Improved dispersion relations for γγ\to π^0π^0
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We perform a dispersive theoretical study of the reaction γγ\to pi^0π^0 emphasizing the low energy region. The large source of theoretical uncertainty to calculate the γγ\toπ^0π^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 γγ\toπ^0π^0 available one might then distinguish between different parameterizations of the ππisoscalar S-wave. We also elaborate on the width of the σresonance to γγand provide new values.
10 pages, 5 figures. Extended discussion on the width of the sigma to gamma gamma
10 pages, 5 figures. Extended discussion on the width of the sigma to gamma gamma