A Few Remarks on the W Boson Mass Measurement

Based on some questions I received about yesterday’s post, I thought I’d add some additional comments this morning.

A natural and persistent question has been: “How likely do you think it is that this W boson mass result is wrong?” Obviously I can’t put a number on it, but I’d say the chance that it’s wrong is substantial. Why? This measurement, which took several many years of work, is probably among the most difficult ever performed in particle physics. Only first-rate physicists with complete dedication to the task could attempt it, carry it out, convince their many colleagues on the CDF experiment that they’d done it right, and get it through external peer review into Science magazine. But even first-rate physicists can get a measurement like this one wrong. The tiniest of subtle mistakes will undo it.

And that mistake, if there is one, might not even be their own, in a sense. Any measurement like this has to rely on other measurements, on simulation software, and on calculations involving other processes, and even though they’ve all been checked, perhaps they need to be rechecked.

Another question about the new measurement is that it seems inconsistent not only with the Standard Model but also with previous, less precise measurements by other experiments, which were closer to the Standard Model’s result. (It is even inconsistent with CDF’s own previous measurement.) That’s true, and you can see some evidence in the plot in yesterday’s post. But

• it could be that one or more of the previous measurements has an error;
• there is a known risk of unconscious experimental bias that tends to push results toward the Standard Model (i.e. if the result doesn’t match your expectation, you check everything again and tweak it and then stop when it better matches your expectation. Performing double-blinded experiments, as this one was, helps mitigate this risk, but it doesn’t entirely eliminate it.);
• CDF has revised their old measurement slightly upward to account for things they learned while performing this new one, so their internal inconsistency is less than it appears, and
• even if the truth lies between this new measurement and the old ones, that would still leave a big discrepancy with the Standard Model, and the implication for science would be much the same.

I’ve heard some cynicism: “Is this just an old experiment trying to make a name for itself and get headlines?” Don’t be absurd. No one seeking publicity would go through the hell of working on one project for several years, running down every loose end multiple times and checking it twice and cross-checking it three times, spending every living hour asking oneself “what did I forget to check?”, all while knowing that in the end one’s reputation will be at stake when the final result hits the international press. There would be far easier ways to grab headlines if that were the goal.

Someone wisely asked about the Z boson mass; can one study it as well? This is a great question, because it goes to the heart of how the Standard Model is checked for consistency. The answer is “no.” Really, when we say that “the W mass is too large,” what we mean (roughly) is that “the ratio of the W mass to the Z mass is too large.” One way to view it (not exactly right) is that certain extremely precise measurements have to be taken as inputs to the Standard Model, and once that is done, the Standard Model can be used to make predictions of other precise measurements. Because of the precision with which the Z boson mass can be measured (to 2 MeV, two parts in 100,000), it is effectively taken as an input to the Standard Model, and so we can’t then compare it against a prediction. (The Z boson mass measurement is much easier, because a Z boson can decay (for example) to an electron and a positron, which can both be observed directly. Meanwhile a W boson can only decay (for example) to an electron and a neutrino, but a neutrino can only be inferred indirectly, making determination of its energy and momentum much less precise.)

In fact, one of the ways that the experimenters at CDF who carried out this measurement checked their methods is that they remeasured the Z boson mass too, and it came out to agree with other, even more precise measurements. They’d never have convinced themselves, or any of us, that they could get the W boson mass right if the Z boson mass measurement was off. So we can even interpret the CDF result as a measurement of the ratio of the W boson mass to the Z boson mass.

One last thing for today: once you have measured the Z boson mass and a few other things precisely, it is the consistency of the top quark mass, the Higgs boson mass and the W boson mass that provide one of the key tests of the Standard Model. Because of this, my headline from yesterday (“The W Boson isn’t Behaving”) is somewhat misleading. The cause of the discrepancy may not involve the W boson at all. The issue might turn out to be a new effect on the Z boson, for instance, or perhaps even the top quark. Working that out is the purview of theoretical physicists, who have to understand the complex interplay between the various precise measurements of masses and interactions of the Standard Model’s particles, and the many direct (and so far futile) searches for unknown types of particles that could potentially shift those masses and interactions. This isn’t easy, and there are lots of possibilities to consider, so there’s a lot of work yet to be done.