Pion Transition Form Factor in Lattice QCD

Abstract

We investigate the neutral pion transition form factor $F_{π^0γ^\astγ^\ast}(q_1^2,q_2^2)$ in lattice QCD and confirm that the connected and disconnected contributions have the same sign. We employ the recently proposed blending method, which supplies an unbiased and cheap estimators for the required all-to-all propagators. The external pion states are treated within the distillation framework, while the electromagnetic currents are evaluated in the full blending space. Numerical tests are performed on an $N_f=2+1$ lattice ensemble. Our result shows that the contribution of the disconnected part is approximately $1\%$ of that of the connected part and enables constructive interference of probability amplitudes.