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Structure-dependent radiative corrections to $e^+ e^- \to π^+ π^- γ$ in the GVMD approach

Carlo M. Carloni Calame, Marco Ghilardi, Andrea Gurgone, Guido Montagna, Mauro Moretti, Oreste Nicrosini, Fulvio Piccinini, Francesco P. Ucci

Abstract

We compute the radiative corrections to the process of two-pion production in association with a hard photon in $e^+ e^-$ annihilation by taking into account the non-perturbative structure of the pion in the one-loop calculation. For this purpose, we adopt the generalised vector meson dominance model to insert the pion form factor in loop integrals for the treatment of final-state radiation and initial-final state interference at next-to-leading order. We compare our predictions with the results of the naive factorised scalar QED approach for experimentally relevant observables in the measurement of the $e^+ e^- \to π^+ π^- γ$ process. The computation extends previous results obtained for the energy scan process $e^+ e^- \to π^+ π^-$ and can be used to quantify the uncertainty due to the model describing the pion-photon interaction in radiative return experiments at flavour factories.

Structure-dependent radiative corrections to $e^+ e^- \to π^+ π^- γ$ in the GVMD approach

Abstract

We compute the radiative corrections to the process of two-pion production in association with a hard photon in annihilation by taking into account the non-perturbative structure of the pion in the one-loop calculation. For this purpose, we adopt the generalised vector meson dominance model to insert the pion form factor in loop integrals for the treatment of final-state radiation and initial-final state interference at next-to-leading order. We compare our predictions with the results of the naive factorised scalar QED approach for experimentally relevant observables in the measurement of the process. The computation extends previous results obtained for the energy scan process and can be used to quantify the uncertainty due to the model describing the pion-photon interaction in radiative return experiments at flavour factories.

Paper Structure

This paper contains 5 sections, 11 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. One-loop calculation in GVMD approach
  3. Numerical results
  4. Consistency checks
  5. Conclusions

Figures (7)

  • Figure 1: Topologies involved in the calculation of the structure-dependent corrections to $e^+e^-\to\pi^+\pi^-\gamma$. $1\gamma^*$ and $2\gamma^*$ refer to the number of virtual photons connecting initial-state and final-state charged legs, while ISR and FSR are related to the signal photon.
  • Figure 2: The differential cross section of the $e^+e^-\to\pi^+\pi^-\gamma$ process as a function of the invariant mass $M_{\pi\pi}$ in the four scenarios with the F$\times$sQED and GVMD approaches. The ${\rm K}^i_{\rm GVMD}$ factors shown in the lower panels are defined in Eq. \ref{['eq:Kfactor']}.
  • Figure 3: The same as in Fig. \ref{['fig:invmass']} for the differential cross section as a function of the $\theta^+$ scattering angle.
  • Figure 4: The forward-backward asymmetry of the $e^+ e^- \to \pi^+ \pi^- \gamma$ process in the KLOEI LA scenario. The absolute difference in the lower panel is defined in Eq. \ref{['eq:deltaa']}.
  • Figure 5: Differential cross section for the process $e^+e^-\to\pi^+\pi^-\gamma$ as a function of $\theta^+$ in the setup defined in Eq. \ref{['eq:setup_soft']}. In the middle panel, we show the relative difference as defined in Eq. \ref{['eq:deltafsqed']}, while the lower panel shows the ${\rm K}^{(2\gamma^*)}_{\rm GVMD}$ for the two different formulations discussed in the text.
  • ...and 2 more figures