Heavy-light Currents Research Articles

Improvement of heavy-heavy and heavy-light currents with the Oktay-Kronfeld action

The Cabibbo-Kobayashi-Maskawa matrix elements $|{V}_{cb}|$ and $|{V}_{ub}|$ can be obtained by combining data from the experiments with lattice QCD results for the semileptonic form factors for the $\overline{B}\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ and $\overline{B}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays. It is highly desirable to use the Oktay-Kronfeld (OK) action for the form factor calculation on the lattice, since the OK action is designed to reduce the heavy quark discretization error down to the $\mathcal{O}({a}^{4}{\mathrm{\ensuremath{\Lambda}}}^{4})\ensuremath{\simeq}\mathcal{O}({\mathrm{\ensuremath{\Lambda}}}^{4}/(2{m}_{Q}{)}^{4})$ level in the power counting rules of the heavy quark effective theory (HQET). Here, we present a matching calculation to improve heavy-heavy and heavy-light currents up to the ${\ensuremath{\lambda}}^{3}$ order in HQET, the same level of improvement as the OK action. Our final results for the improved currents are being used in a lattice QCD calculation of the semileptonic form factors for the $\overline{B}\ensuremath{\rightarrow}{D}^{*}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ and $\overline{B}\ensuremath{\rightarrow}D\ensuremath{\ell}\overline{\ensuremath{\nu}}$ decays.

Bino variations: Effective field theory methods for dark matter direct detection

We apply effective field theory methods to compute bino-nucleon scattering, in the case where tree-level interactions are suppressed and the leading contribution is at loop order via heavy flavor squarks or sleptons. We find that leading log corrections to fixed-order calculations can increase the bino mass reach of direct detection experiments by a factor of two in some models. These effects are particularly large for the bino-sbottom coannihilation region, where bino dark matter as heavy as 5-10 TeV may be detected by near future experiments. For the case of stop- and selectron-loop mediated scattering, an experiment reaching the neutrino background will probe thermal binos as heavy as 500 and 300 GeV, respectively. We present three key examples that illustrate in detail the framework for determining weak scale coefficients, and for mapping onto a low energy theory at hadronic scales, through a sequence of effective theories and renormalization group evolution. For the case of a squark degenerate with the bino, we extend the framework to include a squark degree of freedom at low energies using heavy particle effective theory, thus accounting for large logarithms through a "heavy-light current." Benchmark predictions for scattering cross sections are evaluated, including complete leading order matching onto quark and gluon operators, and a systematic treatment of perturbative and hadronic uncertainties.

Form factors for B meson weak decays in QCD light cone sum rules with a chiral current correlator

We report some applications of QCD light cone sum rules (LCSR) to \(B\) meson weak decays. Special emphasis is on estimates of the form factors for \(B\) decays into a pseudoscalar (\(P\))/vector (\(V\)) meson, with a certain chiral current correlator. The main new ingredient, as compared with the case of the standard correlators, is that in the operator product expansion calculations, the contributions due to the twist-3 distribution amplitudes of the related light mesons, which are less known and would bring a larger uncertainty to the calculations with the standard correlators, cancel out fully in the \(B\rightarrow P\) case and do out partially in the \(B\rightarrow V\) one. An important observation, which is similar to that in soft collinear effective theory, is made in twist-3 approximation: whereas only one independent form factor is needed for parameterizing the hadronic matrix elements for a \(B\rightarrow P\) transition induced by all the relevant heavy-light quark currents, there exist two independent form factors under the condition of neglecting the terms suppressed by a factor of \(m_V^2\), for the \(B\rightarrow V\) transition. Therefore, the improved LCSR approach could be of stronger predictive power for the weak form factors. Also, this approach is employed to understand the \(B\rightarrow D\) transitions by introducing a leading twist-2 DA for an energetic \(D\) meson, combined with some of other QCD-based approaches. A detailed QCD next-to-leading order calculation of the \(B\rightarrow \pi \) form factors is presented for an illustrative purpose, and the sum rule results are used to extract the Cabibbo–Kobayashi–Maskawa matrix element \(|V_{ub}|\) from the latest BaBar data.

Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level study

We present a strategy how to match the full set of components of the heavy-light axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/m h -corrections, to QCD. While the ultimate goal is to apply these matching conditions non-perturbatively, in this study we first have implemented them at tree-level, in order to find good choices of the matching observables with small $ \mathcal{O}\left( {{1 \left/ {{m_{\mathrm{h}}^2}} \right.}} \right) $ contributions. They can later be employed in the non-perturbative matching procedure which is a crucial part of precision HQET computations of semileptonic decay form factors in lattice QCD.

A one-loop study of matching conditions for static-light flavor currents

Abstract Heavy Quark Effective Theory (HQET) computations of semi-leptonic decays, e.g. B → πlν, require the knowledge of the parameters in the effective theory for all components of the heavy-light flavor currents. So far non-perturbative matching conditions have been employed only for the time component of the axial current. Here we perform a check of matching conditions for the time component of the vector current and the spatial component of the axial vector current up to one-loop order of perturbation theory and to lowest order of the 1/m-expansion. We find that the proposed observables have small higher order terms in the 1/m-series and are thus excellent candidates for a non-perturbative matching procedure.

Renormalization of heavy-light currents in moving nonrelativistic QCD

Heavy-light decays such as $B \to \pi \ell \nu$, $B \to K^{*} \gamma$ and $B \to K^{(*)} \ell \ell$ can be used to constrain the parameters of the Standard Model and in indirect searches for new physics. While the precision of experimental results has improved over the last years this has still to be matched by equally precise theoretical predictions. The calculation of heavy-light form factors is currently carried out in lattice QCD. Due to its small Compton wavelength we discretize the heavy quark in an effective non-relativistic theory. By formulating the theory in a moving frame of reference discretization errors in the final state are reduced at large recoil. Over the last years the formalism has been improved and tested extensively. Systematic uncertainties are reduced by renormalizing the m(oving)NRQCD action and heavy-light decay operators. The theory differs from QCD only for large loop momenta at the order of the lattice cutoff and the calculation can be carried out in perturbation theory as an expansion in the strong coupling constant. In this paper we calculate the one loop corrections to the heavy-light vector and tensor operator. Due to the complexity of the action the generation of lattice Feynman rules is automated and loop integrals are solved by the adaptive Monte Carlo integrator VEGAS. We discuss the infrared and ultraviolet divergences in the loop integrals both in the continuum and on the lattice. The light quarks are discretized in the ASQTad and highly improved staggered quark (HISQ) action; the formalism is easily extended to other quark actions.

Deep-inelastic scattering and the operator product expansion in lattice QCD

We discuss the determination of deep-inelastic hadron structure in lattice QCD. By using a fictitious heavy-quark, direct calculations of the Compton scattering tensor can be performed in Euclidean space that allow the extraction of the moments of structure functions. This overcomes issues of operator mixing and renormalization that have so far prohibited lattice computations of higher moments. This approach is especially suitable for the study of the twist-two contributions to isovector quark distributions, which is practical with current computing resources. While we focus on the isovector unpolarized distribution, our method is equally applicable to other quark distributions and to generalized parton distributions. By looking at matrix elements such as (where V{sup {mu}} and A{sup {nu}} are vector and axial-vector heavy-light currents) within the same formalism, moments of meson distribution amplitudes can also be extracted.

Erratum: Application of heavy-quark effective theory to lattice QCD. II. Radiative corrections to heavy-light currents [Phys. Rev. D65, 094513 (2002)

We apply heavy-quark effective theory to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this approach, the inverse heavy-quark mass and the lattice spacing are treated as short distances, and their effects are lumped into short-distance coefficients. We show how to use this formalism to match lattice gauge theory to continuum QCD, order by order in the heavy-quark expansion. In this paper, we focus on heavy-light currents. In particular, we obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of heavy-light decay constants, and heavy-to-light transition form factors. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.

Matching of the Heavy-Light Currents with NRQCD Heavy and Improved Naive Light Quarks

One-loop matching of heavy-light currents is carried out for a highly improved lattice action, including the effects of mixings with dimension 4 O ( 1 / M ) and O ( a ) operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive action for light quarks, and the Symanzik improved glue action. These results are being used in recent heavy meson decay constant and semileptonic form factor calculations on the MILC dynamical configurations.

One-loop matching of the heavy-lightA0andV0currents with nonrelativistic QCD heavy and improved naive light quarks

One-loop matching of heavy-light currents is carried out for a highly improved lattice action, including the effects of dimension 4 O(1/M) and O(a) operators. We use the NRQCD action for heavy quarks, the Asqtad improved naive action for light quarks, and the Symanzik improved glue action. As part of the matching procedure we also present results for the NRQCD self energy and for massless Asqtad quark wavefunction renormalization with improved glue.

Heavy-light meson semileptonic decays with staggered light quarks

We report on exploratory studies of heavy-light meson semileptonic decays using Asqtad light quarks, NRQCD heavy quarks and Symanzik improved glue on coarse quenched lattices. Oscillatory contributions to three-point correlators coming from the staggered light quarks are found to be handled well by Bayesian fitting methods. B meson decays to both the Goldstone pion and to one of the point-split non-Goldstone pions are investigated. One-loop perturbative matching of NRQCD/Asqtad heavy-light currents is incorporated.

Collinear effective theory at subleading order and its application to heavy-light currents

We consider a collinear effective theory of highly energetic quarks with energy E, interacting with collinear and soft gluons by integrating out collinear degrees of freedom to subleading order. The collinear effective theory offers a systematic expansion in power series of a small parameter $\ensuremath{\lambda}\ensuremath{\sim}{p}_{\ensuremath{\perp}}/E,$ where ${p}_{\ensuremath{\perp}}$ is the transverse momentum of a collinear particle. We construct the effective Lagrangian to first order in $\ensuremath{\lambda}$ and discuss its features, including additional symmetries such as collinear gauge invariance and reparametrization invariance. Heavy-light currents can be matched from the full theory onto the operators in the collinear effective theory at one loop and to order $\ensuremath{\lambda}.$ We obtain heavy-light current operators in the effective theory, calculate their Wilson coefficients at this order, and the renormalization group equations for the Wilson coefficients are solved. As an application, we calculate the form factors for decays of B mesons to light energetic mesons to order $\ensuremath{\lambda}$ and at leading-logarithmic order in ${\ensuremath{\alpha}}_{s}.$

Application of heavy-quark effective theory to lattice QCD. II. Radiative corrections to heavy-light currents

We apply heavy-quark effective theory to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this approach, the inverse heavy-quark mass and the lattice spacing are treated as short distances, and their effects are lumped into short-distance coefficients. We show how to use this formalism to match lattice gauge theory to continuum QCD, order by order in the heavy-quark expansion. In this paper, we focus on heavy-light currents. In particular, we obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of heavy-light decay constants, and heavy-to-light transition form factors. Results for the Brodsky-Lepage-Mackenzie scale ${q}^{*}$ are also given.

Application of heavy-quark effective theory to lattice QCD. III. Radiative corrections to heavy-heavy currents

We apply heavy-quark effective theory (HQET) to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this paper we focus on flavor-changing currents that mediate transitions from one heavy flavor to another. We stress differences in the formalism for heavy-light currents, which are discussed in a companion paper, showing how HQET provides a systematic matching procedure. We obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of zero-recoil form factors for the semileptonic decays $B\to D^{(*)}l\nu$. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.

Nonperturbative calculation of Z A/ Z V for heavy-light currents using Ward-Takahashi identity

We determine the ratio of renormalization factors of vector and axial-vector heavy-light currents. The calculation is performed nonperturbatively using the axial Ward-Takahashi identity for the heavy-light currents. We find that the effect of the O( a)-improvement of the heavy-light current is sizable in the strong coupling region g 2 0 > 0.9. Since the nonperturbative determination of its coefficient is not yet available, it leads to an error of order 10% in the nonperturbative determination of the ratio Z hl A / Z hl V . Our result for Z hl A / Z hl V is smaller than the one-loop evaluation, but the difference is within expected two-loop uncertainty.

One-loop renormalization of heavy-light currents

We calculate the mass dependent renormalization factors of heavy-light bilinears at one-loop order of perturbation theory, when the heavy quark is treated with the Fermilab formalism. We present numerical results for the Wilson and Sheikholeslami-Wohlert actions, with and without tree-level rotation. We find that in both cases our results smoothly interpolate from the static limit to the massless limit. We also calculate the mass dependent Brodsky-Lepage-Mackenzie scale q *, with and without tadpole-improvement.

O(a)-improved quark action on anisotropic lattices and perturbative renormalization of heavy-light currents

We investigate the Symanzik improvement of the Wilson quark action on anisotropic lattices. Taking first a general action with nearest-neighbor and clover interactions, we study the mass dependence of the ratio of the hopping parameters, the clover coefficients, and an improvement coefficient for heavy-light vector and axial vector currents. We show how tree-level improvement can be achieved. For a particular choice of the spatial Wilson coupling, the results simplify, and $O(m_0a_\tau)$ improvement is possible. (Here $m_0$ is the bare quark mass and $a_\tau$ the temporal lattice spacing.) With this choice we calculate the renormalization factors of heavy-light bilinear operators at one-loop order of perturbation theory employing the standard plaquette gauge action.

Comparison studies of finite momentum correlators on anisotropic and isotropic lattices

We study hadronic two- and three-point correlators relevant for heavy to light pseudoscalar meson semileptonic decays, using Symanzik improved glue, a D234 light quark, and nonrelativistic QCD heavy quark actions. Detailed comparisons are made between simulations on anisotropic and isotropic lattices involving finite momentum hadrons. We find evidence that having an anisotropy helps in extracting better signals at higher momenta. Initial results for the form factors f(+)(q(2)) and f(0)(q(2)) are presented with tree-level matching of the lattice heavy-light currents.

Scaling and further tests of heavy meson decay constant determinations from nonrelativistic QCD

We present results for the B_s meson decay constant f_{B_s} from simulations at three lattice spacings in the range a^{-1}=1.1 to 2.6 GeV using NRQCD heavy quarks and clover light quarks in the quenched approximation. We study scaling of this quantity and check the consistency between mesons decaying from rest and from a state with nonzero spatial momentum. The cancellation of power law contributions that arise in the NRQCD formulation of heavy-light currents is discussed. On the coarsest lattice the D_s meson decay constant f_{D_s} is calculated. Our best values for the decay constants are given by f_{B_s} = 187(4)(4)(11)(2)(7)(6) MeV and f_{D_s} = 223(6)(31)(38)(23)(9)(^{+3}_{-1}) MeV.

One-loop renormalization of the heavy-light currents in lattice QCD

One-loop renormalization of the heavy-light currents in lattice QCD