Exclusive semileptonic B → πℓνℓ and Bs → Kℓνℓ decays through unitarity and lattice QCD

Abstract

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element ∣Vub∣ is obtained from exclusive semileptonic B → πℓνℓ and Bs→ Kℓνℓ 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-q2 regime in order to derive their behavior in the low-q2 region without assuming any specific momentum dependence and without constraining their shape using experimental data. Then, we address the extraction of |Vub| from the experimental data, obtaining |Vub| = (3.62 ± 0.47) · 10−3 from B → π and |Vub| = (3.77 ± 0.48) · 10−3 from Bs→ K, which after averaging yield |Vub| = (3.69 ± 0.34) · 10−3. These results are compatible with the most recent inclusive value |Vub|incl = 4.13 (26) · 10−3 at the 1σ level. We also present purely theoretical estimates of the ratio of the τ/μ decay rates $$ {R}_{\pi (K)}^{\tau /\mu } $$ R π K τ / μ , the normalized forward-backward asymmetry $$ {\overline{\mathcal{A}}}_{FB}^{\ell, \pi (K)} $$ A ¯ FB ℓ , π K and the normalized lepton polarization asymmetry $$ {\overline{\mathcal{A}}}_{\mathrm{polar}}^{\ell, \pi (K)} $$ A ¯ polar ℓ , π K .

A novel approach to semileptonic heavy-to-light $B$ decays through the Dispersive Matrix method

“…In this contribution we have reviewed the results of the application of the Dispersion Matrix approach to semileptonic 𝐵 → 𝜋 and 𝐵 𝑠 → 𝐾 decays [6]. In Figure 2 we have condensed the results obtained so far from the application of the DM method, enlarging the discussion also to the semileptonic 𝐵 → 𝐷 ( * ) [24,25] and 𝐵 𝑠 → 𝐷 ( * ) 𝑠 [26] transitions.…”

“…From the mathematical point of view, the idea is to obtain bounds on the hadronic FFs by using the computations of the FFs on the lattice and of the derivatives of suitable Green functions of bilinear quark operators, that hereafter we will refer to as susceptibilities. To be more specific, the susceptibilities follow from the dispersion relation associated to a particular spin-parity quantum channel and have been computed for the first time on the lattice in [6,7] for 𝑏 → 𝑢 and 𝑏 → 𝑐 quark transitions, respectively. Using the DM method, one can obtain from first principles the lower and the upper bounds of a generic FF 𝐹 for each generic value of 𝑞 2 , 𝑖.𝑒.…”

“…Let us discuss the application of the Dispersive Matrix method to the 𝐵 → 𝜋ℓ𝜈 decays [6]. The FFs 𝑓 𝜋 + (𝑞 2 ), 𝑓 𝜋 0 (𝑞 2 ) have been studied by the RBC/UKQCD [8] and the FNAL/MILC [9] Collaborations (the results of a new computation of these hadronic FFs have been recently published also by the JLQCD Collaboration [10]).…”

“…At present, several experiments [11][12][13][14] have measured the differential branching fractions of the semileptonic 𝐵 → 𝜋 transition. All the details of this study can be found in [6]. Our final result for |𝑉 𝑢𝑏 | reads…”

“…Also in this case the LQCD values of the FFs have been considered at three values of the momentum transfer in the large-𝑞 2 regime, namely 𝑞 2 = {17.6, 20.8, 23.4} GeV 2 . We have then implemented the DM method to obtain unitary bands for the FFs (see all the details in [6]).…”