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Register a new userAn exploratory study of heavy-light semileptonic form factors using distillation
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We present our exploratory study with the aim of simulating heavy-light semileptonic form factors as part of the RBC-UKQCD charm (to bottom) physics programme. We are using a distillation-based setup as a strategy to get optimised plateaus in semileptonic $D_{(s)}$ and $B_{(s)}$ decays, and compare our results to form factors obtained from sequential $Z_2$-Wall propagators. The study is done in a centre-of-mass frame as well as in several moving frames. We use an $N_f=2+1$ domain wall fermion ensemble with a pion mass of $340$ MeV, with the aim of extending the study to a variety of other domain-wall ensembles, including physical-pion mass ensembles.
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We calculate, in the continuum limit of quenched lattice QCD, the matrix elements of the heavy-heavy vector current between heavy-light pseudoscalar meson states. We present the form factors for different values of the initial and final meson masses at finite momentum transfer. In particular, we calculate the non-perturbative correction to the differential decay rate of the process B --> D l nu including the case of a non-vanishing lepton mass.
Comparisons of lattice-QCD calculations of semileptonic form factors with experimental measurements often display two sets of points, one each for lattice QCD and experiment. Here we propose to display the output of a lattice-QCD analysis as a curve and error band. This is justified, because lattice-QCD results rely in part on fitting, both for the chiral extrapolation and to extend lattice-QCD data over the full physically allowed kinematic domain. To display an error band, correlations in the fit parameters must be taken into account. For the statistical error, the correlation comes from the fit. To illustrate how to address correlations in the systematic errors, we use the Becirevic-Kaidalov parametrization of the D -> pi l nu and D -> K l nu form factors, and a analyticity-based fit for the B -> pi l nu form factor f_+.
We present a study of $D rightarrow K, l u$ semileptonic decays on the lattice which employs the HISQ action for both the charm and the light quarks. We work with MILC unquenched $N_f = 2 + 1$ lattices and determine the scalar form factor $f_0(q^2)$. This form factor is obtained from a scalar current matrix element that does not require any operator matching. We find $f^{D rightarrow K}_0(0) equiv f^{D rightarrow K}_+(0) = 0.747(19)$ in the chiral plus continuum limit and hereby improve the theory error on this quantity by a factor of $sim$4 compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product $f^{D rightarrow K}_+(0) * |V_{cs}| $ from BaBar and CLEO-c leads to a very precise direct determination of the CKM matrix element $|V_{cs}| $, $|V_{cs}| = 0.961(11)(24)$, where the first error comes from experiment and the second is the lattice QCD theory error.
We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4$d$ overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of $am_happrox 0.4$, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range $2.0-5.7,mathrm{GeV}$. We observe very mild $a^2$ scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.
We formulate Non-Relativistic Quantum Chromodynamics (NRQCD) on a lattice which is boosted relative to the usual discretization frame. Moving NRQCD (mNRQCD) allows us to treat the momentum for the heavy quark arising from the frame choice exactly. We derive mNRQCD through O(1/m^2,v^4), as accurate as the NRQCD action in present use, both in the continuum and on the lattice with O(a^4) improvements. We have carried out extensive tests of the formalism through calculations of two-point correlators for both heavy-heavy (bottomonium) and heavy-light (B_s) mesons in 2+1 flavor lattice QCD and obtained nonperturbative determinations of energy shift and external momentum renormalization. Comparison to perturbation theory at O(alpha_s) is also made. The results demonstrate the effectiveness of mNRQCD. In particular we show that the decay constants of heavy-light and heavy-heavy mesons can be calculated with small systematic errors up to much larger momenta than with standard NRQCD.
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