Precision calculations of Bd,s → π, K decay form factors in soft-collinear effective theory

Abstract

A bstract We improve QCD calculations of the semileptonic B d , s → π , K decay form factors at large hadronic recoil by implementing the next-to-leading-logarithmic resummation for the obtained leading-power light-cone sum rules in the soft-collinear effective theory (SCET) framework and by computing for the first time the non-vanishing spectator-quark mass correction dictating the SU(3)-flavour symmetry breaking effects between these fundamental quantities at the one-loop accuracy. Additionally, we endeavour to investigate a variety of the subleading-power contributions to these heavy-to-light form factors at $$ \mathcal{O}\left({\alpha}_s^0\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> with the same methodology, by including the higher-order terms in the heavy-quark expansion of the hard-collinear quark propagator, by evaluating the desired effective matrix element of the next-to-leading-order term "Image missing" in the SCET I representation of the weak transition current, by taking into account the off-light-cone contributions of the two-body heavy-quark effective theory (HQET) matrix elements as well as the three-particle higher-twist corrections from the subleading bottom-meson light-cone distribution amplitudes (LCDAs), and by computing the twist-five and twist-six four-body higher-twist effects with the aid of the factorization approximation. Having at our disposal the SCET sum rules for the exclusive B -meson decay form factors under discussion, we further explore in detail numerical implications of the newly computed subleading-power corrections by employing the three-parameter model for both the leading-twist and higher-twist B -meson distribution amplitudes. Taking advantage of the customary Bourrely-Caprini-Lellouch (BCL) parametrization for the complete set of the semileptonic B d , s → π , K form factors, we then determine the correlated numerical results for the interesting series coefficients, by carrying out the simultaneous fit of the exclusive B -meson decay form factors to both the achieved SCET sum rule predictions at small momentum transfer ( q 2 ) and the available lattice QCD results at large momentum transfer. Subsequently, we perform a comprehensive phenomenological analysis of the full angular observables, the lepton-flavour university ratios and the lepton polarization asymmetries for the flavour-changing charged- current $$ B\to \pi \ell {\overline{\nu}}_{\ell } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>π</mml:mi> <mml:mi>ℓ</mml:mi> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:math> and $$ {B}_s\to K\ell {\overline{\nu}}_{\ell } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>K</mml:mi> <mml:mi>ℓ</mml:mi> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:math> decays (with ℓ = μ , τ ) together with the differential q 2 -distribution for the exclusive rare $$ B\to K{\nu}_{\ell }{\overline{\nu}}_{\ell } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>K</mml:mi> <mml:msub> <mml:mi>ν</mml:mi> <mml:mi>ℓ</mml:mi> </mml:msub> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:math> decays in the Standard Model.

Topics & Concepts