Light-cone sum rules for B → K π form factors and applications to rare decays

Abstract

We derive a set of light-cone sum rules relating the hadronic form factors relevant for B → Kπ + − decays to the B-meson light-cone distribution amplitudes (LCDAs). We obtain the sum rule relations for all B → Kπ form factors of (axial)vector and (pseudo)tensor b → s currents with a P -wave Kπ system. Our results reduce to the known light-cone sum rules for B → K * form factors in the limit of a single narrow-width resonance. We update the operator-product expansion for the underlying correlation function by including a more complete set of B-meson LCDAs with higher twists, and produce numerical results for all B → K * form factors in the narrow-width limit. We then use the new sum rules to estimate the effect of a non-vanishing K * width in B → K * transitions, and find that this effect is universal and increases the factorizable part of the rate of B → K * X decays by a factor of 20%. This effect, by itself, goes in the direction of increasing the current tension in the differential B → K * µµ branching fractions. We also discuss B → Kπ transitions outside the K * window, and explain how measurements of B → Kπ observables above the K * region can be used to further constrain the B → K * form factors.

B →P and B →V form factors from B-meson light-cone sum rules beyond leading twist

“…We are very grateful to Sébastien Descotes-Genon, Paolo Gambino and Javier Virto for helpful discussions, and to Martin Jung, David Straub and Javier Virto for comments on the manuscript. We are also grateful to the authors of [34,35] for discussing their results prior to publication.…”

“…A dedicated programme has emerged in recent years to study ππ [10,[24][25][26][27][28][29] and Kπ [30][31][32][33] final states beyond a simple resonance ansatz. LCSR analyses of B → P 1 P 2 form factors require ongoing updates [34,35] by other authors to improve our understanding of the semileptonic processes as well as purely hadronic multi-body B decays [36][37][38][39][40][41][42].…”

Exact NLO matching and analyticity in b → sℓℓ

“…Contributions to the amplitude from semileptonic ([sΓb][¯ Γ ]) or dipole ([sσ µν P R b]F µν ) operators are exactly factorizable and proportional to local form factors -matrix elements of local fermionic currents-to all orders in QCD (but to the leading order in QED effects). These local form factors are known relatively well and can be calculated with Light-Cone Sum Rules (LCSRs) or Lattice QCD (LQCD) methods, both agreeing well with each other [8][9][10][11][12][13]. On the contrary, contributions from four-quark operators such as [sγ µ P L c][cγ µ P L b] are proportional to non-local form factors, more precisely, the matrix elements of time-ordered products of a four-quark operator and an electromagnetic current.…”

“…To the leading non-trivial order in QED, the effective theory amplitude for the exclusive decaȳ B → M + − , with M an undetermined meson (or hadronic state in general [13]), is given in terms of local and non-local form factors [7,13,25]:…”

Contributions of $$ {K}_0^{\ast } $$(1430) and $$ {K}_0^{\ast } $$(1950) in the three-body decays B → Kπh

“…The F Kπ + (s) is the vector form factor which has been discussed in detail in the refs. [87,[128][129][130][131][132][133][134][135]. The the scalar form factor F Kπ 0 (s) is defined as [136][137][138]…”