Abstract
The LHCb collaboration has recently presented their result on R_K = BR(B+ -> K+ mu+ mu-)/ BR(B+ -> K+ e+ e-) for the dilepton invariant mass bin m_{ll}^2 = 1-6 GeV^2 (l = mu, e). The measurement shows an intriguing 2.6 sigma deviation from the Standard Model (SM) prediction. In view of this, we study model independent New Physics (NP) explanations of R_K consistent with other measurements involving b -> s l l transition, relaxing the assumption of lepton universality. We perform a Bayesian statistical fit to the NP Wilson Coefficients and compare the Bayes Factors of the different hypotheses in order to quantify their goodness-of-fit. We show that the data slightly favours NP in the muon sector over NP in the electron sector.
Highlights
≈ 0.07 and that the NP in C7 is severely constrained by the measured branching ratio of B → Xsγ, the expression of RK can be approximated by, C1S0M + C1μ0 + C1μ0 2 + C9SM + C9μ + C9μ 2 RK ≈ C1S0M + C1e0 + C1e0 2 + C9SM + C9e + C9e 2
This simplified expression clearly shows that the theoretical error in RK is very small even in the presence of NP
We took the theoretical error into account by taking a gaussian prior for a parameter called b0 and marginalizing over it, with its central value and standard deviation given by 15.86 and 1.51 respectively
Summary
We have used the data for B(B+ → K+μ+μ−) only in the low-q2 bin 1 − 6 GeV2, the main reason being that a resonance structure in the dilepton invariant mass distribution was observed around m2μ μ = 17.3 GeV2 by the LHCb collaboration last year [26]. This means that even though form factors in the high-q2 region were recently computed from lattice QCD [27,28,29,30], the theoretical prediction for this observable is affected by non-factorisable hadronic uncertainties. We expect a shift of the best fit points in the direction of the SM values, since these extra measurements are generally in good agreement with the SM predictions
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