On the Pion Distribution Amplitude Shape

TL;DR

This paper argues that recent experimental data supports a flat pion distribution amplitude shape, which has significant implications for theoretical models and other hard exclusive processes in particle physics.

Contribution

It proposes that the pion distribution amplitude is close to unity with a flat shape, challenging the standard Gegenbauer expansion and suggesting new endpoint behaviors based on chiral models.

Findings

BaBar data supports a flat pion DA shape.

Flat pion DA implies divergence in Gegenbauer expansion.

Two-pion DA exhibits anomalous endpoint behavior for S-wave.

Abstract

We argue that the recent BaBar data on $\gamma \to \pi$ e.m. transition form factor at large photon virtuality supports the idea that pion distribution amplitude (DA) is close to unity with $\phi_\pi^\prime(0)/6\gg 1$ at a normalization point of $\mu=0.6\div 0.8$ GeV. Such pion DA can be obtained in the effective chiral quark model. The possible flat shape of the pion DA implies that the standard expansion of the DA in Gegenbauer polynomials can be divergent. On basis of chiral models we predict that the two-pion DA should exhibit anomalous endpoint behaviour for pions in the S-wave and that such feature is absent for higher partial waves. The latter implies that the $\rho, f_2$, etc. meson DAs have no anomalous endpoint behaviour. Possible implications of such pion DA for other hard exclusive processes are shortly discussed.