Studies of low energy $l+p\to l+p+γ$ process in covariant chiral perturbation theory

TL;DR

The paper develops a covariant Chiral Perturbation Theory framework to compute the tree-level amplitudes for $l p \to l p \gamma$ including hard photon emission, using the nucleon-pion Lagrangians up to $O(p^3)$. It presents Bethe-Heitler and Virtual Compton Scattering contributions with full lepton-mass dependence, derives the corresponding amplitudes, and fits the low-energy constants to JLab Hall A data, finding that $O(p^3)$ improvements are necessary to achieve a reasonable description. However, the high-$Q^2$ region accessed by the data lies outside the formal validity of standard \chi PT, indicating possible sizable effects from resonances and vector mesons and motivating future extensions. The work also analyzes radiative corrections for low-energy $lp$ scattering with massive leptons, providing predictions for muon-proton scattering relevant to the MUSE experiment and highlighting the importance of lepton-mass effects on differential cross sections and the radiative tail.

Abstract

This study presents a tree-level calculation of the scattering amplitude for the $lp\to lpγ$ (with a hard photon) process within the framework of Chiral Perturbation Theory. Our calculations, based on the $O(p^2)$ and $O(p^3)$ nucleon-pion Lagrangians, aim to provide a theoretical prediction for the differential cross-section. The result shows that explicit inclusion of the nonzero lepton mass significantly influences the low energy differential cross section for $μp\to μp γ$ process. The kinematic region of the present experimental data is beyond the validity domain of the $χ$PT and is therefore not suitable for determining the low-energy constants (LECs). By comparing our results with future experimental data, we expect to determine the values of the LECs as a further test of $χ$PT as an effective low-energy theory of QCD. The process is of significant interest as it can help to determine the generalized polarizabilities of the nucleon.

Figures (12)

• Figure 1: The $\gamma p$ interaction vertex for $e p\to e p\gamma$ up to $O(p^3)$.
• Figure 2: The $e p\to e p\gamma$ process.
• Figure 4: Definition of azimuthal angles for the $ep\to ep \gamma$ process in the target rest frame.
• Figure 5: Global fit results for all data sets from defurne2015e00.The data are displayed sequentially according to Tables VII, VIII, XII, and XIII of Ref. defurne2015e00, reading the columns of each table from left to right.
• Figure 6: Contour plots displaying the kinematic dependence of the momentum transfer $t$ (left panel) and the virtuality $Q^2$ (right panel) on the scattered lepton polar angle $\theta_{k_2}$ and the photon polar angle $\theta_\gamma$. The calculations are performed at an incident beam energy of $E_{\text{beam}} = 0.4\,\text{GeV}$ with a fixed photon energy $E_\gamma = 0.1\,\text{GeV}$ and azimuthal angle $\phi_\gamma = 50^\circ$.