Peak Finding

September 22, 2007

The CLAS Collaboration is unusual in having observed and then later seen no evidence for the same particle, an oddity called the Θ+(1540). If it existed, it would have been the first known “pentaquark” state, composed of four quarks and an antiquark (uudds, to be precise), which would have made it the first time quarks had been seen combining in ways other than pairs (mesons) or triplets (baryons, such as the proton and neutron). The initial excitement made it as far as the BBC, but since then, most attempts to find the Θ+ again have come up negative, and is generally considered to have been a statistical fluctuation combined with some wishful thinking.

To confirm their earlier (5σ!) positive result, CLAS repeated the analysis on six times more data, and drew a blank. In the face of this, they’ve put out a rather interesting statistics paper, in which they try out a general technique to ask the question “is there a statistically significant peak somewhere in this data?” To do this, you have to account for the fact that fluctuations will produce fake peaks, a fact neatly demonstrated in the first figure of the paper, where they split the original sample in five, one of which has a rather convincing “signal” which vanishes in the total dataset.

The method essentially compares two classes of models for data (e.g. “all smooth background” versus “smooth background plus Gaussian peak”). A Bayesian procedure discounts differences in the number of parameters between the models (the priors chosen here are probably the most iffy part). The procedure results in “evidence ratios” that give the preferred model, and the strength of that preference.

They find, in fact, that all their data (including the first set which they used to claim observation) weakly prefer the no-signal model. If, on the other hand, the signal seen in the first dataset had held up in the second, this analysis would have found “decisive” evidence for it. (They also find absolutely conclusive evidence for the existence of the Λ(1520), which is a Good Thing.)

The method looks quite interesting; the question it attempts to resolve comes up in any low-statistics claim of an unexpected state, and some kind of sensible algorithm for quantifying the evidence would be very useful to have.

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2 Responses to “Peak Finding”

  1. Chanda Says:

    a reminder to all us theorists that the results we are so desperate for may get lost in statistical oblivion, and also to be glad for the people who are willing to futz with the statistics and find what’s real in them :)

  2. [...] item which strikes me is a post written in Charm, etc. in which the author describes how a very nice 5-sigma pentaquark signal came and went! This may [...]

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