Dispersive construction of two-loop P->3π(P=K,η) amplitudes

Abstract

The branching ratio of the η->3πdecay is an important source of information on the value of the quark mass ratio 1/R=(m_d-m_u)/(m_s-\hat m). Furthermore, isospin breaking effects in the decays K->3πprovide information on the pion scattering lengths. The cusp effect in the K->3πdecays is presently being analyzed by the NA48 and KTeV experiments. From the theoretical point of view, these processes have been studied by different methods. We propose a unified and relativistic treatment relying on very general principles, unitarity, analyticity and crossing symmetry, combined with chiral counting, in order to construct model-independent representations of the corresponding amplitudes that are valid at two loops. A general description of the procedure is given and is illustrated in the case of the ηdecay amplitude in the leading order in the isospin breaking.

Talk given at "International Workshop on Effective Field Theories: from the pion to the upsilon", February 2009, Valencia, Spain. 8 pages. PoS style