Radiative corrections to neutral pion-pair production

N. Kaiser

doi:10.1140/epja/i2010-11050-9

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2023 Impact factor 2.6

Hadrons and Nuclei

Eur. Phys. J. A (2010) 46: 373-378
https://doi.org/10.1140/epja/i2010-11050-9

Regular Article - Theoretical Physics

Radiative corrections to neutral pion-pair production

N. Kaiser^*

Physik-Department T39, Technische Universität München, D-85747, Garching, Germany

^* e-mail: nkaiser@ph.tum.de

Received: 4 August 2010
Accepted: 30 September 2010
Published online: 30 October 2010

Abstract

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $\pi^-\gamma \ensuremath \rightarrow\pi^-\pi^0\pi^0$ . At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral $\pi^{+}_{}$ $\pi^{-}_{}$ $\rightarrow$ $\pi^{0}_{}$ $\pi^{0}_{}$ 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 $\ensuremath R\sim \alpha/2\pi$ 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 $\ensuremath 7m_{\pi}$ . We study also the radiative corrections to the $\ensuremath \pi^0\pi^0$ mass spectrum.