Non-perturbative results for the coefficients b and b−b in O(a) improved lattice QCD

Abstract

We determine the improvement coefficients b m and b A − b P in quenched lattice QCD for a range of β-values, which is relevant for current large scale simulations. At fixed β, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g 2 0 . Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.

Modified instanton profile effects from lattice Green functions

“…We calibrate all these simulations with the ratios of lattice spacings for different β's given in ref. [18] and a…”

“…18 It is in fact a matter of power reduction because kρ > 1 in the most and more numerically relevant part of the fitting interval, for ρ = 1.5 GeV −1 . This may be due to: (i) the strong correlation of our lattice estimates of the coupling for the different momenta, all computed from the same set of gauge field configurations 19 ; (ii) the small number of points in our fitting window (only 3 for 5.8(24 4 )).…”

“…Coefficients in [18] are fitted for β = 6/g 2 ≥ 6. In this work, we make use of rather low values β < 6.0, in order to have larger volumes.…”

Towards a non-perturbative matching of HQET and QCD with dynamical light quarks

“…This is achieved by exploiting the O(a) improved relation between the (subtracted) bare heavy quark mass m q,h and the RGI mass [20,27], viz.…”

Decays of mesons with charm quarks on the lattice

“…The nonperturbatively determinated value of b m is taken from Ref. [4]. As a measure for the heavy quark masses we use the mass of the heavy-light meson, where the light quark mass is extrapolated to the average of the u and d quark mass.…”