The rare decay $Btopiell^+ell^-$ arises from $bto d$ flavor-changing neutral currents and could be sensitive to physics beyond the Standard Model. Here, we present the first $ab$-$initio$ QCD calculation of the $Btopi$ tensor form factor $f_T$. Toget
her with the vector and scalar form factors $f_+$ and $f_0$ from our companion work [J. A. Bailey $et~al.$, Phys. Rev. D 92, 014024 (2015)], these parameterize the hadronic contribution to $Btopi$ semileptonic decays in any extension of the Standard Model. We obtain the total branching ratio ${text{BR}}(B^+topi^+mu^+mu^-)=20.4(2.1)times10^{-9}$ in the Standard Model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij $et~al.$, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted for publication, LHCb announced a new measurement of the differential decay rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to the shape and normalization of the Standard-Model prediction.
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 anisotr
opic 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.
A calculation of the ratio of leptonic decay constants f_{K^+}/f_{pi^+} makes possible a precise determination of the ratio of CKM matrix elements |V_{us}|/|V_{ud}| in the Standard Model, and places a stringent constraint on the scale of new physics
that would lead to deviations from unitarity in the first row of the CKM matrix. We compute f_{K^+}/f_{pi^+} numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings a ~ 0.06, 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain f_{K^+}/f_{pi^+} = 1.1947(26)(37), where the errors are statistical and total systematic, respectively. This is our first physics result from our N_f = 2+1+1 ensembles, and the first calculation of f_{K^+}/f_{pi^+} from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f_{K^+}/f_{pi^+}, with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of |V_{us}|/|V_{ud}| = 0.2309(9)(4) where the errors are theoretical and experimental, respectively.
The semileptonic decay channel B -> D tau nu is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently the BaBar experiment reported the first observation of the exclusive semileptonic decay B -> D tau
nu, finding an approximately 2-sigma disagreement with the Standard-Model prediction for the ratio R(D)=BR(B->D tau nu)/BR(B->D l nu), where l=e,mu. We compute this ratio of branching fractions using hadronic form factors computed in unquenched lattice QCD and obtain R(D) = 0.316(12)(7), where the errors are statistical and total systematic, respectively. This result is the first Standard-Model calculation of R(D) from ab initio full QCD. Its error is smaller than that of previous estimates, primarily due to the reduced uncertainty in the scalar form factor f_0(q^2). Our determination of R(D) is approximately 1-sigma higher than previous estimates and, thus, reduces the tension with experiment. We also compute R(D) in models with electrically charged scalar exchange, such as the type II two-Higgs doublet model. Once again, our result is consistent with, but approximately 1-sigma higher than, previous estimates for phenomenologically relevant values of the scalar coupling in the type II model. As a byproduct of our calculation, we also present the Standard-Model prediction for the longitudinal polarization ratio P_L (D)= 0.325(4)(3).
We calculate the masses of bottom mesons using an improved relativistic action for the b-quarks and the RBC/UKQCD Iwasaki gauge configurations with 2+1 flavors of dynamical domain-wall light quarks. We analyze configurations with two lattice spacings
: a^{-1} = 1.729 GeV (a ~ 0.11 fm) and a^{-1} = 2.281 GeV (a ~ 0.086 fm). We use an anisotropic, clover-improved Wilson action for the b-quark, and tune the three parameters of the action nonperturbatively such that they reproduce the experimental values of the B_s and B_s* heavy-light meson states. The masses and mass-splittings of the low-lying bottomonium states (such as the eta_b and Upsilon) can then be computed with no additional inputs, and comparison between these predictions and experiment provides a test of the validity of our method. We obtain bottomonium masses with total uncertainties of ~0.5-0.6% and fine-structure splittings with uncertainties of ~35-45%; for all cases we find good agreement with experiment. The parameters of the relativistic heavy-quark action tuned for b-quarks presented in this work can be used for precise calculations of weak matrix elements such as B-meson decay constants and mixing parameters with lattice discretization errors that are of the same size as in light pseudoscalar meson quantities. This general method can also be used for charmed meson masses and matrix elements if the parameters of the heavy-quark action are appropriately tuned.
We calculate the leptonic decay constants of B_{(s)} and D_{(s)} mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light meson correlation functions on the MILC asqtad-improved staggered gau
ge configurations which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence- and sea-quark masses (down to ~m_s/10) and at three lattice spacings (a ~ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory and higher-order terms are expected to be small. We obtain f_{B^+} = 196.9(8.9) MeV, f_{B_s} = 242.0(9.5) MeV, f_{D^+} = 218.9(11.3) MeV, f_{D_s} = 260.1(10.8) MeV, and the SU(3) flavor-breaking ratios f_{B_s}/f_{B} = 1.229(26) and f_{D_s}/f_{D} = 1.188(25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.
We calculate the form factor f_+(q^2) for B-meson semileptonic decay in unquenched lattice QCD with 2+1 flavors of light sea quarks. We use Asqtad-improved staggered light quarks and a Fermilab bottom quark on gauge configurations generated by the MI
LC Collaboration. We simulate with several light quark masses and at two lattice spacings, and extrapolate to the physical quark mass and continuum limit using heavy-light meson staggered chiral perturbation theory. We then fit the lattice result for f_+(q^2) simultaneously with that measured by the BABAR experiment using a parameterization of the form factor shape in q^2 which relies only on analyticity and unitarity in order to determine the CKM matrix element |V(ub)|. This approach reduces the total uncertainty in |V(ub)| by combining the lattice and experimental information in an optimal, model-independent manner. We find a value of |V(ub)| x 10^3 = 3.38 +/- 0.36.
We study discretization effects in a mixed-action lattice theory with domain-wall valence quarks and Asqtad-improved staggered sea quarks. At the level of the chiral effective Lagrangian, discretization effects in the mixed-action theory give rise to
two new parameters as compared to the lowest order Lagrangian for staggered fermions -- the residual quark mass, m_res, and the mixed valence-sea meson mass-splitting, Delta_mix. We find that the size of m_res is approximately four times smaller than our lightest valence quark mass on our coarser lattice spacing, and comparable to that of simulations by RBC and UKQCD. We also find that the size of Delta_mix is comparable to the smallest of the staggered meson taste-splittings measured by MILC. Because lattice artifacts are different in the valence and sea sectors of the mixed-action theory, they give rise to unitarity-violating effects that disappear in the continuum limit. Such effects are expected to be mild for many quantities of interest, but are significant in the case of the isovector scalar (a_0) correlator. Specifically, once m_res, Delta_mix, and two other parameters that can be determined from the light pseudoscalar spectrum are known, the two-particle intermediate state bubble contribution to the scalar correlator is completely predicted within mixed-action chiral perturbation theory (MAChPT). We find that the behavior of the scalar meson correlator is quantitatively consistent with the MAChPT prediction; this supports the claim that MAChPT describes the dominant unitarity-violating effects in the mixed-action theory and can be used to remove lattice artifacts and recover physical quantities.
