A Quantum Diaries Survivor

Spending some time looking back at the second plot in the former post on the top and W masses made me wonder on the second most frequent source of error in a scientific measurement: namely, the insufficient or imprecise definition of the quantity being measured.

It is a surprising but true fact, indeed, that the one mentioned above is a very important source of uncertainty in scientific measurements. We think that once we set out to perform a measurement, the object of our investigation is perfectly well defined. Not so!

When one talks about a particle mass, for instance, at level zero one shrugs one’s shoulders and says “what do you want from me, dude ? The mass of this particle is a fundamental constant”. Bad idea. Better go to level one and say “Well, I know this is a resonance which lives just 10^(-24) seconds, so its real mass - whatever mass is - is actually the central value of a Breit-Wigner distribution. But that is a perfectly well determined quantity, ain’t it ?”.

But that is still imprecise. Indeed, interactions change the mass of a resonance. If, for instance, the particle is affected by QCD interactions (that is to say, if it carries color charge), then a whole lot of punctualizations need to be made. What are we talking about, constituent mass or interaction mass ? Pole mass ? What about lambda_QCD, which gives a 0.2 GeV limit to the accuracy with which you can define the mass of a strong-interacting body ?

Most of this does not affect the W mass. The W boson is a very distinct gentleman which only interacts through the electroweak interaction, and even then it does so with a strong English accent.  No messy QCD effects at work, and the W mass is a well-defined quantity.

However. Let’s imagine that there is some effect at work in proton-antiproton collisions that is not there in electron-positron collisions. It’s easy if you try. The exchange of bodies that attach to leptons and not to quarks, for instance, would change the interactions panorama quite a bit, even if these did so only at 1- or more than 1- loop level.

Where am I heading ? I am just saying that when we make a world average W mass we put everything in a bid cauldron, but we should first make some distinguo.

Take the LEP II measurements on one side, and the Tevatron measurements on the other. I cannot make a very precise estimate of the combined measurements of W mass from these experiments, since I do not know the internal correlations of the experiments well enough. However, a simple weighted mean of the LEP II results yields Mw= 80372 MeV, while Tevatron results yield Mw=80431 MeV. Is that a signal of the dreaded “imperfect definition of the quantity being measured” systematics ? I think not, since the difference carries a uncertainty of the order of 40 MeV or so.

On the other hand, take the NuTeV result. They measure the rate of charged current neutrino-nucleon interactions and the rate of neutral current neutrino-nucleon interactions, and they pretend these, along with the precise knowledge of the Z boson mass (TM LEP), allow to determine the W mass. They so obtain Mw=80136+-84 MeV. Is that a signal of some subtle systematics at work, or what ?

Taken at face value, the 80136 MeV point is 2.8 sigma away from the world average. Is the LEP electroweak working group right in excluding this measurement from their fits, or what ? I acknowledge I did not study the issue in detail (there is a lot written on the NuTeV anomaly in the arXiv), but my two pence says whatever reason was used to argue that result away from global electroweak fits, it seems uncovincing to me. And my point of view must be shared by others, since the blue-band plot always has a parabola overlaid which includes the NuTeV result too - a sign of a bad conscience, or of a thoughtful choice.

The NuTeV anomaly can be thought to be due to the ambition of the program of determining the on-shell measurement of sin^2 theta_W from such a incredibly complex thing as a neutrino-nucleon interaction going too far, when the nucleon is something we don’t know enough about. QCD effects appear under control, but large isospin violation in parton distribution functions might be a source of uncertainty that makes the Weinberg angle determination by NuTeV erroneous.

A nice paper by Kevin Mc Farland (a CDF collaborator who also worked on NuTeV) can be consulted on this topic at http://xxx.lanl.gov/pdf/hep-ph/0306052 .