by Tommaso Dorigo

After a lot of agonizing work on tiny systematic uncertainties, the ATLAS collaboration released in time for the Moriond conference their latest measurement of the W boson mass (in fact the only one so far). The result is in close match with previous determinations, and has a slightly larger error bar than those. So why bother discussing it here ?

There is a reason. The W boson is one of the most important subatomic particles when it comes to experimental studies. It intervenes in the decay of heavy quarks, it plays a big role in Higgs boson phenomenology, and it may be the key to gain further knowledge on subnuclear physics.

W bosons carry the “charged-current” electroweak interactions. Without them stars would not burn, radioactive nuclei would not be radioactive, and heavy quarks would be stable. Because of the intervention of W bosons in much of the phenomenology of electroweak processes, the W boson mass is a quite critical parameter of the standard model. The W weighs 80.4 GeV – over 85 proton masses! Modify it by a bit, and everything changes. Or put in another way: finding out that the W boson mass is different from what theory predicts would immediately point to new physics we have not yet figured out.

But, how do we measure the mass of the W ? We need to first produce this particle in large amounts, through energetic collisions. Then we measure the energy of the two particles that the bosons decay into: the W mass is a function of the energies and emission angles of the two bodies. We of course need to analyze all sources of uncertainty that may cause us to err in the determination of those inputs, but conceptually the measurement is not a hard one to make.

Why, then, did ATLAS take so much time since its startup to cook up a W mass result ? And why is CMS still fiddling with it ? The reason is that we want our measurement to be very precise – we are not satisfied with an approximated one. In fact, we already know the W mass to within 2 parts per ten thousand: a measurement with a one-percent accuracy is irrelevant at this point. This makes the determinations by the LHC experiments a grievous task, as at the per-ten-thousand level one needs to consider a very large number tiny systematic effects, each of which is a nightmare to pinpoint to the required precision.

Historically, the first determination of the W mass came from the UA1 and UA2 experiments at CERN, who studied handfuls of W’s produced in 560-GeV (and then 630-GeV) proton-antiproton collisions after the discovery of that particle in 1983. Those results had relative uncertainties of about 5 percent. Then, starting in 1989, the CDF experiments entered the fray, and with its higher center-of-mass could produce more W bosons, and shrink the uncertainty to a few hundred MeV – 0.5% accuracy. The DZERO experiment started to compete with CDF since 1992, and together the two Tevatron experiments reached uncertainties close to permille level.

Above: recent determinations of the mass of the W boson, compared to theoretical predictions based on the validity of the Electroweak model (grey band)

The LEP II collider, using electron-positron collisions at 160 GeV and beyond, could dub itself as a “W boson factory”, producing pairs of W bosons with almost no background. The four experiments could determine the mass of the W boson by looking at how many were produced as a function of the center-of-mass energy of the machine, very precisely measured thanks to subtle beam-tuning tricks. By combining their data they reached a precision of 33 MeV on the W mass, but they ended up losing the battle with the Tevatron experiments; and the larger statistics collected in the first decade of the XXI century by CDF and DZERO allowed those collaborations to further halve the uncertainty.

The new ATLAS result is the best single-experiment determination, 80370+-19 MeV. Together with previous results from LEP and Tevatron, it combines to yield about 80379 MeV. This is a value higher, but not incompatible, with the one obtained by indirect information that assumes the validity of the standard model. This latter determination rests at 80358+-8 MeV. If you are a believer of new physics, you could argue that this 21-MeV discrepancy hides the failure of the standard model and the presence of new subtle effects that involve new particles and new forces of nature. I tend to rather believe that this is a splendid agreement, and that it is one further nail in the coffin of the “new physics at the TeV scale” paradigm we have been lectured about by theorists for the last couple of decades.

Am I a pessimist ? Well, you judge by yourself. In the meantime, even Lubos Motl has lost a bet on Supersymmetry (with Adam Falkowsky) – SUSY keeps deluding all its believers, and fails to show up. Should we find supersymmetric particles in the new run of the LHC, it would by now not look such a beautiful fixing of the standard model shortcomings, fine-tuned as itself needs to be in order to do its magic trick (cancelling the large radiative contributions to the Higgs mass). It is time for all of us to think deep whether collider physics has reached a point when it is not any longer the most direct avenue to new fundamental knowledge gains. It is tough to accept this, of course, if you have spent your best years to make ATLAS or CMS work the way they do (beautifully)… But we have to be pragmatic: building a new, more powerful collider is not so clearly called for by the present status of our knowledge.