$B_{K}$ is a parameter which is related with the Kaon mixing and is one of the targets of Lattice QCD. Naive calculation of $B_{K}$ with the Wilson fermion is difficult because the chiral symmetry is explicitly broken. In this talk we shall present on our calculation of $B_{K}$ with the Wilson fermion by applying the gradient flow method both to the gauge and quark fields. Our study is based o ... More

We compute, up to order $g^4$ in perturbation theory, the fermionic contribution to the strong coupling $\alpha_{qq}$ extracted from the static force in Lattice QCD. To this aim, we calculate perturbatively Wilson loops using a simplified version of QCD: a SU(3) gauge theory coupled to two degenerate quarks. In particular, we have considered the following discretization: Wilson's plaquette ga ... More

We study the effective theory of decoupling of a charm quark at low energies. We do this by simulating a model, QCD with two mass-degenerate charm quarks. At leading order the effective theory is a pure gauge theory. We compare the mass dependence of hadronic scales to the prediction based on perturbative matching of the gauge couplings. By computing ratios of hadronic scales we have direct acces ... More

We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using the stochastic approach. The spectral density at relatively high eigenvalues can be used to extract the mass anomalous dimension. We use 2+1-flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings (a=0.083, 0.055, 0.044 fm) to estimate the continuum limit. The discretization ef ... More

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining transition, the gradient flow, and the cooling flow to set the scale. Of those, the cooling flow turns out to be computationally most efficient. We explore systematic errors due to use of three different energy observables and two distinct reference values for the flow ... More

It has been shown that the choice of renormalization scheme is crucial for four-quark operators, in particular for neutral kaon mixing beyond the standard model. In the context of SMOM schemes the choice of projector is not unique, it is part of the definition of the renormalisation scheme. I will present the non-diagonal Fierz relations which relate some projectors which differ by their Dira ... More

We upload a summary that allows participants to write their proceeding contribution starting from a template tex file.

We present results for the strong coupling constant ($alpha_s$) and the charm quark mass ($m_c$) obtained from the moments of pseudoscalar current-current correlators. Our calculation employs the four flavor (2+1+1) HISQ ensembles generated by the MILC collaboration with six lattice spacings, including five with physical light-quark masses. We improve upon earlier calculations by including in our ... More

We present our preliminary results of the non perturbative determination of the valence mass dependent coefficients $b_A-b_P$ and $b_m$ (as well as the ratio ${Z_P/}{(Z_S Z_A)}$) entering the flavour non singlet PCAC relation in lattice QCD with $N_f=3$ dynamical flavours. We apply the method proposed in the past for quenched approximation and $N_f=2$ case, employing a set of finite-volume ALP ... More

We report on non-perturbative computations of the improvement coefficient $c_{\rm V}$ and the renormalization factor $Z_{\rm V}$ of the vector current in three-flavour O($a$) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the ... More

We report on progress in our programme of non-perturbative improvement and renormalization of operators composed of Wilson fermions based on correlators in position space. We concentrate on the CLS $N_f=2+1$ ensembles. We discuss an updated determination of $b_J$ and $\tilde{b}_J$ improvement coefficients. We introduce a new strategy for non-perturbative renormalization which alleviates the wind ... More

We present our studies of renormalization constants of non-singlet overlap quark bilinear opertors on 2+1-flavor domain wall configurations. The renormalization is performed in RI/MOM and RI/SMOM schemes. We compute the scale-independent renormalization constant for the axial vector current via the Ward identity both in the two schemes and obtain other RCs from $Z_A$. We compare the difference ... More

We present our result for the strong coupling constant computed from the u-d vector Hadronic Vacuum Polarisation function. We use nf=2+1 flavours of Domain Wall fermions at 3 lattice spacings, generated by the RBC-UKQCD collaboration. We identify several possible pitfalls in this method for determining the coupling and illustrate how to resolve them.