B → Kℓ + ℓ − decay at large hadronic recoil

Abstract

Abstract:We predict the amplitude of the B → Kℓ + ℓ − decay in the region of the dilepton invariant mass squared 0 < q 2 ≤ m 2 J/ψ , that is, at large hadronic recoil. The B → K form factors entering the factorizable part of the decay amplitude are obtained from QCD light-cone sum rules. The nonlocal effects, generated by the four-quark and penguin operators combined with the electromagnetic interaction, are calculated at q 2 < 0, far below the hadronic thresholds. For hard-gluon contributions we employ the QCD factorization approach. The soft-gluon nonfactorizable contributions are estimated from QCD light-cone sum rules. The result of the calculation is matched to the hadronic dispersion relation in the variable q 2 , which is then continued to the kinematical region of the decay. The overall effect of nonlocal contributions in B → Kℓ + ℓ − at large hadronic recoil is moderate. The main uncertainty of the predicted B → Kℓ + ℓ − partial width is caused by the B → K form factors. Furthermore, the isospin asymmetry in this decay is expected to be very small. We investigate the deviation of the observables from the Standard Model predictions by introducing a generic new physics contribution to the effective Hamiltonian.

B s → Kℓν ℓ and B (s) → π(K)ℓ + ℓ − decays at large recoil and CKM matrix elements

“…We recalculate the nonlocal amplitudes, following [12,13]. In appendix B a brief outline of the calculational method is given.…”

“…These hadronic matrix elements in the B → π + − decay amplitude are multiplied by the CKM parameters other than V td , making the determination of the latter not straightforward. We take into account the nonlocal hadronic effects in B → K + − and B → π + − , employing the methods used in [12,13] and originally suggested in [11]. The nonlocal hadronic matrix elements are calculated at spacelike q 2 , using OPE, QCD factorization [14] and LCSRs, and are then matched to their values at timelike q 2 via hadronic dispersion relations.…”

“…In refs. [11,12], this part of hadronic input was cast in the form of an effective (process-and q 2 -dependent) addition ∆C BP 9 (q 2 ) to the Wilson coefficient C 9 . Here, as in ref.…”

“…and (2.19), with Bπ replaced by B s K. Here we do not consider the decays B 0 →K 0 + − andB 0 → π 0 + − , which are the isospin counterparts of, respectively, B − → K − + − and B − → π − + − and can be treated in a similar way (see [12,13]). We also postpone to a future study the time-dependent CP -asymmetry in theB s → K 0 + − decay.…”

Perturbative corrections to B → D form factors in QCD

“…Employing the massive quark propagator near the light cone from the background gluon field method [46][47][48] S(x, 0, m c ) = 0|T {c(x), c(0)}|0 (4.1)…”