Pion Polarizabilities from $\gamma\gamma\to\pi\pi$ Analysis

TL;DR

This paper predicts pion polarizabilities using dispersion relations based on amplitude analysis of photon-induced meson pair production data, emphasizing the need for precise cross-section measurements to confirm and refine these fundamental properties.

Contribution

The study provides stable predictions for pion polarizabilities and highlights the importance of targeted experiments to improve measurement accuracy, especially for the neutral pion.

Findings

Helicity-zero polarizabilities are stable and insensitive to uncertainties.

Precise cross-section measurements are crucial for confirming charged pion polarizability results.

The neutral pion's $( ext{alpha}_1- ext{beta}_1)$ is estimated as $(-0.9 extpm0.2) imes 10^{-4}$ fm$^3$.

Abstract

We present results for pion polarizabilities predicted using dispersion relations from our earlier Amplitude Analysis of world data on two photon production of meson pairs. The helicity-zero polarizabilities are rather stable and insensitive to uncertainties in cross-channel exchanges. The need is first to confirm the recent result on $(\alpha_1-\beta_1)$ for the charged pion by COMPASS at CERN to an accuracy of 10\% by measuring the $\gamma\gamma\to\pi^+\pi^-$ cross-section to an uncertainty of ~1\%. Then the same polarizability, but for the $\pi^0$, is fixed to be $(\alpha_1-\beta_1)_{\pi^0}=(-0.9\pm0.2)\times 10^{-4}$ fm$^{3}$. By analyzing the correlation between uncertainties in the meson polarizability and those in $\gamma\gamma$ cross-sections, we suggest experiments need to measure these cross-sections between $\sqrt{s}\simeq 350$ and 600 MeV. The $\pi^0\pi^0$ cross-section then makes the $(\alpha_2-\beta_2)_{\pi^0}$ the easiest helicity-two polarizability to determine.