Contrary to what you might have read in my April Fools post, the Higgs excess at the LHC is not due to a loose cable but is almost certainly a manifestation of the real beast. While experimentalists keep a cautious stance, at least in public, most theorists are already at the next level of cognition. The question being asked is whether the Higgs boson is the one predicted by the Standard Model, or whether the data point to one of its numerous possible realizations beyond the Standard Model. That question of course cannot be yet answered with any decent statistical significance. Nevertheless, theorists are already launching reconnaissance attacks, so as to pass the time until more data arrive. At the moment the most up-to-date analysis is this one collecting 16 measurements from ATLAS, CMS and the Tevatron, and interpreting them in a general framework where the Higgs couplings are allowed to deviate from to the Standard Model predictions. This is of course a simplistic theorist-level analysis that doesn't take into account some relevant pieces of information jealously guarded by the experimental collaborations. However, a good guess is that at this point more sophisticated procedures would give very similar results.

The plot here shows the break up of the 125 GeV Higgs signal into the final states analyzed by the experiments. The first thing to observe is that, on average, the production rate is consistent with that predicted by the Standard Model (the green line). Furthermore, one can read off that the the null hypothesis (the red line) is disfavored at the more than 4 sigma level. Thus, black-market combinations confirm that Higgs is practically discovered, which is probably the reason why the LHC is reluctant to release an official one.

Next thing, the current data show an intriguing tendency: while the Standard Model is a good fit to the combined data (chi-squared of 16 per 15 degrees of freedom), there are a few glitches here and there. Namely, the inclusive rate in the diphoton channel is somewhat enhanced (in both ATLAS and CMS) while that in the WW* and ZZ* channel is somewhat suppressed (especially ZZ* in CMS and WW* in ATLAS). Moreover, the exclusive final states studied in the diphoton channel (with 2 forward jets in CMS, and with a large diphoton transverse momentum in ATLAS) show even more dramatic enhancements, by more than a factor of 3. It may well be a fluke that will go away with more data, or maybe the simulations underestimate the Higgs event rates in these channels. Or, something interesting is going on, for example the way the Higgs boson is produced in proton collisions not exactly the way predicted by the Standard Model....

To see an example of what could be going on, have a look at this plot. It shows the fit to the data when the Higgs couplings to other particles are free parameters that can be varied. More precisely, the couplings to gauge bosons are allowed to be rescaled by the common factor a,

and likewise the couplings to fermions are allowed to be rescaled by the common factor c. Under this hypothesis the Standard Model point (a=c=1) is far from being the best fit, and the data are better explained when c is smaller than 1. That's because, for c<1, the Higgs production via gluon fusion (which is a loop process dominated by the top quark contribution and therefore it is sensitive to the Higgs coupling to the top quark) is suppressed. This in turn allows one to explain the smaller-than-expected event rate observed in the WW* and ZZ* final states. Amusingly, an even better fit is obtained when the sign of the Higgs couplings to fermions is flipped. The reason is that, for c<0, the W and top one-loop contributions to the Higgs decay to photons interfere constructively and, as a consequence the Higgs branching fraction into photons is increased. Incidentally, this plot also shows that the so-called fermiophobic Higgs hypothesis (c=0) does not explain the data well.

The above example shows that playing with the Higgs couplings we can explain some funny tendencies in the current data; of course, many other, possibly more motivated deformations of the Standard Model can be confronted against the data. At this point these are all children's games but, once the data from the ongoing 8 TeV run become available, measuring the Higgs couplings will become the central point of the LHC program. Realistically, the most probable outcome is that the data will drift toward the Standard Model predictions, as it's been for the last 30 years. However, for the moment, we can cherish a hope that the glitches in the existing Higgs data will grow larger and become evidence of new physics beyond the Standard Model. An exciting year ahead :-)

## 10 comments:

Dear Jester, your comment about the better inverted sign of the Higgs coupling to fermion is funny.

Just to be sure, is the axis the coupling itself, an amplitude of the vertex, or its square that normally shouldn't be negative?

In the former case, haven't people made an unjustifiable assumption about the signs? Are the signs of the Yukawa couplings physical? Can they be reverted? Does it change physics? Is that an equivalence in the CKM matrix description?

To summarize, haven't folks missed a possibility, a whole region of the parameter space?

I am going to find answers to these simple questions but I will come back to check whether you or others answered the same way...

The y-axis is the Higgs coupling to fermions relative to the SM one. The sign of Yukawa by itself is non-physical, but the relative sign between Higgs couplings to gauge bosons and to fermions is physical. The tree-level processes don't care about the signs but there are loop processes sensitive to the relative sign, notably the Higgs decay to 2 photons. That's why the plots are not exactly symmetric wrt to the c=0 line. In the SM when talking about the signs one assumes that the fermion mass terms have been canonically normalized, which takes care of the phase ambiguity of the Yukawas. In that case one find the relative sign is always positive.

Talking about glitches at this point is crazy. One should ask given the statistics what the probability is of seeing signals in all channels compatible within 1 sigma of the SM prediction. There's 16 channels!

Being incredibly naive: the probability to find ONE signal within 1 sigma is 68%. Assuming statistical independence, I can raise that to the 16th power and I find 0.2% chance of all 16 channels being within 1 sigma.

On the other hand, a signal will be within 3 sigma 99.73% of the time. Raising that to the 16th power gives 96%. So it would be somewhat worth our time to talk if we had a 3 sigma discrepancy.

Right now, there's nothing non-SM about this! So, no, the "second thing to notice" is not glitches! It's "wow, I hope we get better statistics soon." Feel free to think about the best case / weird case scenarios, but don't claim signals right now. It's a boy who cried wolf type risk.

No one says there are any serious hints for BSM Higgs in the data, at least I didn't.

An experimental context reason for diphoton counts to be high in early data is that the diphoton data was the strongest indicator for determining that the other data fit the existence of a Higgs at all. If your Higgs discovery trigger is a diphoton excess, you are much more likely to discover a Higg boson in runs with an excess of diphotons compared to random chance than you are during runs which have below average diphoton production rates. Hence, if any of the indicators would be expected to be unusually high at first, that would be it. If the excess trends down over the next few years after we know what to look for, then this was probably the cause. If it doesn't, then the error bars will get smaller and the Standard Model Higgs will need a tweak.

As the exchange between Lubos and Jester illustrates, this is something of a "who ordered that" moment if the BSM physics here do hold up. The experimentalists may finally be getting an upper hand over the experimentalists for a little while.

Very clear and probably right, Jester.

Jester, Lubos, the relative sign that matters here is the one between the Yukawa coupling and the fermion mass.

"The experimentalists may finally be getting an upper hand over the experimentalists for a little while." Andrew Oh-Willeke

Huh?

"The experimentalists may finally be getting an upper hand over the experimentalists for a little while." Andrew Oh-Willeke

Huh?

Fat fingers. Meant to say The experimentalists may finally be getting an upper hand over the theorists for a little while. In other words, theorists are having to respond to new data which don't fit into any theories, rather than waiting for experiments to be powerful enough to determine if the theories that they already have are correct.

It seems that they depend a lot on the Tevatron "signal" in order to fix the tau and botton channels, do they?

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