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I Is this thesis a plausible explanation for muon weirdness?

  1. Aug 8, 2017 #1


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    Background and Motivation

    In the Standard Model, a muon is simply an electron with a bigger mass.

    But, measurements of the radius of muonic hydrogen and the muon magnetic dipole moment (muon g-2), show a fairly significant discrepancy between theory an experiment in that respect, at the five sigma and three sigma levels, respectively (references found in the PhD thesis linked below). In other words, muons don't behave precisely as we would expect them to if a muon was simply a heavy electron, although they come quite close to behaving like that (the differences are subtle).

    There are also experimental indications from B meson decays that the lepton universality is violated by the charged leptons (i.e. the muons and electrons do not behave identically apart from the differences predicted as a result of their respective masses in B meson decays). These discrepancies are individually not quite even 3 sigma in significance, but they are all in the "same direction" and collectively, viewed as independent confirmations of the same effect, these discrepancies rise to something like 3.7 sigma in significance. See also this LHCb paper. (The thesis linked below does not address these phenomena, but they seem to be of a piece with other forms of muon weirdness and lepton non-universality.)

    There are many possible explanations for the observed discrepancies between muon behavior and electron behavior after controlling for the mass differences between them. The most plausible explanations involve experimental measurement issues, understated error bars and flawed theoretical calculations using Standard Model physics (perhaps, for example, due to conceptual issues in how the problems are formulated). These scientific error based explanations are attractive because while there are three to five sigma discrepancies, experiment still does confirm the Standard Model prediction to many significant digits even though it doesn't exactly match because the theoretical prediction and experimental measurements are so precise.

    Also, in general, to oversimplify, muon measurements are often more precise than electron measurements of the same quantities in many kinds of experiments because the greater muon mass makes for an easier to observe experimental signal, so discrepancies could have not come up before simply because electron measurements wouldn't be sensitive to details that are observable with muons.

    But, I don't reference any papers on these ideas because I want to assume, at least for the sake of argument, that this is not what is going on and that new measurements and theoretical analysis will confirm the discrepancies already observed to date.

    So, it makes sense to come up with a BSM model to explain the phenomena observed because, if the discrepancies persist despite improved experimental precision and confirmed theoretical correctness, one needs some sort of BSM explanation.

    The Thesis

    A new PhD thesis by Yu-Sheng Liu at the University of Washington explores what kind of new physics could give rise to this discrepancy. (I would quote the abstract here but it only explains the experimental results that motivate the thesis and notes the goal of explaining it theoretically with new physics, without explaining the author's answer to it to any useful degree.)

    As I read it, the thesis appears to conclude that a scalar boson whose couplings to the charged leptons differ by the ratio of the muon mass to the electron mass (mu/me)^n for some n>1 could resolve the subtle discrepancy between theory and experiment in cases where muons seem to behave differently than electrons. In this theory, the new scalar boson couples more strongly to muons than to electrons.

    The thesis then looks at the experimental bounds on the relevant coupling constants of this minimally flavor violating scalar boson. A vector boson or much of the rest of the parameter space (e.g. n<1) is ruled out.

    The paper does not suggest how such an electron-phobic scalar boson would fit into any larger theoretical model, for example, at high energies.

    This humble but thorough study (it is 90 pages long) seems to present a fairly parsimonious and plausible beyond the Standard Model theories to explain these phenomena (adding just one new scalar boson with fairly straightforwards properties), and to rule out a lot of other alternative explanations.


    Is my summary of the conclusions of the thesis accurate?

    For example, I had trouble discerning if there were free parameters in the theory other than "n" (the exponent of the mass ratios). Have I missed some free parameters in this scalar boson hypothesis?

    Does anyone see any obvious flaws in the analysis by Yu-Sheng Liu?

    Has anyone seen more plausible explanations for why muons might act differently than electrons (if indeed they do), or any BSM theories in which such a scalar boson would be expected a priori? For example, could this idea potentially be embedded in string theory?

    Lubos discussed some BSM models that could give rise to lepton universality violations in a 2015 post, but when I read it, I found those explanations to be baroque, but perhaps others would disagree.

    Can anyone see unintended consequences of such a model? Does it solve problems not obviously related to muon weirdness?
    Last edited: Aug 8, 2017
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  3. Aug 9, 2017 #2


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    Together with @dukwon I collected various theory papers focused on the b,s,µ,µ interaction in this older thread, some of the theory models discuss muon g-2, and if I remember correctly at least one discusses the proton radius puzzle as well.
    Muon g-2 and proton/deuteron radius puzzle are basically just two measurements, so it is not too hard to fit new particles to them.
  4. Aug 9, 2017 #3


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    Thanks for the pointer. In theory, physics forum threads are searchable, but in practice, to find threads worth reading you need someone who remembers them and knows what to look for.
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