Bumps part III – how significant is that peak? February 1, 2007Posted by dorigo in personal, physics, politics, science.
In the previous part of this story we left Paolo Giromini busy with the examination of the dimuon mass spectrum obtained from Run I data of the CDF experiment: 100/pb of proton-antiproton collisions, which contained a large signal of vector meson resonances – about 200,000 J/psi and psi(2S) decays, and more than 10,000 Upsilon(1S) decays.
Giromini (pictured on the left upon entering his office, slightly perplexed to see me and Maria Spiropulu with our feet on top of his keyboard, sitting in his chairs and smoking his cigarettes) was looking for the decay of a bound state of two scalar quarks, in a p-wave configuration – basically, the two quarks would orbit each other with one unit of angular momentum. The mass of such a particle -let’s call it E, for Epsilon – would have to be roughly twice as large as that of the scalar quark of which he was seeing some weird evidence in other datasets – twice 3.5-4 GeV, that is, or 7-8 GeV. What was he to expect about the number of decays of such a particle in his dataset ?
In the absence of a detailed model for the production of a new particle, one has to resort to extrapolations from known facts in order to compute a production rate. The Upsilon(1s) meson (Y) provides a nice extrapolation point: it has a slightly larger mass (9.5 GeV), and one can assume that the production processes of Y and E are similar. For example, if two gluons collide yielding the Y and a gluon in the final state – and we know they do -, the same can happen to this new state E, if it exists.
Ok, let’s assume that Y and E are produced alike. But they not only have a different mass: they also must have different lifetimes. And the lifetime, or better its inverse -what we call width – affects the production rate.
Ever poked one of the lowest keys on a piano ? If the note is short enough, you cannot get the tone precisely. It is as if your ear needs more time to make that out than if you play a higher pitched note. The reason is that the oscillation frequency of a string – that is, its tone – cannot be determined precisely if you cannot listen to enough repetitions of the oscillation; and low tones have a lower frequency, so you need more time. Well, the same holds for all kinds of oscillatory motions, and just as well for subatomic resonances: the tone of the particle – its mass – is not perfectly defined if it lives too short a life before disintegrating. So the “uncertainty” on the mass – that is, the width – is inversely proportional to the lifetime. Confused ? It’s ok, read on. We can forget about this detail in the following.
Now, the lifetime of two scalar quarks orbiting each other could be inferred from theoretical work [C.Nappi, Spin-zero quarks in e+e- annihilation, PRD25 (1981) p.24]: 17 eV. Giromini could then do a calculation, using the supposed ratio of the E and Y masses, and the ratio of the E and Y lifetimes (17 eV and 1320 keV, respectively). He obtained the result that in his sample of dimuon decays for each thousand of Y there could be 23 or more E. That meant a signal of 200-300 E particles. Few, but maybe observable!
To observe a 200-event bump in a huge background of fake muons and non-resonant muon pairs meant performing a careful selection. The Frascati team imposed tight requirements on the quality of muon candidate tracks, on their kinematical characteristics, and on other subtleties. They could show that the same requirements were indeed enhancing the known and quite visible Y signal – so it did not really look like a filter crafted purposedly with the aim of increasing the significance of a random fluctuation.
And, sure enough, after the selection Giromini could indeed fit roughly 200 events sitting at 7.2 GeV, with a gaussian shape of the required width (mind you, not 17 eV: much larger, and due not to the intrinsic properties of the resonance but rather to the experimental resolution with which the energy of the muons was measurable). On the right is one of the plots produced by the Frascati group, aimed at showing that the bump survived the application of a few additional physics-motivated cuts; the bump shown has fewer than 200 events due to the additional cuts.
As I mentioned in the first post on this story, the scrutiny of the dimuon sample by the CDF collaboration became urgent, as Giromini threatened to publish the whole stuff, still unapproved and not passed through any blessing procedure. The fact is that the previous years of fights over the top cross section first, and over the superjet events later, had rendered it useless for the Frascati analyses to try to bless their controversial results: they had failed each and every time for three years in a row. What they needed was to first reach a consensus from a panel of reviewers.
The uneasy situation put a heavy burden on the oversite godparenting committee of which I was part, since the committee was then responsible more directly of any decision on the analyses proposed by Frascati.
Sure, we were not alone. Many collaborators were willing to investigate on the dimuon bump, and indeed the analysis had been repeated completely at least once, with more controversy ensuing instead than a clarification. It seemed Giromini was indeed quite skilled at creating controversy: his explanation of the analysis was sufficiently clear in his analysis notes, but it usually lacked a detail or two which were obvious for Giromini and for nobody else – and this made his results impossible to reproduce down to the last digit. It was a nightmare, especially for the poor souls who took the pains to follow his steps, who worked for nothing and got criticized as a bonus.
But the bump was there, and it flew in the face of those who wanted to bury the whole stuff and move on. What was to be done ? Should we believe in the claimed significance of the bump ? Sure, if you looked at the likelihood fit of the mass distribution, you would observe that the excess fitted by Giromini was something like 200+-40 events: a five-sigma signal ???
So here came my little contribution to the dimuon bump investigations. Of course, it was clear to me that what was really needed was a toy Monte Carlo approach: that is, create a large pool of fake spectra, each made of 53,000 mass values fished at random from the background distribution from 6 to 9 GeV (purely exponential: no signal!), and then fit each of them with the same methodology used by Giromini, that is allowing not only for the exponentially falling background shape, but also for a gaussian signal on top of it.
What is the rationale of fitting a spectrum obtained randomly from a smooth distribution with a functional form which is the sum of that same distribution plus a gaussian ? Well, it is a fishing expedition, no less a fishing expedition than the one Giromini had -successfully, it appeared- put together when he had started looking for an E in the dimuon mass spectrum. With the difference that in my case, I would know for a fact that any bump I would fit were just statistical fluctuations: I had designed them to be so by the random generation of the spectra. By counting the fish I caught in a simulated fishing expedition to a distilled water tank, I would know how likely it was that Giromini’s fish was real.
[to be continued – last part tomorrow]