B→πllForm Factors for New Physics Searches from Lattice QCD

Abstract

The rare decay B → πl þ l − arises from b → d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B → π tensor form factor f T . Together with the vector and scalar form factors f þ and f 0 from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B → π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BRðB þ → π þ μ þ μ − Þ ¼ 20.4ð2.1Þ × 10 −9 in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) Motivation.-Hadron decays that proceed through flavor-changing neutral currents may be sensitive to new physics, because their leading standard model contributions are loop suppressed. Here we study the semileptonic decay B → πl þ l − , which proceeds through a b → d transition. Hadronic effects in this decay are parametrized by three form factors. In this Letter, we present the first ab initio QCD calculation of the tensor form factor f T , based on lattice-QCD work that also yielded the vector and scalar form factors, f þ and f 0 [1]. Lattice QCD has several advantages over other approaches to the form factors [2][3][4][5][6][7][8][9], particularly in providing a path to controlled uncertainties that can be systematically reduced [10].The LHCb experiment recently made the first observation of B þ → π þ μ þ μ − [11], while the B factories have set limits on the e þ e − and τ þ τ − channels [12][13][14]. Below we

QCD calculations of B → π, K form factors with higher-twist corrections

“…For concreteness, we will adopt the simplified series expansion for B → P form factors originally proposed in [73] (see [74] for an alternative parametrization) Figure 7: The momentum-transfer dependence of B → π, K form factors predicted from the B-meson LCSR are displayed with the pink bands. For a comparison, we also present the Lattice QCD calculations from Fermilab/MILC Collaborations [1][2][3] with an extrapolation to small q 2 in terms of the z-series expansion (69) as indicated by the blue bands. Table 2: Theory predictions for the shape parameters and the normalizations of B → π, K form factors at q 2 = 0 entering the z expansion (69) with the dominant uncertainties from variations of different input parameters.…”

“…Precision calculations of the semileptonic B → π, K form factors are of essential importance for the determination of the CKM matrix element |V ub | exclusively and the theory description of the flavour-changing neutral current process B → K in QCD. At small hadronic recoil the Lattice QCD calculations of these form factors have been performed in [1][2][3], using the gauge-field ensembles with (2+1)-flavour lattice configurations. Diverse QCD techniques for computing the heavy-to-light form factors at large hadronic recoil have been developed with distinct theory assumptions and approximations.…”

Rare B decays as tests of the Standard Model

“…At high q 2 , where the hadronic recoil is small, the form factors can be simulated in lattice QCD and significant progress in this direction has been made recently. The uncertainties are smallest for the B to pseudoscalar transitions B → K [189] and B → π [190,65,191]. In these transitions, there are only three independent form factors, one of which does not contribute to the SM prediction in the limit of massless leptons (which is a good approximation for electrons and muons).…”

“…Photon-mediated contributions to these decays are absent. Using B → K * form factors from a combined fit to LCSR and lattice results [131], B → ρ form factors from LCSR [131], and B → K and B → π form factors from lattice QCD [189,65,191], one obtains the SM predictions…”

Summary of the CKM 2016 working group on rare decays

“…For these reasons it is common to see analyses using lattice QCD at low recoil and LCSR at high recoil. Recently, very high quality calculations of the three form factors f +,0,T (q 2 ) for the B → π [55,56,57], B s → K [58,55], and B → K [59, 60, 61] channels have been performed. Decays into vector mesons are considerably more complex because there are seven independent form factors for each channel and the vector mesons undergo strong decays.…”