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Register a new userLattice $B to D^{(*)}$ form factors, $R(D^{(*)})$, and $|V_{cb}|$
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Authors
Andrew Lytle
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I discuss recent progress in lattice calculations of $B to D^{(*)} ell u$ form factors, important for the precision determination of $|V_{cb}|$ in the Standard Model (SM), and for testing SM expectations of lepton flavor universality in observables $R(D^{(*)})$. I also discuss progress in calculations of the related $b to c$ semileptonic decays $B_s to D_s^{(*)} ell u$ and $B_c to J/psi , ell u$ now experimentally accessible at the LHC.
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We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay $overline{B} rightarrow D ell overline{ u}$ at nonzero recoil. We carry out numerical simulations on fourteen ensembles of gauge-field configurations generated with 2+1 flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4. For the $b$ and $c$ valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate our results to the physical point using rooted staggered heavy-light meson chiral perturbation theory. We then parameterize the form factors and extend them to the full kinematic range using model-independent functions based on analyticity and unitarity. We present our final results for $f_+(q^2)$ and $f_0(q^2)$, including statistical and systematic errors, as coefficients of a series in the variable $z$ and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BaBar to determine the CKM matrix element, $|V_{cb}|=(39.6 pm 1.7_{rm QCD+exp} pm 0.2_{rm QED})times 10^{-3}$. As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. Finally, we use them to update our calculation of the ratio $R(D)$ in the Standard Model, which yields $R(D) = 0.299(11)$.
Stringent relations between the $B^{(*)} to D^{(*)} $ form factors exist in the heavy quark limit and the leading symmetry breaking corrections are known. We reconsider their uncertainty and role in the analysis of recent Belle data for $Bto D^{(*)}ell u$ with model-independent parametrizations and in the related prediction of $R(D^{(*)})$. We find $|V_{cb}|=41.5(1.3) 10^{-3}$ and $|V_{cb}|=40.6(^{+1.2}_{-1.3}) 10^{-3}$ using input from Light Cone Sum Rules, and $R(D^{*})=0.260(8)$.
The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $vert V_{cb}vert$ is extracted from exclusive semileptonic $B to D^{(*)}$ decays adopting a novel unitarity-based approach which allows to determine in a full non-perturbative way the relevant hadronic form factors (FFs) in the whole kinematical range. By using existing lattice computations of the $B to D^{(*)}$ FFs at small recoil, we show that it is possible to extrapolate their behavior also at large recoil without assuming any specific momentum dependence. Thus, we address the extraction of $vert V_{cb}vert$ from the experimental data on the semileptonic $B to D^{(*)} ell u_ell$, obtaining $vert V_{cb}vert = (40.7 pm 1.2 ) cdot 10^{-3}$ from $B to D$ and $vert V_{cb}vert = (40.6 pm 1.6 ) cdot 10^{-3}$ from $B to D^*$. Our results, though still based on preliminary lattice data for the $B to D^*$ form factors, are consistent within $sim 1$ standard deviation with the most recent inclusive determination $vert V_{cb} vert_{incl} = (42.00 pm 0.65) cdot 10^{-3}$. We investigate also the issue of Lepton Flavor Universality thanks to new theoretical estimates of the ratios $R(D^{(*)})$, namely $R(D) = 0.289(8)$ and $R(D^{*}) = 0.249(21)$. Our findings differ respectively by $sim 1.6sigma$ and $sim1.8sigma$ from the latest experimental determinations.
We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a=0.04 fm (corresponding to a^{-1}=4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy quark expansion. For decays of D and D_s mesons, our results for the physical form factors at q^2=0 are as follows: f_+^{D to pi}(0)= 0.74(6)(4), f_+^{D to K}(0)= 0.78(5)(4) and f_+^{D_s to K}(0)=0.68(4)(3). Similarly, for B and B_s we find: f_+^{B to pi}(0)=0.27(7)(5), f_+^{B to K}(0)=0.32(6)(6) and f_+^{B_s to K}(0)=0.23(5)(4). We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.
We report on our calculation of the B to D^(*) ell u form factors in 2+1 flavor lattice QCD. The Mobius domain-wall action is employed for light, strange, charm and bottom quarks. At lattice cutoffs 1/a sim 2.4, 3.6 and 4.5 GeV, we simulate bottom quark masses up to 0.7/a to control discretization errors. The pion mass is as low as 230 MeV. We extrapolate the form factors to the continuum limit and physical quark masses, and make a comparison with recent phenomenological analyses.
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