Matrix elements of the electromagnetic operator between kaon and pion states

Abstract

We compute the matrix elements of the electromagnetic operator $\overline{s}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\sigma}}^{\ensuremath{\mu}\ensuremath{\nu}}d$ between kaon and pion states, using lattice QCD with maximally twisted-mass fermions and two flavors of dynamical quarks (${N}_{f}=2$). The operator is renormalized nonperturbatively in the RI'/MOM scheme and our simulations cover pion masses as light as 270 MeV and three values of the lattice spacing from $\ensuremath{\simeq}0.07$ up to $\ensuremath{\simeq}0.1\text{ }\text{ }\mathrm{fm}$. At the physical point our result for the corresponding tensor form factor at zero-momentum transfer is ${f}_{T}^{K\ensuremath{\pi}}(0)=0.417({14}_{\mathrm{stat}})({5}_{\mathrm{syst}})$, where the systematic error does not include the effect of quenching the strange and charm quarks. Our result differs significantly from the old quenched result ${f}_{T}^{K\ensuremath{\pi}}(0)=0.78(6)$ obtained by the ${\mathrm{SPQ}}_{\mathrm{cd}}\mathrm{R}$ Collaboration with pion masses above 500 MeV. We investigate the source of this difference and conclude that it is mainly related to the chiral extrapolation. We also study the tensor charge of the pion and obtain the value ${f}_{T}^{\ensuremath{\pi}\ensuremath{\pi}}(0)=0.195({8}_{\mathrm{stat}})({6}_{\mathrm{syst}})$ in good agreement with, but more accurate than the result ${f}_{T}^{\ensuremath{\pi}\ensuremath{\pi}}(0)=0.216(34)$ obtained by the QCDSF Collaboration using higher pion masses.