Radiative corrections to neutral pion-pair production

Abstract

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process ${\pi }^{-}\gamma \to {\pi }^{-}{\pi }^0{\pi }^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral ${\pi }^{+}{\pi }^{-}\to {\pi }^0{\pi }^0$ contact-vertex depends only on the final-state invariant-mass it factors out of all photon-loop diagrams. We give analytical expressions for the multiplicative correction factor $R\sim \alpha /2\pi$ arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. The radiative corrections to the total cross section vary between $+2\%$ and $-2\%$ for center-of-mass energies from threshold up to $7m_{\pi }$. The finite part of the electromagnetic counterterm gives an additional constant contribution of about $1\%$, however with a large uncertainty.

arXiv comment10 pages, 6 figures, submitted to Eur. Phys. J. A

References in corpus (14)

• ππscattering
• The COMPASS Experiment at CERN
• Observation of a J^PC = 1-+ exotic resonance in diffractive dissociation of 190 GeV/c pi- into pi- pi- pi+
• Virtual Photons in Low Energy pi-pi Scattering
• High statistics measurement of Ke4 decay properties
• Revisiting γγ->π^+π^- at low energies
• Measurement of the pi^+ meson polarizabilities via the gamma p->gamma pi^+ n reaction
• Determination of the S-wave pi pi scattering lengths from a study of K+- -> pi+- pi0 pi0 decays
• Cross sections for low-energy ${\pi }^{-}\gamma$ reactions
• Electromagnetic corrections to gamma pi(+) -> pi(0) pi(+)
• The anomalous process gamma pi -> pi pi to two loops
• Chiral corrections to ${\pi }^{-}\gamma \to 3\pi$ processes at low energies
• Radiative corrections to pion Compton scattering
• Radiative corrections to pion-nucleus bremsstrahlung

Cited by in corpus (2)

• First Measurement of Chiral Dynamics in π^- γ-> π^- π^- π^+
• Radiative corrections to the charged pion-pair production process {\boldmath${\pi }^{-}\gamma \to {\pi }^{+}{\pi }^{-}{\pi }^{-}$} at low energies