Radiative corrections to pion Compton scattering

Abstract

We calculate the one-photon loop radiative corrections to charged pion Compton scattering, $\pi^- \gamma \to \pi^- \gamma $. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Analytical expressions for the ${\cal O}(\alpha)$ corrections to the invariant Compton scattering amplitudes, $A(s,u)$ and $B(s,u)$, are presented for 11 classes of contributing one-loop diagrams. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy threshold $\lambda$, and its relation to the experimental detection threshold is discussed. We find that the radiative corrections are maximal in backward directions, reaching e.g. -2.4% for a center-of-mass energy of $\sqrt{s}=4m_\pi$ and $\lambda=5 $MeV. Furthermore, we extend our calculation of the radiative corrections by including the leading pion structure effect (at low energies) in form of its electric and magnetic polarizability difference, $\alpha_\pi - \beta_\pi \simeq 6\cdot 10^{-4} $fm$^3$. We find that this structure effect does not change the relative size and angular dependence of the radiative corrections to pion Compton scattering. Our results are particularly relevant for analyzing the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.Comment: 14 pages, 5 figure

Measurement of the Charged-Pion Polarizability

“…2 as a function of x γ . The simulated cross section dσ 0 πγ =dx γ contains, besides the Born term, the following corrections: (i) radiative corrections [11]; (ii) chiral loop corrections [12]; (iii) corrections for the electromagnetic form factor of the nickel nucleus, which is approximated for simplicity by the equivalent sharp-radius formula FðQ 2 Þ ¼ j 1 ðrqÞ with r ¼ 5.0 fm, where q is the modulus of the 3-momenta transfer to the nucleus. More precise form-factor parametrizations were checked with no visible influence on the results.…”

Chiral Dynamics and the Pion Polarisability at COMPASS

“…Radiative corrections have been applied on the level of the simulation event-wise, starting from the published calculations [5,6] for the case of pion and muon Compton scattering, respectively, and extrapolating to the Primakoff kinematics at Q 2 = 0. The small difference between the corrections for pion and muon stem from their spin-0 and spin-1 2 nature, respectively.…”

“…figure). For the pion, there are more graphs due to the additional point-couplings in case of a spin-0 particle [5]. The lower graphs (from [5,6]) show the radiative corrections, to be employed as multiplicative factor to the non-radiative process, for different CM-energies in the region of interest for the pion polarisability measurement.…”

Isospin breaking in pion Compton scattering

“…The consistent theoretical framework to extract the pion polarizabilities from the measured cross-sections for (low-energy) pion Compton scattering π − γ → π − γ or the primary pion-nucleus bremsstrahlung process π − Z → π − Zγ has been described (in one-loop approximation) in refs. [12,13]. It has been stressed that at the same order as the polarizability difference α π − β π there exists a further (partly compensating) pion structure effect in form of a unique pion-loop correction (interpretable as photon scattering off the "pion-cloud around the pion").…”

“…In addition to these strong interaction effects, the QED radiative corrections to real and virtual pion Compton scattering π − γ ( * ) → π − γ have been calculated in refs. [13,14]. The relative smallness of the pion structure effects in low-energy pion Compton scattering [12] makes it necessary to include such higher-order electromagnetic corrections.…”