Isospin breaking in decays I: strong isospin breaking

Abstract

The CP conserving amplitudes for the decays K → 3π are calculated in Chiral Perturbation Theory. The calculation is made at the next-to-leading order including strong and local electromagnetic isospin breaking. A comparison is made between the squared amplitudes with and without isospin violation to estimate the size of the effect. We find corrections of order five percent in the amplitudes.

Dispersive construction of two-loop P→πππ(P=K,η) amplitudes

“…From the theoretical point of view, this process is also covered by the chiral perturbation theory computations up to NLO presented in Refs. [21][22][23][24].…”

Facets of chiral perturbation theory

“…The two basic couplings of the leading-order nonleptonic chiral Lagrangian L ∆S=1 G F p 2 (2), usually called G 8 , G 27 , are by now well established from studies of the dominant nonleptonic L chiral order (# of LECs) loop order kaon decays K → 2π, 3π up to NLO, including isospin-violating and radiative corrections [10,11,12,13,14,15]. [16,17].…”

Pion-pion scattering and the K→3π decay amplitudes

“…Rescattering effects in K → 3π decays have already been widely discussed in the literature in the framework of CHPT (see e.g. reference [9,10,11]). However, most of these analyses have been performed only up to the first non-trivial order in the chiral expansion (with the exception of reference [10], where the imaginary parts of the amplitudes are analysed up to the next-to-leading order) and ignoring isospin-breaking effects (with the exception of reference [11]).…”

“…reference [9,10,11]). However, most of these analyses have been performed only up to the first non-trivial order in the chiral expansion (with the exception of reference [10], where the imaginary parts of the amplitudes are analysed up to the next-to-leading order) and ignoring isospin-breaking effects (with the exception of reference [11]). The approach presented in this paper differs from these previous works being more focused on the cusp effect and, in this respect, being more general than ordinary CHPT calculations: we shall use the effective field theory only for an explicit estimate of the irreducible 3π → 3π rescattering (that turns out to be negligible).…”