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Register a new userForm factor ratios for $B_s rightarrow K , ell , u$ and $B_s rightarrow D_s , ell , u$ semileptonic decays and $|V_{ub}/V_{cb}|$
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We present a lattice quantum chromodynamics determination of the ratio of the scalar and vector form factors for two semileptonic decays of the $B_s$ meson: $B_s rightarrow K ell u$ and $B_s rightarrow D_s ell u$. In conjunction with future experimental data, our results for these correlated form factors will provide a new method to extract $|V_{ub}/V_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of these Cabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form factor results, we determine the ratio of the differential decay rates, and forward-backward and polarization asymmetries, for the two decays.
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Semi-leptonic $B_s to K ell u$ and $B_s to D_s ell u$ decays provide an alternative $b$-decay channel to determine the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ or to obtain $R$-ratios to investigate lepton flavor universality violations. In addition, these decays may shed further light on the discrepancies seen in the analysis of inclusive vs. exclusive decays. Using the nonperturbative methods of lattice QCD, theoretical results are obtained with good precision and full control over systematic uncertainties. This talk will highlight ongoing efforts of the $B$-physics program by the RBC-UKQCD collaboration.
We provide a 0.8%-accurate determination of $V_{cs}$ from combining experimental results for the differential rate of $D rightarrow K$ semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that $V_{cs}$ has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the Highly Improved Staggered Quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC collaboration that include the effect of $u$, $d$, $s$ and $c$ HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical $u/d$ quarks for the first time. Our calculated form factors cover the full $q^2$ range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of $V_{cs}$ from a correlated weighted average over $q^2$ bins. We obtain $|V_{cs}|= 0.9663(53)_{text{latt}}(39)_{text{exp}}(19)_{eta_{EW}}(40)_{text{EM}}$, where the uncertainties come from lattice QCD, experiment, short-distance electroweak and electromagnetic corrections, respectively. This last uncertainty, neglected for $D rightarrow K ell u$ hitherto, now needs attention if the uncertainty on $V_{cs}$ is to be reduced further. We also determine $V_{cs}$ values in good agreement using the measured total branching fraction and the rates extrapolated to $q^2=0$. Our form factors enable tests of lepton flavour universality violation. We find the ratio of branching fractions for $D^0 rightarrow K^-$ with $mu$ and $e$ in the final state to be $R_{mu/e}=0.9779(2)_{text{latt}}(50)_{mathrm{EM}}$ in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections.
We calculate the $B topiell u$ and $B_s to K ell u$ form factors in dynamical lattice QCD. We use the (2+1)-flavor RBC-UKQCD gauge-field ensembles generated with the domain-wall fermion and Iwasaki gauge actions. For the $b$ quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze two lattice spacings $a approx 0.11, 0.086$ fm and unitary pion masses as light as $M_pi approx 290$ MeV. We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) hard-pion chiral perturbation theory. We provide complete error budgets for the form factors $f_+(q^2)$ and $f_0(q^2)$ at three momenta that span the $q^2$ range accessible in our numerical simulations. We extrapolate these results to $q^2 = 0$ using a model-independent $z$-parametrization and present our final form factors as the $z$-coefficients and the matrix of correlations between them. Our results agree with other lattice determinations using staggered light quarks and provide important independent cross-checks. Both $B topiell u$ and $B_s to K ell u$ decays enable a determination of the CKM matrix element $|V_{ub}|$. To illustrate this, we perform a combined $z$-fit of our numerical $Btopiell u$ form-factor data with the experimental branching-fraction measurements leaving the relative normalization as a free parameter; we obtain $|V_{ub}| = 3.61(32) times 10^{-3}$, where the error includes statistical and systematic uncertainties. This approach can be applied to $B_sto K ell u$ decay to determine $|V_{ub}|$ once the process has been measured experimentally. Finally, in anticipation of future measurements, we make predictions for $B to piell u$ and $B_sto K ell u$ Standard-Model differential branching fractions and forward-backward asymmetries.
We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_sto K ell u$. In combination with future measurement, this calculation will provide an alternative exclusive semileptonic determination of $|V_{ub}|$. We compare our results with previous model calculations, make predictions for differential decay rates and branching fractions, and predict the ratio of differential branching fractions between $B_sto Ktau u$ and $B_sto Kmu u$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_sto K$ form factors with those of the fictitious $B_stoeta_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaborations $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.
Using the MILC 2+1 flavor asqtad quark action ensembles, we are calculating the form factors $f_0$ and $f_+$ for the semileptonic $B_s rightarrow K ell u$ decay. A total of six ensembles with lattice spacing from $approx0.12$ to 0.06 fm are being used. At the coarsest and finest lattice spacings, the light quark mass $m_l$ is one-tenth the strange quark mass $m_s$. At the intermediate lattice spacing, the ratio $m_l/m_s$ ranges from 0.05 to 0.2. The valence $b$ quark is treated using the Sheikholeslami-Wohlert Wilson-clover action with the Fermilab interpretation. The other valence quarks use the asqtad action. When combined with (future) measurements from the LHCb and Belle II experiments, these calculations will provide an alternate determination of the CKM matrix element $|V_{ub}|$.
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