# Is There A Reason lepton flavor violation (LFV) In $B^+$ Meson Decays Can't Be Explained By $K+πº$ Decays?

Physicists at Moriond 2021 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 $$B+→K+μ+μ-$$vs. $$B+→K+e+e-$$ comparison (i.e. there is apparent lepton flavor universality violation (LFV)). Muons are less common than electrons in the decay products. The ratios seem to be coming up at about 86% of the expected Standard Model number of muon pair decays relative to electron-positron decays.

The simplest answer in the Standard Model would seem 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 vanishingly 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 almost 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.

I looked at the methodology section of the paper on event selection and didn't see anything showing any kind of event selection that would weed out πº decays to electron-positron pairs.

Does this make sense, or am I missing something?

I am not an expert in this area, but I see that they apply a cut on the invariant mass-squared of the two leptons: $$1.1 < q^2 < 6.0\,\mathrm{GeV}^2/c^4.$$
The pion mass (squared) is way outside this cut, and so I suppose that the contribution from that decay mode doesn't pollute their measurement, though they don't say so explicitly. [Note that on page 3 they do discuss the value of the cut for excluding other resonances such as the $$J/\psi$$ or $$\phi(1020$$)]