# Did the researchers at Fermilab find a fifth force?

Please consider the publication

Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in $p\bar{p}$ Collisions at $\sqrt{s} = 1.96$ TeV

by the CDF-Collaboration, already with huge media attention. I must admit that I am puzzled, astonished and excited at the same time. Not being an expert, it would be really nice if someone could shed light on the following question they posed:

### Did we find a fifth fundamental force that cannot be explained by the standard model?

What do you think?

PS.: A part of figure 1 in the publication that is re-printed over and over again:

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-1: a good question to ask, with educational answers, but this is so tied to a particular press release, at a particular moment in time. Chances are this will be of no interest in a few months. –  DarenW May 16 '11 at 20:18
@DarenW: Thank you for pointing out that it was a good question with nice answers. Please be aware to rate the question, not the paper here. –  Robert Filter May 17 '11 at 7:13
For what it's worth, this turned out to be a statistical fluke. –  David Z Sep 15 '11 at 17:38
+1 to reverse the downvote. –  Dimensio1n0 Jul 21 '13 at 5:15

The likely answer is No, the whole signal is just an artifact of the difficult statistical manipulations. A Weizmann Institute physicist has noted that the peak has been shifted by one bin and the whole discovery could therefore be due to a pile-up effect or jet energy calibration; a small shift of the jet energy removes the effect. See also

http://motls.blogspot.com/2011/04/fermilab-cdf-new-force-press-conference.html

for more details. Additional doubts about the valid statistical procedures were mentioned on Tommaso Dorigo's blog, too.

An adjustment of jet energy by 3 percent is enough to make the signal totally insignificant. Animation by Tommaso Tabarelli de Fatis, a member of CMS.

The text above also reviews some theoretical literature and clarifies that if the signal happens to be real - and the D0 Collaboration is going to release its own verdict about the phenomenon in a few weeks - the most likely explanations are

1. a new, fifth force - one mediated by a Z' boson (with the mass of 144 GeV or so) which is the particle that was decaying to two jets in those events. It must be leptophobic - (almost) no interactions with the leptons - and such Z' bosons, messengers of new $U(1)$ groups similar to the electroweak Z' boson but independent from them, are predicted by a very large fraction of grand unified theories and/or string theory models; articles by Alon Faraggi and many others are listed above; the simplest (but not the only) way to get a new leptophobic $U(1)$ is to obtain it as a piece of a color $SU(4)$ broken to $SU(3)\times U(1)$

2. a technipion, a particle analogous to a pion in technicolor theories that break the electroweak symmetry by similar composite particles, and not necessarily scalar ones (so there is no true Higgs particle in those theories); a paper by Kenneth Lane et al. is linked above, too; technicolor has been thought to be nearly dead for years - the optimistic proposal to interpret the bump as a technicolor effect doesn't solve all the detailed problems with technicolor theories

3. a stop squark in a supersymmetric theory - but it must be an R-parity-violating version of supersymmetry (e.g. because the new superpartners were not produced in pairs) which is unattractive for many other reasons (in simple terms, R-parity-violating theories are only consistent with proton stability given immense new assumptions, and they don't produce natural well-behaved dark-matter candidates); an article is linked to by the weblog above, too

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Dear Lubos, thank you for the answer and your blog. However, does "If you read this 2000 paper, it's easy to see how a discovery of an appropriate Z' boson could provide us with solid evidence for string theory - long before evidence for SUSY or GUT themselves." imply that the finding is a strong evidence towards a verification of (predictions of) string theory? Greets –  Robert Filter Apr 8 '11 at 10:02
Dear Robert, I wrote "could" - it could assuming that many additional things would have happened. First, it would have to be showed that the signal is genuine new physics which is far from certain now - and in fact, somewhat unlikely. Second, it would have to be showed that it is a new Z' boson. Third, the conventional GUT-induced models of such a new U(1) group would have to be sufficiently eliminated, and the specific stringy properties of such Z' bosons would have to be proved. This could happen but it has certainly not happened yet. It'd be crazy to claim evidence for string theory now. –  Luboš Motl Apr 8 '11 at 10:25
Lubos, can you explain what a "pile-up effect" is? This isn't terminology I'm familiar with. –  Mr X Apr 8 '11 at 12:28
Hi, see page 8 of cdsweb.cern.ch/record/888430/files/note05_013.pdf?version=1 for an explanation of the pile-up effect. –  Luboš Motl Apr 8 '11 at 13:24
(bumping @Jeremy for Luboš' response) –  Tobias Kienzler Apr 8 '11 at 14:30

Let me add an experimentalist's opinion. From the plots shown by Lubos above, one sees that two distributions are being subtracted in order to bring up the signal. A Monte Carlo background from expected interactions with a number like 500 events/8GeV, and a similar number for the experimental data. As the Monte Carlo background has no error bars, I presume the statistics are much higher and the histogram is just normalized to the number of events in the data.

The statistical error in number of events for each data bin is about $\sqrt{500}$=22.4 events. If I measure the error in the difference plot you show above, it is not larger than this number for each bin. This means they have not included systematic errors in their error estimates. One such is the error produced by the shift in energy as discussed by Lubos. This should have been added to the errors by varying the Monte Carlo background according the the 1-sigma error of the energy of the jet, and added to the error bars. There are other systematic errors one can think about in subtracting data from Monte Carlo events and in cut decisions. The effect of each cut, should be in a systematic error. Each variable used in the cuts (including the 8 Gev binning above) should be varied in the Monte Carlo within the error bars of the variable and the error estimated.

Note that systematic errors are added linearly and not in quadrature.

If this bump is not a statistical fluctuation but a result of underestimation of systematic errors, even if CDF doubles the statistics the problem will remain. It is independent experiments that will inform us of whether it is a statistical fluctuation, an analysis artifact or a true signal.

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thanks for your analysis, +1. Are they that desperate for PR that they will publish an announcement as provocative as this without making such elementary checks before? If one wouldn't know better, one would have to conclude that they are trying to buy the tevatron a bit more time. Honestly, i really don't care and we should give thumbs up for strategic thinking. But probably we should wait a bit more for the "real science" to percolate before getting too excited –  lurscher Apr 10 '11 at 14:12
@lurscher: Preliminary results like this are part of how science is done. It may be difficult to get enough data to check definitively at Fermilab, and to check it at the LHC you need to run an experiment, which I don't think is easy to get started without having a Fermilab publication. I think in this case, they've been reasonably honest with the media, and the media just has a strong tendency to overhype things. –  Peter Shor Apr 10 '11 at 17:03
@Peter Shor Hmm. Preliminary results, yes, are always excitedly discussed in conferences. But there is more to this, I would call it the "Nobel complex". Many group leaders in High Energy Physics are very ambitious and keep pushing iffy results so as to preempt a discovery. One well known one who finally got it for the discovery of the Z, had been pushing neutral current results for years to the point of people ironically calling them "alternating neutral current", now you see it, now you don't. With the two LHC experiments on their tail, they are rushing for glory, not only budget, imo. –  anna v Apr 10 '11 at 17:46
continued: Atlas and CMS have already data and are accumulating more. No need for new experiments. –  anna v Apr 10 '11 at 17:47
Thank you @anna for your analysis. So, I think one will have to basically design an experiment that is only there to answer if this effect is real or not - taking errors as you pointed out into account makes the whole thing look pretty ambiguous. Greets –  Robert Filter Apr 10 '11 at 19:01