Radiative corrections to the charged pion-pair production process {\boldmath$π^-γ\to π^+π^-π^-$} at low energies

N. Kaiser; S. Petschauer

doi:10.1140/epja/i2013-13159-7

paper

Radiative corrections to the charged pion-pair production process {\boldmath $π^{-} γ \to π^{+} π^{-} π^{-}$ } at low energies

arXiv:1312.0517 · doi:10.1140/epja/i2013-13159-7

Abstract

We calculate the one-photon loop radiative corrections to the charged pion-pair production process $π^{-} γ \to π^{+} π^{-} π^{-}$ . In the low-energy region this reaction is governed by the chiral pion-pion interaction. The pertinent set of 42 irreducible photon-loop diagrams is calculated by using the package FeynCalc. Electromagnetic counterterms with two independent low-energy constants $k_{1}$ and $k_{2}$ are included in order to remove the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved by including soft photon radiation below an energy cut-off $λ$ . The purely electromagnetic interaction of the charged pions mediated by one-photon exchange is also taken into account. The radiative corrections to the total cross section (in the isospin limit) vary between $+ 10%$ close to threshold and about $- 1%$ at a center-of-mass energy of $7 m_{π}$ . The largest contribution comes from the simple one-photon exchange. Radiative corrections to the $π^{+} π^{-}$ and $π^{-} π^{-}$ mass spectra are studied as well. The Coulomb singularity of the final-state interaction produces a kink in the dipion mass spectra. The virtual radiative corrections to elastic $π^{-} π^{-}$ scattering are derived additionally.

19 pages, 17 figures, accepted for publication in Eur. Phys. J. A

Radiative corrections to the charged pion-pair production process {\boldmathπ−γ→π+π−π−} at low energies

Abstract

References in corpus (13)

Radiative corrections to the charged pion-pair production process {\boldmath $π^{-} γ \to π^{+} π^{-} π^{-}$ } at low energies