# Diphotons: Moriond Update

Updated Theorist Analysis of LHC Diphoton Data

(Note: the first part of this is a non-specialist description of the results of Moriond. About halfway through it will transition into a more technical discussion. Around where the plots are is where the nitty-gritty physics shows up.)

This week and next is the 51st annual winter conference “Rencontres de Moriond” (or just Moriond), which is the big winter conference in La Thuile where traditionally the LHC experiments (and others) make official announcements of new results.

Of course, there are many talks, and many new analyses which deserve attention. Also of course, this year all the oxygen in the LHC room is being sucked up by the diphoton anomaly (see my posts here and here for a discussion, along with my article in the Boston Review for a popular audience). So everyone was very interested to see what, if anything, ATLAS and CMS would have to say about diphotons at Moriond.

Now, going in to Moriond we couldn’t expect very much to change. The LHC has not been operational since last year, and we already saw the initial analyses of diphoton data from both ATLAS and CMS in the winter; that’s what caused all this insanity in the first place. So they shouldn’t have new data (more on that in a moment), so before we saw anything, we should not expect to a definitive answer to the question “is the diphoton anomaly real new physics, or just a statistical fluctuation or experimental error in both ATLAS and CMS?”

However, both experiments could take the opportunity to re-assess their analysis techniques, improving their calibration of photon energies and momenta, and re-release the results. This is an approach is often fraught with complications, as fiddling with what data you are using and how you’re doing statistics on that data can increase or decrease your statistical significance in surprising ways. In science, futzing with the data to get the desired result is sometimes called “$p$-value hacking” (the p-value is a measure of statistical preference the data has for a hypothesis), and it is rightfully frowned upon. The LHC experimentalists are very honest in this regard: they try to lock in as much of their analysis as possible before they check the results. So official re-analysis is somewhat unusual. However, given the focus on these results, it appears the experiments decided to go with a re-analysis of their already-published data, and since the major analysis change comes from the recalibration, they haven't altered the guts of their analysis. So they were careful and didn't get all crazy with finding their preferred explanation, as you’ll see the re-analysis of the pre-existing 13 TeV LHC data doesn’t change that much of the results.

In addition, both experiments went back to their 8 TeV data. If any signal was present in the newest data, it should be present in the old, lower energy data, though with a smaller rate (about 1/5th as big, if whatever this presumed new particle is produced though interactions with gluons or heavy flavor quarks, 1/2 to 1/3 if its produced through light quarks). ATLAS in particular had a very difficult to interpret analysis of their 8 TeV data who’s applicability to this anomaly was somewhat unclear to the experiment and to outsiders like me. They had discussed the 8 TeV result at the winter data release, and I (and other theorists) had taken it into account when we did our homebrewed fits to the data, but what it was saying about the diphoton anomaly was a bit shaky.

Finally, during the initial 13 TeV run, CMS had some difficulties with their experiment. I am told that these sorts of shake-down problems are common in big experiments, remember that CMS is one of the most complicated objects humanity has ever constructed, and it doesn’t come “off-the-shelf:” it had to be carefully and lovingly built from scratch, and things can go wrong and need to be fixed on the fly. We young theorists actually got incredibly spoiled; our previous one experience with a new experiment turning on was the 8 TeV run at the LHC, where both experiments performed flawlessly and indeed beyond expectations (of course, some of that might have been due to the experimentalists getting extra time because of the disaster with the LHC beam itself, but let’s still call it a win). So CMS’s teething problems caused endless concern in the non-experimentalist world (and doubtlessly, inside CMS), but these things happen.

In particular for this story, CMS’s cooling system, which allows the powerful magnetic field inside CMS (the solenoid in the Compact Muon Solenoid) to be turned on, was getting contaminated somehow. This meant they couldn’t turn the magnet on. The magnet bends charged particles, which allows for better particle identification. Remember, particles don’t come with little signs clearly saying what they are, and Star Trek-type tricorders which just tell you what you’re looking at don’t exist (or, our version of a Star Trek tricorder is a 40 foot tall ten-thousand ton behemoth). It takes works to figure out what all the stuff coming out of a particle collision is, and the magnetic field is part of that process. As a result, while ATLAS had 3.2 fb$^{-1}$ of usable data in their diphoton analysis, CMS only had 2.6 fb$"^{-1}$ (though at Moriond, CMS announced that the actual dataset was 2.7 fb$^{-1}$, after recalibrating the rate of data collection, increasing the central value of the estimate and greatly decreasing the errors on that value. Experimental physics is hard, folks).

Except, CMS had another 0.6 fb$^{-1}$ of data collected while the magnet was off. And photons aren’t charged, so they don’t really need the magnet to look at diphoton events in that data set. However, redoing the analysis for the “$B = 0$T” data ($B$ is the magnetic field, measured in tesla T, so this is the “zero-field” data. In the plots I'll denote it as 0T) is non-trivial, since the entire experiment is subtly different in ways that need to be accounted for. Normally I bet CMS wouldn’t have ever bothered to throw the grad student-power at the problem to analyze this small amount of data when in a few months we’re going to get many orders of magnitude more, but this is here is Diphoton Country now, and we want answers immediately, damnit. So this extra data was added.

Thus, leading into Moriond we knew the following:

1. ATLAS and CMS would release re-analyses of the diphoton events at 13 and 8 TeV
2. CMS had an extra 0.6 fb$^{-1}$ of 0T data to throw into the mix.
3. We could not expect any big changes in the statistical significance from this data.
4. Regardless of the previous point, we were all going to obsess over the results anyway.

So three talks (one from CMS, one from ATLAS, and one about the theoretical 50-car pile-up) were given yesterday. Here’s my executive summary of the experimental results (for simplicity I will concentrate on the scalar interpretation, assuming gluon couplings. Though the new analyses nicely split the spin-2 analysis out and do that separately):

1. ATLAS now has a local significance of $3.9 \sigma$ in the 13 TeV data for a 750 GeV scalar resonance with a width of 45 GeV. Previously, this number was also $3.9 \sigma$. The global significance is $2.0 \sigma$, as before.
2. ATLAS now claims $1.2 \sigma$ compatibility with the 8 TeV data. Previously, this was $2.2 \sigma$. So this is a reasonably big change, and should relax the 8 TeV constraint on the new-physics interpretation.
3. ATLAS now shows some analysis of what else is present in the diphoton events. Nothing seems out of order, but it will help constrain some non-standard theory interpretations of the anomaly.
4. CMS now has a $2.9 \sigma$ local significance of the anomaly at 13 TeV, including the new data set. Previously, this was $2.6 \sigma$. The global significance is $< 1 \sigma$. Previously, this was $< 1.2 \sigma$, though it is not clear how much less. The decrease in global significance while the local increased looks really weird, but I think I understand it now: the new data is a bit “bumpier” than it was before, since the data set is still very small. Thus if you ask how often you might expect to see resonances in the data, it will happen pretty often. By luck of the draw, this wasn’t the case in the previous (smaller data set), which looked slightly smoother. Global significance is calculated using the data set, so small data sets can give counterintuitive results like this. Statistics is strange.

Now for my reanalysis. Previously, I wrote a paper just taking all the available data and throwing it together, as the CMS and ATLAS collaborations hadn’t done a combined analysis themselves (that takes a lot of time and work on their part, and they’re busy). I added in the new CMS 13 TeV 0T data, added the redone ATLAS 8 TeV data, and reran the code. Unfortunately, though the experiments had done a lot to improve their understanding of the photon events, that sort of improvement can’t translate into my results, as I don’t have access to that level of data, and wouldn’t be really able to use it effectively if I did.

I find the best way for me to understand this sort of thing is to do it myself, even though my results can’t be as accurate as the experiments themselves. Other people might find the results useful, so here they are. Again, for simplicity, I will only show results assuming gluon production and a scalar particle (in my case, this is because running all the options takes a week or so, as my code was written by someone — me — who didn’t think about making it easily parallelizable). For the same reason, I don’t show global significances, as that takes a lot of computing to get right.

OK, now for the technical stuff.

First, here are the plots showing the best fit regions for ATLAS13 (red), CMS13 (blue), CMS13 0T (purple), the combination of 13 TeV data (dotted black lines), the upper limits from 8 TeV data (dashed black), and the combination of all data (solid black). I show both the narrow width and 45 GeV width assumptions, and compare with the similar plots from my paper (which don’t have the purple CMS13 0T region).

Overall, I find that the addition of the new data doesn’t change the best fit too much: ATLAS13 is still clearly an outlier, requiring much larger signals than CMS and the 8 TeV is comfortable with. Thus, my initial attitude remains the same: if there is a new particle here, ATLAS is seeing an upward fluctuation, and the best-fit production cross section is closer to what CMS is seeing: something like 4-5 fb, not the 9-10 or so ATLAS likes. The addition of the 0T data doesn’t push things that much: they are seeing something consistent with an excess, but at slightly higher mass, and the data set is small so it doesn’t pull things around that much.

However, all the new data does slightly change the combined statistical significance of the signal, which I show here. With all the new changes, I find the best-fit local significance to be now $4\sigma$, compared to $3.4 \sigma$ last time. This is for a narrow resonance. A wide resonance has nearly the same preference, and unlike last time, the addition of the CMS data to ATLAS doesn’t drag down the local significance of a wide resonance; this is due to the events in the 0 $B$ CMS data.

So overall, this is the best possible result for the new physics interpretation we can reasonable expect to have from the Moriond: the result didn’t get less significant, it got slightly more. Not by much, but we didn’t expect things to change at much in either direction, given the lack of significant new data. It’s not a discovery, it shouldn’t be considered anything too significant, but for us theorists, it is enough to guarantee the continuation of the diphoton party bus for a few more months, until we get new results from the next set of data in August or so.

Finally, here’s what the best-fit signals would look like in the various available data sets (red crosses are the digitized experimental data, blue is the best-fit without a new particle, and black solid and dashed are best-fit with the best-fit narrow or wide particle signal added)

(note: after initial publication of this post, I made a few changes and corrections. I want to thank André David Tinoco Mendes for bringing them to my attention.)