B s  → K (*)ℓ$ \overline{\nu} $, angular analysis, S-wave contributions and |V ub |

Abstract

We analyse the $ \overline{B}_s^0\to {K^{+}}{l^{-}}\overline{\nu} $ and $ \overline{B}_s^0\to {K^{*+ }}\left( {\to K\pi } \right){\ell^{-}}\overline{\nu} $ decays that are valuable for extracting the CKM matrix element |V ub|. We calculate the differential and integrated partial widths in units of |V ub|2 based on various calculations of hadronic form factors and in particular the latest Lattice QCD calculation of the B s → K * form factors. For the decay $ \overline{B}_s^0\to K\pi \ell \overline{\nu} $ , we formulate the general angular distributions with the inclusion of the various partial-wave Kπ contributions. Using the results for the Kπ scalar form factor calculated from unitarized chiral perturbation theory, we explore the S-wave effects on angular distribution variables and demonstrate that they may not be negligible, considering the high precision expected in future measurements. We also briefly discuss the impact of the S-wave ππ contributions in the $ {B^{-}}\to {\pi^{+}}{\pi^{-}}\ell \overline{v} $ decay and provide estimates for the mode $ {B^{-}}\to {K^{+}}{K^{-}}\ell \overline{\nu} $ . The studies of these channels in future can not only be used to determine |V ub|, but may also provide valuable information on the Kπ and ππ phase shifts.

B →Vℓ+ℓ− in the Standard Model from light-cone sum rules

“…Similar conclusions can be reached when considering the figures in [41] with and without the ρ(1450) and ρ(1700) contributions. We note that 5% is of the same order as the S-wave background found in B → ππ ν [42]. other sizeable uncertainties we refrain from adding any further error due to this effect and reemphasise the importance of comparing our result only with the P -wave contribution of the corresponding ππ-pair.…”

“…In ref. [42] (cf. figure 9 of that reference) this effect has been analysed and it has been found that the integrated line-shapes of the S-wave over the interval [m ρ − Γ ρ , m ρ + Γ ρ ] is around 12% of the corresponding P -wave contribution.…”

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

“…To go beyond this approximation requires further studies. 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].…”

Dipion light-cone distribution amplitudes and B→ππ form factors

“…At large dipion invariant mass, the QCD factorization is available [2,3], when the invariant mass is small and the hadronic recoil is low, the chiral effective theory of heavy meson is proposed to combine with the dispersion theory [4]. The light-cone sum rules (LCSRs) approach is operative in the regions of large hadronic recoil at low invariant mass, i.e., the S−wave generated B → ππ, Kπ form factors has been calculated [5,6] with the combination of the perturbative theory based on the operator production expansion and the low-energy effective theory inspired by the chiral symmetry, corresponding to the effect from the LCDAs and from the scalar form factors, respectively, and recently the B 0 → π + π 0 form factors has been derived from LCSRs approach with the generalized 2πDAs [7][8][9]. In principle, the low invariant mass in LCSRs approach to deal with B → ππ ν decays goes from the threshold 4m 2 π to the resonance intervals, the previous works follow closely around the threshold while the running on the invariant mass is less attended, but actually this part is indispensable to show the resonance contribution.…”