Abstract
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.
Highlights
Terms of order 1/m2 in the effective theory
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
Since the ALPHA strategy consists of matching in a finite volume with Schrodinger functional boundary conditions, the size of different terms in the expansion is given in terms of z−n = (Lm)−n with L the linear extent of the finite volume
Summary
We are interested in matrix elements MQCD(L, m) = Xud, L|Jνub(x)|Xbd, L , of the QCD heavy-light current operators which correspond to the classical field (2.1). The renormalization factors ZJ of the flavor currents are to be chosen such that the currents satisfy the chiral Ward identities [18, 19]. (MQCD)(1)(z) z→∼∞ H(1) − γ0 log(z)H(0) , γ0 = −1/(4π2) , z = Lm This limit of QCD is described by an effective field theory, HQET. Chiral Ward identities fix the relative normalization of the static vector and axial vector currents but not the overall normalization. When we set μ = m, they are equal to the corresponding QCD matrix elements up to higher order terms in 1/m, MQJνCD(L, m) = CJmνatch(g2(m)) MsJtνat(L, m) + O(1/m) , and up to the finite renormalization factor (2.10). The renormalization of the fields and in particular BJν are independent of the states in eq (2.1)
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