## Tuesday, April 13, 2021

### Lepton Universality Violation Considered Again

Moriond 2021 has reported New results on theoretically clean observables in rare B-meson decays from LHCb 3.1 sigma away from the SM prediction of lepton universality in the B+→K+μμ vs. B+→K+ee comparison. Again the same direction, muons are less common than electrons. 9/fb, i.e. the whole LHCb dataset so far. Preprint on arXiv

Statistics Issues

Statistically, my main issue is cherry picking.

They've found several instances where you have LFV and they combine those to get their significance in sigma. They ignore the many, many other instances where you have results that are consistent with LFU when the justification for excluding those results is non-obvious.

For example, lepton universality violations are not found in tau lepton decays or pion decays, and are not found in anti-B meson and D* meson decays or in Z boson decays. There is no evidence of LFV in Higgs boson decays either.

As one paper notes: "Many new physics models that explain the intriguing anomalies in the b-quark flavour sector are severely constrained by Bs-mixing, for which the Standard Model prediction and experiment agreed well until recently." Luca Di Luzio, Matthew Kirk and Alexander Lenz, "One constraint to kill them all?" (December 18, 2017).

Similarly, see Martin Jung, David M. Straub, "Constraining new physics in b→cℓν transitions" (January 3, 2018) ("We perform a comprehensive model-independent analysis of new physics in b→cℓν, considering vector, scalar, and tensor interactions, including for the first time differential distributions of B→D∗ℓν angular observables. We show that these are valuable in constraining non-standard interactions.")

An anomaly disappeared between Run-1 and Run-2 as documented in Mick Mulder, for the LHCb Collaboration, "The branching fraction and effective lifetime of B0(s)→μ+μ− at LHCb with Run 1 and Run 2 data" (9 May 2017) and was weak in the Belle Collaboration paper, "Lepton-Flavor-Dependent Angular Analysis of B→K∗ℓ+ℓ−" (December 15, 2016).

When you are looking a deviations from a prediction you should include all experiments that implicate that prediction.

In a SM-centric view, all leptonic or semi-leptonic W boson decays arising when a quark decays to another kind of quark should be interchangeable parts (subject to mass-energy caps on final states determined from the initial state), and since all leptonic or semi-leptonic W boson decays (either at tree level or removed one step at the one loop level) and are deep down the same process. See, e.g., Simone Bifani, et al., "Review of Lepton Universality tests in B decays" (September 17, 2018). So, you should be lumping them all together to determine if the significance of evidence for LFV.

Their justification for not pooling the anomalous results with the non-anomalous ones is weak and largely not stated expressly. At a minimum, the decision to draw a line regarding what should be looked at in the LFV bunch of results to get the 3.1 sigma and what should be looked at in the LFU bunch of results that isn't used to moderate the 3.1 sigma in any way is highly BSM model dependent, and the importance of that observation is understated in the analysis (and basically just ignored).

The cherry picking also gives rise to look elsewhere effect issues. If you've made eight measurements in all, divided among three different processes, the look elsewhere effect is small. If the relevant universe is all leptonic and semi-leptonic W and Z boson decays, in contrast, there are hundreds of measurements out there and even after you prune the matter-energy conservation limited measurements, you still have huge look elsewhere effects that trim one or two sigma from the significance of your results.

Possible Mundane Causes

It is much easier to come up with a Standard Model-like scenario in which there are too many electron-positron pairs produced, than it is to come up with one where there are too muon or tau pairs produced.

The ratios seem to be coming up at more than 80% but less than 90% of the expected Standard Model number of muon pair decays relative to electron-positron decays.

The simplest answer would be that there are two processes.

One produces equal numbers of electron-positron and muon pair decays together with a positively charged kaon in each case, as expected.  The pre-print linked above states this about this process:
The B+ hadron contains a beauty antiquark, b, and the K+ a strange antiquark, s, such that at the quark level the decay involves a b → s transition. Quantum field theory allows such a process to be mediated by virtual particles that can have a physical mass larger than the mass difference between the initial- and final-state particles. In the SM description of such processes, these virtual particles include the electroweak-force carriers, the γ, W± and Z bosons, and the top quark. Such decays are highly suppressed and the fraction of B+ hadrons that decay into this final state (the branching fraction, B) is of the order of 10^−6.
A second process with a branching fraction of about 1/6th that of the primary process produces a positively charged kaon together with an electromagnetically neutral particle that has more than about 1.22 MeV of mass (enough to decay to a positron-electron pair), but less than about 211.4 MeV mass necessary to produce a muon pair when it decays.

It turns out that there is exactly one such known particle fundamental or composite, specifically, a neutral pion, with a mass of about 134.9768(5) MeV.

About 98.8% of the time, a πº it decays to a pair of photons and that decay would be ignored as the end product doesn't match the filtering criteria. But about 1.2% of the time, it decays to an electron-positron pair together with a photon, and all other possible decays are vanishing rare by comparison.

So, we need a decay of a B+ meson to a K+ meson and a neutral pion with a branching fraction of about (10^-6)*(1/6)*(1/0.012)= 1.4 * 10^-5.

It turns out that B+ mesons do indeed decay to K+ mesons and neutral pions with a branching fraction of 1.29(5)*10^-5 which is exactly what it needs to be to produce the apparent violation of lepton universality.

It also appears to me that the theoretical calculation of the K+µ+µ- to K+e+e- ratio isn't considering this decay, although it seems mind boggling to me that so many physicists in such a carefully studied process would somehow overlook the B+ --> K+πº decay channel impact on their expected outcome, which is the obvious way to reverse engineer the process.

Time will tell if this will amount to anything. I've posted this analysis at the thread at the Physics Forums linked above, to get some critical review of this hypothesis.

If by some crazy twist of fate, this analysis isn't flawed, then it resolves almost all of one of the biggest anomalies in high energy physics outstanding today.

#### 1 comment:

andrew said...

Physics Stack Exchange thinks that a cut on the lepton invariant mass squared of 1.1 to 6 GeV culls out pion decay produced leptons. https://physics.stackexchange.com/questions/629254/is-there-a-reason-lepton-flavor-violation-lfv-in-b-meson-decays-cant-be-e