Improved dispersion relations for γγ→π0π0

We perform a dispersive theoretical study of the reaction γγ→π0π0 emphasizing the low energy region. The large source of theoretical uncertainty to calculate the γγ→π0π0 total cross section for s≳0.5GeV 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 f0(980) region. This allows us to make sharper predictions for the cross section for s≲0.8GeV, below the onset of D-wave contributions. In this way, were new more precise data on γγ→π0π0 available one might then distinguish between different parameterizations of the ππ isoscalar S-wave. We also elaborate on the width of the σ resonance to γγ and provide new values.