Lattice QCD determination of the normalization of the leading-twist photon distribution amplitude and susceptibility of the quark condensate

Abstract

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 $J_{\mathrm{em}}^{\mu }$ 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 $f_{\gamma }^{\perp }(2\mathrm{GeV})$ 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 $f_{\gamma ,s}^{\perp }(2\mathrm{GeV})$, 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 ${\chi }_d^{\overline{\mathrm{MS}}}(2\mathrm{GeV})\simeq {\chi }_u^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=2.17(12)\mathrm{Ge}{\mathrm{V}}^{-2}$.

Comments: 16 pages, 5 figures, 4 tables