Improved dispersion relations for \gamma\gamma\to \pi^0\pi^0

TL;DR

This paper refines dispersive theoretical predictions for the  o  reaction at low energies by reducing uncertainties through additional subtractions and constraints, enabling more precise cross section estimates and  width determinations.

Contribution

It introduces an extra subtraction in dispersion relations with new low energy constraints, improving the accuracy of  o  predictions and  resonance width estimates.

Findings

Reduced theoretical uncertainty in cross section calculations.

Sharper predictions for energies below 0.8 GeV.

New estimates for the  resonance width.

Abstract

We perform a dispersive theoretical study of the reaction \gamma\gamma\to pi^0\pi^0 emphasizing the low energy region. The large source of theoretical uncertainty to calculate the \gamma\gamma\to\pi^0\pi^0 total cross section for \sqrt{s}\gtrsim 0.5 GeV within the dispersive approach is removed. This is accomplished by taking one more subtraction in the dispersion relations, where the extra subtraction constant is fixed by considering new low energy constraints, one of them further refined by taking into consideration the f_0(980) region. This allows us to make sharper predictions for the cross section for \sqrt{s}\lesssim 0.8 GeV, below the onset of D-wave contributions. In this way, were new more precise data on \gamma\gamma\to\pi^0\pi^0 available one might then distinguish between different parameterizations of the \pi\pi isoscalar S-wave. We also elaborate on the width of the \sigma resonance to \gamma\gamma and provide new values.