# Standard Model: 1, Diphotons: 0

Alas, poor diphotons.

This week is the ICHEP2016 meeting in Chicago, which serves as one of the major summer conferences where experiments release their accumulated results. One of the most anticipated results this year was the update on the diphoton anomaly which was found in ATLAS and CMS data collected last year in the first bit of 13 TeV data from the LHC.

If you want a reminder of that full story of that anomaly, I wrote a quick reaction post to that initial excitement here. A month later, I had completed some statistical analysis of the combined ATLAS and CMS data set, and wrote a paper which I put on arXiv, which you can read about here. There was an update after Moriond, which increased the statistical preference mildly, I wrote about it here.

In addition, I’ve had the opportunity to write about LHC physics for the Boston Review, the first article in the series focused on the diphoton anomaly.

I will actually be ended the Boston Review series with a wrap up on this anomaly. So I won’t be spending too much time in this blog post discussing the broader impact of this result on the community, or the search for new physics in general. Here, I just want to put down some of the figures and facts, in a slightly more technical discussion than I will later.

So, a reminder of where we were. After Moriond, ATLAS had analyzed 3.2 fb$^{-1}$ of 13 TeV and reported a $3.9\sigma$ local ($2.0\sigma$) local excess. CMS had two sets of data, with and without their magnetic field, combined they had 2.7 fb$^{-1}$+0.6 fb$^{-1}$ with a $2.6\sigma$ local ($1.0\sigma$ global) excess.

My combination of their data (the only one available, since real experimental combinations take a long time to do) gave a $4.0\sigma$ total local significance for an excess. I couldn’t actually do the global significance, but I estimated it to be on the order of $2.0\sigma$. That means that, if you believed the experimental data, you should have believed that new physics was favored at about 20:1 odds. Personally, I would have taken a bet on new physics existing only at 1:20 odds, so if nothing else this diphoton anomaly has experimentally proven my Bayesian prior for new physics is about 400:1.

Data collected by CMS as a function of time.

Since May, the experiments have been collecting data at a staggering rate. They each are approaching 20 fb$^{-1}$ total collected. In time for ICHEP, CMS had 12.9 fb$^{-1}$ of data available for this analysis and ATLAS had 12.2 fb$^{-1}$. So roughly 4 times the data, each. The way statistics work, 4 times the data means the number of events in a signal should go up by a factor of 4. The background should also increase by 4, but critically, the size of the fluctuations in the background go up only by a factor of $\sqrt{4}=2$. Thus, the statistical strength of a signal should increase by $4/\sqrt{4} = 2$ (in general, for $N$ times the data, a signal should roughly grow as $\sqrt{N}$, assuming that the major issue is raw statistics, rather than systematic errors).

So, where’s our grand $8\sigma$ discovery?

In late June, ATLAS and CMS internally opened their data sets (with about 3-4 fb$^{-1}$ available) to check their analysis techniques. This was supposed to remain internal. However, operational security for the experiments is terrible, and the results leaked while the internal meetings were in progress. The results: the signal wasn’t seen in the new data. Now, one could argue that this was a downward fluctuation in the signal — that can happen. But it was a sobering shock through the theoretical community. People began stopping working on diphoton papers, and the sense that this was going to disappear for real began to spread. The outside hope that more data would save us was further sunk when it was clear that the results would be shown at ICHEP itself, rather than a special session at CERN.

ATLAS Diphoton Invariant Mass Spectrum (ATLAS-CONF-2016-059)

CMS Diphoton Invariant Mass Spectrum (CMS-EXO-16-027)

Then, the results themselves. Here’s the raw data from ATLAS (ATLAS-CONF-2016-059). On the left is the old data, bump at 750 GeV clearly seen. On the right is the new data: no bump. Similarly, the new data from CMS (CMS-EXO-16-027) also is bump-free.

This by-eye glance can be quantified into the $p$-values for the Standard Model versus new physics. Here, ATLAS’s nearly $3\sigma$ deviation (blue line) drops to $2\sigma$ (black) with the new data added — but that $2\sigma$ is all from the old result. The new data itself (red) has essentially no preference for an excess at this mass. When you add this much data, the signal should go up — assuming there’s a signal there at all, not a fluctuation. Similarly, the CMS result drops when you add data, and there’s no evidence at all for a diphoton anomaly at 750 GeV in the much larger new data set.

Now, from my own data analysis, I had been expecting that — if a signal existed — its rate would be somewhat smaller than the ATLAS result (which was the number people were throwing around). This is because the ATLAS and CMS anomalies, though at the same mass in the diphoton spectrum, were not really compatible in the rate. Which was fine, the tension wasn’t that much. So I was a bit concerned that at ICHEP the data collected would rule out the ATLAS rate, but not the “real” value I had in mind.

ATLAS p-values for diphoton anomaly

CMS p-values

Turns out, that wasn’t a concern. Here are the upper limits in cross section (rate, essentially) from ATLAS, as of today. I’ve added a little ellipse in the region I had identified as the best-fit value. It’s firmly excluded.

And so ends the diphoton anomaly. As I said, I’ll have more to say about what this means in my article for the Boston Review. It’s certainly disappointing, new physics is the dream of all particle physicists. However, the Universe is as it is, and we cannot do anything to change it. New physics is out there. Dark matter is evidence of that, among other things. However, we didn’t find it today. Maybe tomorrow.

ATLAS upper limits on cross section (red ellipse preferred signal region, added by Me)