Non-perturbative determination of improvement coefficients using coordinate space correlators in $N_f=2+1$ lattice QCD

Understand

We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space.

• We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $\beta=3.4,3.46,3.55$ and $\beta=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm.
• We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determining the $\bar{b}_J$ coefficients which are proportional to the trace of the quark mass matrix.