https://doi.org/10.1140/epjc/s10052-015-3359-z
Regular Article - Theoretical Physics
On some aspects of isospin breaking in the decay
1
Groupe de Physique Théorique, Institut de Physique Nucléaire Bât. 100, CNRS/IN2P3/Univ. Paris-Sud 11 (UMR 8608), 91405, Orsay Cedex, France
2
Laboratoire de Physique Théorique, CNRS/Univ. Paris-Sud 11 (UMR 8627), 91405, Orsay Cedex, France
3
Centre de Physique Théorique, UMR 7332, Aix-Marseille Univ./CNRS/Univ. du Sud Toulon-Var, CNRS-Luminy Case 907, 13288, Marseille Cedex 9, France
* e-mail: knecht@cpt.univ-mrs.fr
Received:
30
January
2015
Accepted:
13
March
2015
Published online:
9
April
2015
Two aspects of isospin breaking in the decay are studied and discussed. The first addresses the possible influence of the phenomenological description of the unitarity cusp on the extraction of the normalization of the form factor from data. Using the scalar form factor of the pion as a theoretical laboratory, we find that this determination is robust under variations of the phenomenological parameterizations of the form factor. The second aspect concerns the issue of radiative corrections. We compute the radiative corrections to the total decay rate for
in a setting that allows comparison with the way radiative corrections were handled in the channel
. We find that, once radiative corrections are included, the normalizations of the form factor as determined experimentally from data in the two decay channels come to a better agreement. The remaining discrepancy can easily be accounted for by other isospin-breaking corrections, mainly those due to the difference between the masses of the up and down quarks.
© SIF and Springer-Verlag Berlin Heidelberg, 2015