Isospin breaking in $K\to3\pi$ decays II: radiative corrections

Abstract

The five different CP conserving amplitudes for the decays K → 3π are calculated using Chiral Perturbation Theory. The calculation is made to next-to-leading order and includes full isospin breaking. The squared amplitudes are compared with the corresponding ones in the isospin limit to estimate the size of the isospin breaking effects. In this paper we add the radiative corrections to the earlier calculated m u −m d and local electromagnetic effects. We find corrections of order 5-10 percent.

Radiative corrections in K→π ℓ + ℓ − decays

“…[22][23][24] are performed in the framework of Chiral Perturbation Theory. Such a framework is not suited to an extraction of the ππ scattering lengths from experimental data, as these do not appear directly as parameters of the theory.…”

“…Furthermore, the effects corresponding to our corrections of O(e 2 a) that modify the analytic structure of the cusp are beyond the accuracy considered in Refs. [22][23][24] and are not considered there.…”

“…Our work is not the first one to consider radiative corrections to K → 3π decays -recent examples include Refs. [22][23][24][25][26][27]. Whereas Isidori's article [25] fits into the framework considered here, the calculations of Refs.…”

“…Whereas Isidori's article [25] fits into the framework considered here, the calculations of Refs. [22][23][24] are of a wider scope and not useful to extract ππ scattering lengths with high precision by use of the approach proposed in Ref. [3], a framework also adapted here.…”

Measurement ofηmeson decays into lepton-antilepton pairs

“…The decays were studied theoretically already 40 years ago by Jarlskog and Pilkhun [8] assuming a FF equal to one. The effect of the FF on the BR is expected to be less than 10% for the decay η → e + e − e + e − [11]. For decays with µ + µ − pair(s) the influence is larger since only large q 2 values are probed.…”