Roy-Steiner equations for $γγ\toππ$

Details Roy-Steiner equations for $γγ\toππ$ Roy-Steiner equations for $γγ\toππ$

2011-08-24

arxiv.org/abs/1108.4776v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

Talk given at the XIV International Conference on Hadron Spectroscopy (hadron2011), June 2011, Munich; 5 pages, 1 figure

Scientific paper

Starting from hyperbolic dispersion relations, we present a system of Roy--Steiner equations for pion Compton scattering that respects analyticity and unitarity requirements, gauge invariance, as well as crossing symmetry, and thus all symmetries of the underlying quantum field theory. To suppress the dependence on the high-energy region, we also consider once- and twice-subtracted versions of the equations, where the subtraction constants are identified with dipole and quadrupole pion polarizabilities. We consider the resolution of the $\gamma\gamma\to\pi\pi$ partial waves by a Muskhelishvili-Omn\`es representation with finite matching point, and discuss the consequences for the two-photon coupling of the $\sigma$ resonance as well as its relation to pion polarizabilities.

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