Some technical details on particle physics today…
Papers are pouring out of particle theorists’ offices regarding the latest significant challenge to the Standard Model, namely the W boson mass coming in about 0.1% higher than expected in a measurement carried out by the Tevatron experiment CDF. (See here and here for earlier posts on the topic.) Let’s assume today that the measurement is correct, though possibly a little over-stated. Is there any reasonable extension to the Standard Model that could lead to such a shift without coming into conflict with previous experiments? Or does explaining the experiment require convoluted ideas in which various effects have to cancel in order to be acceptable with existing experiments?
The most common way (judging from the papers that have appeared this week) for theoretical physicists to try to explain a shift in the W boson mass, and many other details of the Standard Model, is to add new fields and particles which affect the W boson through “quantum fluctuations” — disturbances in the fields which aren’t particles (though they are often called “virtual particles” anyway.) Famous theories which can do this, in principle at least, include models with extra sterile and/or extra Standard Model-like Higgs bosons, minimal supersymmetry, and certain “compositeness models” in which the Higgs boson is understood not to be an elementary particle, but instead to be composite, somewhat like a proton. The problem with this approach is that it generally predicts new particles whose masses are not much bigger than the Higgs boson itself, so small that one would expect they would have been seen at the Large Hadron Collider (LHC). There are plenty of ways around this problem, though they require some finesse.
However, there are a couple of easy, well-known, and very reasonable ways to shift the W boson’s mass without requiring any quantum fluctuations, without leading to low mass particles, and without impacting much else in the Standard Model. Perhaps the simplest is to add another Higgs field, of a type called a “triplet”: let’s call it “T”, to distinguish it from the Standard Model’s own Higgs field “H”. The T field leads to a triplet of new Higgs bosons, one (T0) which is electrically neutral, one (T+) which has electric charge +1 (like a proton), and one (T–) which has electric charge -1 (like a electron). The T+ and T– have the same mass, which typically differs only slightly from the mass of the T0.
Triplet Higgs fields have been discussed for decades, going back to the late 1960s or early 1970s. As for combining the Standard Model with a T field, that too must go back to the 1970s; I know of papers from the mid-1980s whose authors knew everything I’m about to tell you. (A few of the theory papers [1,2,3,4] that appeared on Monday night, and perhaps others that I missed, pointed out parts of what I’m going to say here; I’m sure there will be more of them as the week goes by.)
How does this idea work? First, a quick review. The H field, uniquely among the Standard Model’s fields, has a non-zero, constant and uniform value in empty space (a so-called “vacuum expectation value”). Most of the known elementary particles are affected by the H field’s value, and obtain their mass from it.
But other, as-yet-unknown particles need not follow this rule, and the T field’s particles — the triplet Higgs bosons — are examples. For this reason, it can easily happen that the T bosons can all have mass much larger than the H boson, perhaps by ten times or so. At the LHC, that increase in mass has a huge cost; production rates for the T bosons are tremendously smaller than the production rate for the H boson. As a result, they won’t have been discovered yet, and aren’t discoverable in the near term.
Meanwhile, when the H field switches on, it can cause the T field to switch on too, as a knock-on effect. It can easily happen that the T0 field (but not the T+ or T– fields) develops a non-zero, constant and uniform value — though one that is more than fifty times smaller than that of the H field. The only Standard Model’s particles that can interact directly with the T field are the W boson, the Z boson and the Higgs boson. But here’s the key point: it turns out that the W+ and W– interact with T0 but the Z boson does not! So an appropriate small but non-zero vacuum expectation value for T0 shifts the W boson’s mass upward by about 1/1000, and leaves the Z boson’s mass alone.
Meanwhile the H has its mass shifted too, but its mass is not precisely predicted by the Standard Model, so that effect isn’t measurable. What is measurable is mixing between the T0 and the H, such that the 125 GeV/c2 Higgs boson that we already know and love is mostly H but a little bit T. This alteration, making the known Higgs boson differ slightly from what is predicted in the Standard Model, is probably too small to observe with current LHC data. But it might someday be observable at the LHC, and certainly would be seen at a “Higgs factory” machine that may be built sometime in the future.
[The math behind these statements is not particularly challenging, so maybe I’ll write a post later showing how it works, if there is interest among readers.]
It seems that this very simple addition to the Standard Model can cause a shift in the W mass of a sufficient size to match the CDF result without messing up anything else (or did I overlook a subtle effect?) So it would seem impossible to argue that the CDF measurement’s discrepancy from the Standard Model is too large to be plausible. Even a very simple model from decades ago can potentially generate it.
That said, this model is really too simple — too simple to be interesting, even if it is correct. With just the T field and nothing else new, it would represent merely a small wrinkle on the Standard Model. However, it might be embedded in a larger theoretical structure; for instance, there are composite Higgs models and unusual supersymmetry models (and surely others) that require this kind of triplet Higgs field. Maybe one of these models, or some other like it, might be right, and might help explain one of the various other discrepancies with the Standard Model, such as those in B meson decays and in the magnetic properties of the muon? That would be a lot more satisfying and informative.
But of course, it doesn’t matter what physicists would prefer. And of course, all this assumes the discrepancy observed by CDF is real.