Dispersive construction of two-loop P->3\pi (P=K,\eta) amplitudes
Abstract
The branching ratio of the \eta->3\pi decay 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->3\pi provide information on the pion scattering lengths. The cusp effect in the K->3\pi decays 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 \eta decay amplitude in the leading order in the isospin breaking.
Cite
@article{arxiv.0905.4868,
title = {Dispersive construction of two-loop P->3\pi (P=K,\eta) amplitudes},
author = {M. Zdrahal and K. Kampf and M. Knecht and J. Novotny},
journal= {arXiv preprint arXiv:0905.4868},
year = {2011}
}
Comments
Talk given at "International Workshop on Effective Field Theories: from the pion to the upsilon", February 2009, Valencia, Spain. 8 pages. PoS style