Abstract
We present a new lattice determination of some of the parameters appearing both in the Operator Product Expansion (OPE) analysis of the inclusive semileptonic B-meson decays and in the Heavy Quark Expansion (HQE) of the pseudoscalar (PS) and vector (V) heavy-light meson masses. We perform a lattice QCD (LQCD) computation of PS and V heavy-light meson masses for heavy-quark masses mh in the range from [see formula in PDF] to ≃ [see formula in PDF]. We employed the Nf = 2 + 1 + 1 gauge configurations of the European Twisted Mass Collaboration (ETMC) at three values of the lattice spacing a ≃ (0.062,0.082,0.089) fm with pion masses in the range Mπ ≃ (210 - 450) MeV. The heavy-quark mass is simulated directly on the lattice up to ≃ [see formula in PDF]. The interpolation to the physical [see formula in PDF] is performed using the ETMC ratio method and adopting the kinetic mass scheme. We obtain [see formula in PDF] (1 GeV) = 4.61(20) GeV (m̅b(m̅b) = 4.26(18) GeV in the MS scheme). The lattice data are analyzed in terms of the HQE and the matrix elements of dimension-4 and dimension-5 operators are extracted with good precision, namely: [see formula in PDF] and [see formula in PDF]. The data also allow for an estimate of the dimension-6 operator matrix elements.
Highlights
The precise determination of the CKM element Vcb is crucial in the search of new physics effects in rare decays (FCNC decays like Bs → μ+μ−, K+ → π+νν, KL → π0νν as well as K) and interesting nowadays in view of the anomalies in B → D(∗)τν
In the first case the Operator Product Expansion (OPE) is usually adopted to describe the non-perturbative hadronic physics in terms of few parameters μ2i, ρ3i extracted from experimental data on inclusive B → Xc ν decays together with Vcb : Γ [B → Xc ν ]
Our aim is to present the lattice determination of some of the parameters appearing in the OPE analysis of the inclusive B-meson decays, obtained in Ref. [3]
Summary
The precise determination of the CKM element Vcb is crucial in the search of new physics effects in rare decays (FCNC decays like Bs → μ+μ− , K+ → π+νν , KL → π0νν as well as K) and interesting nowadays in view of the anomalies in B → D(∗)τν. In the first case the OPE is usually adopted to describe the non-perturbative hadronic physics in terms of few parameters μ2i , ρ3i extracted from experimental data on inclusive B → Xc ν decays together with Vcb Our aim is to present the lattice determination of some of the parameters appearing in the OPE analysis of the inclusive B-meson decays, obtained in Ref. Only the charmed and beauty meson masses, MD(∗) and MB(∗) , are used to constrain the HQE parameters The same scheme is often used in the analysis of the inclusive semileptonic B-meson decays relevant for the determination Vcb [1, 2]. The conversion from the MS to the kinetic scheme at the charm mass and the inclusion or not of the last two terms in Eq (5) give rise to what we will call the ()conv uncertainty in the error budget
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