# How correlated are the statistical significances of the same signal/non-signal for CMS and ATLAS?

Consider a diphoton excess for both ATLAS and CMS at the same energy for two cases:

1. false signal: I'd expect the two statistical significances to be uncorrelated
2. true signal: I'd expect the two statistical significances to be strongly correlated

In general, can the statistical significance of the same signal for ATLAS and CMS be compared with one another in determining the significance of the signal?

• There is only so much difference between the two detectors, so it's not obvious why one would expect completely orthogonal systematic errors, and even if that were the case, statistical errors could still by chance line up. That's just not something that one can suppress any other way than by collecting more data. You can try this at home, if you want. Throw a dice and a coin with 1/2 written on both sides. Even these two completely different random sequences will, occasionally, show excesses of 1-1 and 2-2 combinations. – CuriousOne Jul 19 '16 at 0:43
• @CuriousOne If you throw the unbiased dice and coin together 1000 times say, record the 1-1-1-1-1-1 excess for each and then repeat, you'll eventually end up with this being significant for say the coin. But it's extremely unlikely that you'll also record the same excess for the dice over that same set of 1000 throws. Whereas if you bias them in the same way to show a great number of 1s than 2s, they are likely to show the same 1-1-1-1-1-1-1 excess. – Larry Harson Jul 19 '16 at 2:41
• @CuriousOne or put another way: if two ATLAS experiments detect the same 125 Gev Higgs with one at $5\sigma$, how likely will the other detect the signal at the same significance within $0.5\sigma$? – Larry Harson Jul 19 '16 at 2:45
• The result, so far, is like a triple repetition, which is not that rare. I don't think anybody who works with these things has gotten their hopes up. I certainly have not. We have seen these kinds of things before. You also have to distinguish between the statistics for false positives and false negatives. Both detectors were designed to be as sensitive as possible to the expected and observed event types. Moreover, some of the Higgs event channels are not actually rare, they are just marred by a large irreducible background. – CuriousOne Jul 19 '16 at 3:08
• Perhaps you guys could link to the results you're talking about, it would be an interesting read. – Matt Jul 19 '16 at 9:00