Abstract
I show that the neutral pion decay in $B \to K^{(*)} \pi^0 \gamma$, with $\pi^0 \to ee \gamma$, might generate large sources of lepton flavor universality violation (LFUV) in measurements of the ratios, $R_{K^{(*)}}$: If the photons in the $K^{(*)} e e \gamma \gamma$ final state are reconstructed as Bremsstrahlung, the recovered electron-positron invariant mass can be pushed into the $1$-$6$ GeV$^{2}$ signal region, artificially enhancing the measured $B \to K^{(*)} e e$ branching ratio compared to $B \to K^{(*)} \mu\mu$. I present a conservative estimate and simulation of the $B \to K \pi^0 \gamma$ LFUV background at LHCb, that together suggest this effect could reduce the recovered $R_K$ up to several percent. A reliable assessment of the size of this effect will require dedicated simulations within experimental frameworks themselves.
Highlights
Measurements of lepton flavor universality violation (LFUV) involving charged dilepton final states are longknown to exhibit LFUV from virtual photon poles
The virtual photon exchange in B → KÃðγà → llÞ leads to significant LFUV in RKà if q2 ≪ 4m2μ
Another effect of this type can arise in RKðÃÞ from B → η0KðÃÞ, with the subsequent Dalitz decay η0 → llγ
Summary
Measurements of lepton flavor universality violation (LFUV) involving charged dilepton final states are longknown to exhibit LFUV from virtual photon poles. At LHCb in particular, the relatively large boost of the η0 system suggests one could naively expect an Oð1Þ fraction of such photons to look like bremsstrahlung: Noting the branching ratio Br1⁄2B → η0K 1⁄4 7.04ð25Þ × 10−5, this B → η0K LFUV background is known to lead to a percent level correction to RK [1] For this background, the misreconstructed dilepton invariant mass, q2reco ≃ m2η0 < 1 GeV2, and it is only relevant to the signal region with dilepton invariant mass q2 < 1 GeV2. I focus on the B → Kðπ0 → eeγÞγ LFUV background at LHCb, as a representative of a possibly broader class of decays with the following pathology: The photon produced by the b → sγ transition could, on rare occasion, be reconstructed into the π0 daughter electron or positron as bremsstrahlung, so that the misreconstructed q2 of the electron-positron pair may be pushed up into the 1 < q2 < 6 GeV2 signal region This enhances the measured branching fraction for B →.
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