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Description
We present a calculation of the scalar, vector, and tensor form factors for the pion and kaon in lattice QCD. We use two ensembles of maximally twisted mass fermions with clover improvement with two degenerate light, a strange, and a charm quark $(N_f=2+1+1)$ at lattice spacings of 0.093 fm and 0.081 fm. The pion mass of the ensembles is about 250-260 MeV. The excited-states effects are studied by analyzing six values of the source-sink time separation for the rest frame (1.12 − 2.23 fm) and for four values for the boosted frame (1.12 − 1.67 fm). The lattice data are renormalized non-perturbatively and the results for the scheme- and scale-dependent scalar and tensor form factors are presented in the MS scheme at a scale of 2 GeV. We apply different parametrizations to describe $q^2$-dependence of the form factors to extract the scalar, vector and tensor radii, as well as the tensor anomalous magnetic moment. We compare the pion and kaon form factors to study SU(3) flavor symmetry breaking effects. By combining the data for the vector and tensor form factors, we also obtain the lowest moment of the densities of transversely polarized quarks in the impact parameter space. We give an estimate for the average transverse shift in the y direction for polarized quarks in the x direction. We compare all these results across both ensembles for analysis of discretization effects.
