O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory

Abstract

We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schrödinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.

Parameters of heavy quark effective theory from N f = 2 lattice QCD

“…Thus we compute and show the continuum extrapolations in figure 2. They are done linearly in (a/L 1 ) 2 , which is justified by two reasons: (i) The quantity η 3 contains the time-component of the static axial current; we improve this current using the 1-loop value of ac stat A computed in [23]. This is sufficient since the improvement term has almost no numerical influence: even setting c stat A = 0 gives compatible results.…”

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

“…[56][57][58]. For the remaining improvement coefficients b φ and c φ , the situation is more difficult as there is no simple continuum physics condition to match onto: one would have to numerically study the continuum extrapolation of suitably chosen observables and tune the parameters to eliminate the linear dependence on a. Alternatively, the parameters could be computed in lattice perturbation theory, which has been done for the static quark theory using a few different lattice actions [50,[58][59][60][61][62][63] 4 .…”

HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation

“…Thus the by far dominating part of the result can be extrapolated quadratically in a and only a small correction has to be extrapolated linearly to the continuum limit. Since a non-perturbative determination of c stat A has not been carried out, we will here use its one-loop perturbative value [30]. We anyway carried out quadratic extrapolations in a and then studied the effect of incomplete improvement.…”

“…All parameters are given in lattice units a = 1, and for our standard choice of θ angles. As explained in the text, we give the HQET parameters and their covariance matrices for c stat A fixed to its one-loop value [30] and fixed to 0.…”