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

Abstract

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.

D and B leptonic decay constants from lattice QCD

“…We have since extended this calculation to two additional ensembles at our finest lattice spacing a ≈ 0.09 fm and we have replaced a limited set of very coarse (a ≈ 0.18 fm) ensembles with higher statistic ensembles at a somewhat finer spacing a ≈ 0.15 fm. In our last update [4] we reported: f D + = 207(11) and f D s = 249 (11), where f D s is about 0.6σ lower than the recent experimental average [5]. The value of f D s remains an pressing issue given that experimental average is about 2.1σ higher than the most precise lattice result from the HPQCD collaboration [6].…”

“…At tree-level, discretization effects arise from both the quark action and the (improved) current [10,11,12]. We add five extra terms to Equation 2.2:…”

$B^0$-$\bar{B}^0$ mixing with Fermilab heavy quarks

“…The enumeration of the operators Q i , and further operators of dimension 8, is an easy extension of Ref. [6]. In perturbation theory C (S) (δC (S) and the B i ) start at tree (one-loop) level, but they could also be determined nonperturbatively, adapting schemes such as that of Ref.…”

“…At present they are being checked by an additional author. As with currents [6,7], it may prove prudent to write 14) where Z V bb and Z V qq are nonperturbatively determined matching factors for the vector current. The remaining factor ρ (S) could have a tamer perturbative expansion, because of cancellation among diagrams.…”

“…The calculations of the 4-quark operator matrix elements described below thus have discretization errors of the form 16) where the mass dependence of the B (S)i is an Ansatz with the correct asymptotic behavior as m 0 → ∞ and as m 0 a → 0 for the Fermilab action. The functions f (m 0 a) multiplying the O(a 2 ) discretization effects are known [6,9], for the Fermilab action.…”