Of Particular Significance

A Few Remarks on the W Boson Mass Measurement

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 04/08/2022

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.

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10 Responses

  1. The CMB Cold Spot or WMAP Cold Spot :
    A better way to say it is that the experimental observation of photons and electrons, along with a desire to write a local Lagrangian, requires the use of a gauge degree of freedom. If you’re willing to give up a local Lagrangian, you can write everything in gauge invariant form.

    The discrepancy between Right-handed and Left-handed helicity in Gauge theory, is mathematically just a magnetic field. If there is a space time difference in the time direction, then the discrepancy is equivalent to an electric field.
    But if an electron convert into a neutrino. This is of course just don’t, (because electrons have an electric charge, neutrinos do not), so a gauge field must here again, changes an electron into a neutrino (just as the charge).

    At the end of the sixties Salam, Weinberg and Glashow have accepted that the conversion of electrons into neutrinos should be possible after the Gauge theory. The theory is called “electroweak” theory. The theory is possible only, if the gauge particles are massless, but it is untrue (gauge invariance or momentum, “Gauge invariance forbidding mass terms”?).
    Therefore they had invented the Higgs particle which give mass to other particles.
    The W and Z bosons are the ones, they reachts (weakly) only to the left-handed particles and not with the right-handed ones (breakdown of parity conservation in weak interaction).

    Mass, not weight, can be transformed into energy.
    Another way of expressing this idea is to say that matter can be transformed into energy.

    Units of mass are used to measure the amount of matter in something (closed system).
    But the amount of matter confined in a closed system is created by an outside Mass parameter of that system (churning or WMAP Cold Spot?).
    Energy is the masless mode of the matter.

    The mass or the amount of matter in something determines how much energy that thing could be changed into.

  2. The newly reported data would tend to support the notion that the ratios 7 : 9 : 17 might pertain regarding the squares of the W, Z, and Higgs boson masses. (This is not to say that previous numbers [that the Particle Data Group reports] do not also adequately comport with those ratios. Perhaps, see table 12 in https://www.preprints.org/manuscript/202111.0491/v5 . The newly reported result seems to comport “better.”)
    Permit me to ask for ideas about the extent to which the inclusion of the Higgs mass in the above statements might associate (now or later) with the Standard Model.

  3. Aaah another case of ‘groundbreaking if it holds up’. We have seen BICEP2 gravitational waves and FTL neutrinos fall to the wayside, will this anomaly hold? Time will tell.

  4. I don’t know if this is relevant to the W boson discussion, but Professor, could you explain what is going on at the origin of the Maxwell–Boltzmann statistics?

    My point is if the W and Z bosons are the force carriers of the weak force, could the gluons have an effect on the W and Z, so as they scatter away from their interaction with the gluons they would show their true heavier mass?


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