, we have to wait.

  13. OK, I will personally not join this harassment because AMS folks don't deserve it and don't plan to hide the data indefinitely.

  14. One speculation I have not yet seen comes from realizing that CERN is also involved in AMS, and the lecture was given at CERN instead of a conference or workshop. It is within the limits of possibility that they are holding out until the LHC confirms or gives consistent bounds and give a concurrent announcement. This might mean that there is something brewing we do not know about in the supersymmetry analysis.

  15. Dear Anna, nice but if you listen to Ting's talk carefully, you will notice that he had promised to give the first talk at CERN already when AMS was getting started - years ago, long before anything substantial could get brewed at the LHC. ;-)

  16. I meant a cutoff in the ability to tell whether a particle was an electron or positron, not a cutoff in the positron ratio. That might be there.

    Fro distinguishing them, I'm going on what Strassler wrote: "At still higher energies the relative uncertainty will get worse: a
    particle’s electric charge is determined by measuring which direction
    the particle’s trajectory bends in a magnetic field, but the higher the
    energy, the straighter the trajectory becomes, so the challenge of
    determining the bending direction becomes greater."

    Apparently he was wrong about that. I'll have to point him to the ECAL page. Thanks!

  17. "I (the particle physicist) am correct, Lubos (the string theorist) is confused. Are you surprised?"

    heh. Oh well.

  18. LOL, nice. Just to be sure, the knowledge of these technical questions about AMS don't depend on one's background - it's about an ad hoc studying of the facts about this particular device, AMS.

    The article you just linked to made me LOL when I read it for the first time. It started by "The Alpha Muon Spectrometer [AMS] finally reported..." Yes, Matt apparently though that the Alpha Magnetic Spectrometer was all about muons.

    Great to hear that from that hard position three days ago, he became an AMS expert ;-) although the nonsense he is writing may disappointingly suggest that these reasons for celebrations are illusions.

  19. Let me also add that the extra things that Matt wrote on his blog obscure the essence here. Yes, AMS may safely detect the charge so the confusion are protons-vs-positrons. But all the numbers that even Matt has reproduced show how *immensely good* their ability to distinguish protons from positrons is. Consequently, the possible misidentification plays almost no role and - as Ting has stated pretty explicitly - the impossibility to deduce conclusions at the very high energies boils down to low statistics, not systematic things like misidentification.

  20. Hi Lubos,

    It is interesting to guess what they may have beyond 350 GeV.

    I added up all the positron events from 0.5 GeV to 350 GeV that have been published in the PRL supplementary paper and its 395224 positrons. AMS-02 press release however says that they observed positrons "in excess of 400,000." So over 4776 positrons should be either above 350 GeV or below 0.5 GeV. If we naively take the number of positrons below 0.5 GeV to be less than 2740 (the first bin that's 0.5-0.65 GeV has 822 and 822*0.5/0.15 = 2740 is a naive estimate) that still leaves a lot of positron above 350 GeV that appear to have been observed.

    Or maybe the number below 0.5 GeV is much higher?


  21. Thanks, Ravi, well, I would guess that a vast majority of the unreported positrons are below 0.5 GeV - at low energies, one may even have a "IR divergence" in some approximation.

  22. Dear Bill, weren't these potential systematic errors measured/tested on the Earth using artificial radiation?

  23. A good point Lubos, and my answer would be "Yes, but...". Yes, absolutely the detector performance was studied in exquisite detail in test beams, perhaps "helped" by the delays in the space shuttle program. But you can see that the maximum particle energy they studied was 400 GeV. While the extrapolations of expected performance beyond that energy are based on pretty reliable Monte Carlo and semi-analytic methods, I would imagine they are very wary if/when they start to see new physics that just happens to be at or beyond their highest calibrated energy.

  24. Hi. In principle those raw-data, as well as other HEP data, could be made public... But, contrary to other astronomical data (Fermi, Plank..) they are very much complex. Say they are comparable to data from LHC experiments. They appear meaningless for outsiders. In order to analyze them, one has to spend several months to fully understand their format, sub-detector performance, orbit environment etc. as well as to develop tools to manipulate these data properly. This 'training' process can be done only if one stays in close contact with people who developed and tested the detector (the collaboration members). I think an improper use of raw data isn't always a good thing for the advancement of science: it may lead to mis-interpretations, bad analyses, wrong claims...

  25. Hi, AMS is a CERN experiment since the beginning: collaboration meetings are taken at CERN, regularly, and most of members are based there. The control center is also there

  26. Hi. 400k+ is the total number of "observed positron", while 395k is the number of *galactic* positron estimated by the analysis, which do not consider the positrons with energy close (or under) the geo-magnetic cutoff. For sure AMS observed also non-galactic positrons (those trapped into the magnetosphere) that we know they must exist. No "IR devergence", but the geomagnetically trapped e+ are know to be relatively much abundant (if compared to trapped e-)

  27. This can't be an experiment which detects and proves the existance of dark matter (this can be just one more indication).Direct detection of dark matter is the task of the ongoing experiment in South Dakota:

  28. No cutoff