Heavy-light Currents Research Articles

Perturbative matching of lattice and continuum heavy-light currents with NRQCD heavy quarks

The temporal and spatial components of the heavy-light vector current and the spatial components of the axial current are expressed in terms of lattice-regulated operators suitable for simulations of B and D mesons. The currents are constructed by matching the appropriate scattering amplitudes in continuum QCD and a lattice model to one-loop order in perturbation theory. In the lattice theory, the heavy quarks are treated using the nonrelativistic (NRQCD) formulation and the light quarks are described by the tadpole-improved clover action. The light quarks are treated as massless. Our currents include relativistic and discretization corrections through O(alpha_s/M, a alpha_s), where M is the heavy-quark mass, a is the lattice spacing, and alpha_s is the QCD coupling. As in our previous construction of the temporal component of the heavy-light axial current, mixing between several lattice operators is encountered at one-loop order, and O(a alpha_s) dimension-four improvement terms are identified.

Perturbative matching of heavy-light currents with NRQCD heavy quarks

We present further results for one-loop matching of heavy-light axial and vector currents between continuum QCD and a lattice theory with NRQCD heavy quarks and massless clover quarks.

Matching QCD and heavy-quark effective theory heavy-light currents at two loops and beyond.

Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}\gamma^{[\mu_1}\ldots\gamma^{\mu_n]}q$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on $\gamma_5$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}^2/\pi^2 +{\rm O}(\alpha_{\rm s}^3,1/m_b)$ is \[K_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c\] with $N_l=4$ light flavours, and a correction, $\Delta_c=0.18\pm0.01$, that takes account of the non--zero ratio $m_c/m_b=0.28\pm0.03$. Fastest apparent convergence would entail $\alpha_{\rm s}(\mu)$ at $\mu=370$~MeV. ``Naive non--abelianization'' of large--$N_l$ results, via $N_l\to N_l-\frac{33}{2}$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large $\beta_0=11-\frac23N_l$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.

Heavy-light meson studies with O(a)-improved massive quarks

We study heavy mesons using the Fermilab prescription for heavy quarks. We discuss technical issues important to the study of semileptonic form factors: a) We apply the multistate fitting technique to the selection of smearing functions for mesons with momentum in order to improve the signal for matrix elements. b) Momentum dependent discretization errors are investigated. We study heavy and light-meson energy dispersion relations and light-meson decay constants. c) As a guide to the study of heavy-light currents, we determine the flavor-conserving vector current renormalization. A study f m with heavy quarks including charm and bottom is presented. Attention is paid to discretization errors important in determining the 1 / m dependence of f m .

Short-distance expansion of heavy-light currents at order 1/mQ.

The short-distance expansion of the heavy-light currents $\overline{q}{\ensuremath{\gamma}}^{\ensuremath{\mu}}Q$ and $\overline{q}{\ensuremath{\gamma}}^{\ensuremath{\mu}}{\ensuremath{\gamma}}_{5}Q$ is constructed to order $\frac{1}{{m}_{Q}}$, and to next-to-leading order in renormalization-group-improved perturbation theory. It is shown that the 10 \ifmmode\times\else\texttimes\fi{} 10 anomalous dimension matrix, which describes the scale dependence of the dimension-four effective current operators in the heavy quark effective theory, is to a large extent determined by the equations of motion, heavy quark symmetry, and reparametrization invariance. The next-to-leading order expressions for the Wilson coefficients at order $\frac{1}{{m}_{Q}}$ depend on only five unknown two-loop anomalous dimensions, among them that of the chromomagnetic operator.

Spectral functions for heavy-light currents and form factor relations in HQET

We derive relations among form factors describing the current-induced transitions: ( vacuum) → B,B ∗, Bπ, B ∗π, Bϱ and B ∗ϱ using heavy quark symmetry. The results are compared to corresponding form factor relations following from identities between scalar and axial vector, and pseudoscalar and vector spectral functions in the heavy quark limit.