## Friday, December 09, 2011 ... //

### Higgs mass: 124.6 GeV CMS, 126 GeV ATLAS

Every other experimental collaboration with more than 3,000 members harbors a traitor, whistleblower, or a black sheep in general. We're very fortunate that much like University of East Anglia, the CMS Collaboration at CERN obeys this condition, too. The renegade's name is Italian, Tommaso Dorigo, and he brought us a

Fundamental Glossary For The Higgs Broadcast
On Tuesday at 14:00 Prague Winter Time, there will be a CERN webcast at which we will hear about some new and strong yet inconclusive evidence for the existence of the Higgs boson. We have known from some anonymous sources that shared their excitement with the TRF comment section (I deleted the comment but revealed the content once it materialized elsewhere; but then the openness reached a threshold so I wasn't even trying to delete the e-mail from Rolf Heuer anymore) and other physics blogs that the masses will be 125-126 GeV.

However, the message I received talked about 124 GeV for CMS. It's pretty far from 126 GeV that will be reported by ATLAS – comparable to the full width of the expected bump – and I have personally worried about the 2 GeV difference. Fortunately, Dorigo has also told us the following sentence:
The gammas we will be hearing about are those directly coming from a Higgs boson decay, and these have an energy of 62.3 GeV, ...
This is meant to be an exercise in multiplication by two with a secret message as the bounty for the schoolkids who successfully solve it. So what's the result that about 10% of Dorigo's brightest readers are capable of finding? (He trains the readers to guess that statistical distributions look like extraterrestrial aliens: whenever you offer such an answer to one of the "what is it" tests at Dorigo's blog, you receive cookies.) The result is

2 × 62.3 = 124.6 GeV (CMS)
It's nice because it's closer to 126 GeV of ATLAS than the previous "badly rounded" value of 124 GeV. Recall that the statistical significance of the ATLAS bump at 126 GeV is 3.5 sigma while the statistical significance of the CMS bump at 124.6 GeV is 2.5 sigma.

Given no other information (aside from the two mean values and the statistical levels), i.e. assuming the independence of the sources of information etc., how can you determine the best particular "compromise" value of the Higgs mass? It's simple. You just find the most accessible Italian leftist and ask him what is the formula you shouldn't use. Every valid formula is an inconvenient truth for a leftist so he will tell you that "you should never say that [correct formula]" and instead, "you should spread fog that everything is eternally uncertain".

It just happens that the most accessible Italian leftist is Signore Tommaso Dorigo once again. So you open his article about
The Puzzling Weighted Average
and the only formula among the possible answers to the question "what's the right weighted average" may be found in the answer #4 which Dorigo says is wrong (exactly for the foggy reason mentioned above) – which is another good reason to be almost sure that it's right. If you replace the wooden sticks (and their length) by the Higgs boson (and its mass), you will see that the right formula is
$\overline{M} = \frac{126\times 3.5^2 + 124.6\times 2.5^2}{3.5^2 + 2.5^2}{\rm GeV} = 125.53\,\,{\rm GeV}$ So the LHC's best guess for the Higgs mass is going to be 125.5 GeV unless the ATLAS figure has been rounded as brutally as the CMS figure before it got posted here. ;-)

In the weighted average, the figure 126 GeV got a bigger weight because the signal of ATLAS was (will be) stronger, 3.5 sigma, than the signal of CMS, 2.5 sigma. However, I have squared both 3.5 and 2.5 because Dorigo's right formula (where the error margin, and not the statistical significance, was given) had a squaring, too. You need to make your bins 3.5/2.5 wider for ATLAS to achieve the same significance of the excess in a single bin, so a lower confidence level in "sigmas" may be translated to an inversely proportionally higher error margin.

Bonus

Tommaso's brother, Mr Luciano Cornouteli, is a European commissar from the Institute of Friendly Europization. In the speech above, he explains that "Bohemia pretzel sticks" must be sold together with little drills so that they have holes inside them, much like macaroni. If the Czech producers can't obey the condition, Italy will say No.

Bohemia pretzel sticks: we won't allow them to be touched! Bohemia pretzel sticks are the best the way they are! :-)

Helmut Scherer, the German commissar, demanded that all of the sticks must be equally long. Scissors have to be added for every package. If the Czechs say No, then Nein, nein, nein. The French Commisar demands gloves to be added to protect the consumers from germs. A confrontation of the three commissars was recorded later. They mostly claimed they were joking: the sticks are yummy. ;-)

In another text on his blog, Tommaso recalled a scene in which I admitted I was wrong. But he didn't say any details about what we were arguing about.

We were arguing about a paper of Tommaso's Tevatron CDF collaboration on "lepton jets" which made extraordinary claims and which turned out to be a totally wrong paper. The wrongness was first understood by theorists but the paper was later debunked by D0 at the Tevatron, too. I made a claim about one number, saying that they couldn't possibly say that it is really "this high", because such an interpretation would mean that the experimenters were making an even more ludicrous statement.

But I was wrong. The right interpretation of the wording of the paper was really the preposterous thing I couldn't believe (some new process with a huge cross section). Because I have high standards and I promised to apologize if this claim of mine – that the experimenters can't be too stupid – is proved wrong, and because it had indeed been proved wrong, I obviously apologized. I always do when I am wrong. But the essential thing here is that Tommaso "helped" his collaboration to publish a truly embarrassing paper about huge signals known as "lepton jets" which are known not to exist.

The paper was totally wrong and my main mistake was my refusal to believe that people like Tommaso has so much influence that the collaboration is able to publish really silly things. I wouldn't make the same mistake today because the credibility of the CDF has gone to zero after 3-5 more big wrong claims they did in the recent year after lepton jets (top-antitop huge mass difference; various other top asymmetries; and the Wjj bump near 150 GeV, among things I have forgotten). Given Tommaso's excitement, it seems conceivable to me that Tommaso in person was behind the high publication activity of rubbish by the CDF.