The normalization of the leading-twist photon distribution amplitude (DA), $f_{ \gamma}^{ \perp}$, is an important ingredient in the study of exclusive processes involving the photon emission by means of QCD sum-rules. In this paper we determine the up- , down- and strange-quark contribution to $f_{ \gamma}^{ \perp}$ by exploiting its relation to the zero-momentum two-point correlation function of the electromagnetic current $J_{ \rm em}^{ \mu}$ and the electric component of the tensor current $T^{ \mu\nu}$. To that end we employ the gauge ensembles obtained by using $N_{ f}=2+1+1$ Wilson-Clover twisted-mass quark flavors, generated by the Extended Twisted Mass (ETM) Collaboration, and after adding all sources of systematic uncertainties, we obtain a total error of $1.5\%$ and $3.5\%$, respectively, for the light- ($u$ and $d$) and strange-quark contribution to $f_{ \gamma}^{ \perp}(2~{ \rm GeV})$ in the $\overline{ \mathrm{ MS}}$ scheme, thus improving their accuracy by a factor of $2.3$ and $2.8$, respectively. For the strange-quark contribution $f_{ \gamma,s}^{ \perp}(2~{ \rm GeV})$, we observe a discrepancy with respect to previous lattice calculations. By combining our result with the world average lattice value of the chiral condensate, we obtain for the susceptibility of the quark condensate $\chi_d^{ \overline{ \mathrm{ MS}}} (2\, { \rm GeV}) \simeq \chi_u^{ \overline{ \mathrm{ MS}}} (2\, { \rm GeV}) =2.17(12)~{ \rm GeV^{ -2}}$.
Categories: hep-lat hep-ph