Exclusive semileptonic B → πℓνℓ and Bs → Kℓνℓ decays through unitarity and lattice QCD
G. Martinelli, Silvano Simula, Ludovico Vittorio
Abstract
A bstract The Cabibbo-Kobayashi-Maskawa (CKM) matrix element ∣ V ub ∣ is obtained from exclusive semileptonic B → πℓν ℓ and B s → Kℓν ℓ decays adopting the unitarity-based dispersion matrix approach for the determination of the hadronic form factors (FFs) in the whole kinematical range. We use lattice computations of the relevant susceptibilities and of the FFs in the large- q 2 regime in order to derive their behavior in the low- q 2 region without assuming any specific momentum dependence and without constraining their shape using experimental data. Then, we address the extraction of | V ub | from the experimental data, obtaining | V ub | = (3 . 62 ± 0 . 47) · 10 − 3 from B → π and | V ub | = (3 . 77 ± 0 . 48) · 10 − 3 from B s → K , which after averaging yield | V ub | = (3 . 69 ± 0 . 34) · 10 − 3 . These results are compatible with the most recent inclusive value | V ub | incl = 4 . 13 (26) · 10 − 3 at the 1 σ level. We also present purely theoretical estimates of the ratio of the τ / μ decay rates $$ {R}_{\pi (K)}^{\tau /\mu } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>π</mml:mi> <mml:mfenced> <mml:mi>K</mml:mi> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mi>τ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> , the normalized forward-backward asymmetry $$ {\overline{\mathcal{A}}}_{FB}^{\ell, \pi (K)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>FB</mml:mi> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>π</mml:mi> <mml:mfenced> <mml:mi>K</mml:mi> </mml:mfenced> </mml:mrow> </mml:msubsup> </mml:math> and the normalized lepton polarization asymmetry $$ {\overline{\mathcal{A}}}_{\mathrm{polar}}^{\ell, \pi (K)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mover> <mml:mi>A</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mtext>polar</mml:mtext> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>π</mml:mi> <mml:mfenced> <mml:mi>K</mml:mi> </mml:mfenced> </mml:mrow> </mml:msubsup> </mml:math> .