1302.2431 (T. N. Pham)

Pion as a Longitudinal Axial-Vector Meson $q\bar{q}$ Bound State    [PDF]

T. N. Pham

The success of the Adler-Bell-Jackiw(ABJ) chiral anomaly prediction for $\pi^{0}\to \gamma\gamma$ decay rate shows that non-anomaly terms would make a negligible contribution to the decay rate, in agreement with the Sutherland-Veltman theorem. Thus the conventional $q\bar{q}$ bound-state description of the pion could not be valid since it would produce a $\pi^{0}\to \gamma\gamma$ decay amplitude not suppressed in the soft pion limit, in contradiction with the Sutherland-Veltman theorem. Therefore, if the pion is to be treated as a $q\bar{q}$ bound state, this bound state would be a longitudinal axial-vector meson. In this paper, we consider the pion to be a longitudinal axial-vector meson $q\bar{q}$ state with derivative coupling for the pion-$q\bar{q}$ Bethe-Salpeter(BS) amplitude. We shall show that, the longitudinal axial-vector meson solution for the pion $q\bar{q}$ Bethe-Salpeter wave function could produce a suppressed $\pi^{0}\to \gamma\gamma$ decay amplitude in the soft pion limit, in agreement with the Sutherland-Veltman theorem.

View original: http://arxiv.org/abs/1302.2431