Radiative corrections to neutral pion-pair production

TL;DR

This paper calculates one-photon loop radiative corrections to neutral pion-pair production, providing analytical expressions and analyzing their impact on the total cross section with implications for precision measurements.

Contribution

It offers the first detailed analytical calculation of radiative corrections for this specific pion production process, including the effects of counterterms and infrared finiteness.

Findings

Radiative corrections vary between +2% and -2% across energies.

An electromagnetic counterterm adds about 1% with large uncertainty.

Corrections are significant for precise experimental comparisons.

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.