  We compute the matrix elements of the electromagnetic (EM) operator (\bar{s}
F{\mu \nu} \sigma{\mu \nu} d) between kaon and pion states, using lattice QCD
with maximally twisted-mass fermions and two flavors of dynamical quarks (Nf =
2). The operator is renormalized non-perturbatively in the RI'/MOM scheme and
our simulations cover pion masses as light as 270 MeV and three values of the
lattice spacing from ~ 0.07 up to ~ 0.1 fm. At the physical point our result
for the corresponding tensor form factor at zero-momentum transfer is
fT{K\pi}(0) = 0.417 (14_stat) (5_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 fT{K\pi}(0) = 0.78 (6)
obtained by the SPQcdR 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 fT{\pi\pi}(0) = 0.195 (8_stat) (6_syst) in good
agreement with, but more accurate than the result fT{\pi\pi}(0) = 0.216 (34)
obtained by the QCDSF Collaboration using higher pion masses.
