Hard bremsstrahlung for the production of prompt photons

TL;DR

This work addresses the calculation of hard bremsstrahlung contributions to prompt photon production in polarized proton collisions relevant to the NICA program. It develops analytical helicity amplitudes for $\bar{q}q \to g\gamma$ and $qg \to q\gamma$ using the spinor formalism and field-strength bivectors $\mathbf{F}_i$, implemented within the SANC framework with crossing symmetry to cover photon and gluon emission channels. Numerical validation for the $\bar{c}c$ channel at $\sqrt{s}=24$,$91$,$500$ GeV shows agreement with CalcHEP and WHIZARD to 3–5 digits and reveals helicity-dependent suppression patterns as energy increases. The results advance one-loop radiative correction studies for polarized prompt photon production and will be integrated into the ReneSANCe generator for NICA analyses.

Abstract

The analytical calculation of helicity amplitudes for hard photon and gluon bremsstrahlung radiation are described using the spinor formalism for processes of the type $\bar{q} q \to g γ$ and $q g \to q γ$. The presented amplitudes are expressed in terms of field strength bivectors, with allowance for the dependence on the helicities and masses of all particles. Numerical calculations have been performed for the quark-antiquark annihilation process $\bar{c}c$ at the center-of-mass energies of 24, 91, and 500 GeV, considering various combinations of helicities of the quarks and the photon in the final state. This study is part of the ongoing development of theoretical support, based on the SANC system, for the analysis of polarized observables in proton collisions at the NICA collider.

Figures (11)

• Figure 1: One of the diagrams of process (\ref{['zero']}). The indices c and a correspond to different gluons, while j and k denote the color of the antiquark and quark. The vertex indices are $\alpha$, $\beta$, and $\mu$.
• Figure 2: A subset of diagrams for the process with bremsstrahlung gluon emission, or the complete set of diagrams for process (\ref{['zero']}) with bremsstrahlung photon emission $g(p_{5},\chi_{5})\to \gamma(p_{5},\chi_{5})$.
• Figure 3: Diagrams with a three-gluon vertex for process (\ref{['zero']}) with bremsstrahlung gluon emission.
• Figure 4: Differential cross section distributions of process (\ref{['ccA']}) in femtobarns as a function of the photon pseudorapidity, $\eta_{\gamma}$, at a center-of-mass energy of 24 GeV for the helicity combination $\chi_{1} = +$, $\chi_{2} = +$, and photon helicity $\chi_{4} = \pm$. $R$ denotes ReneSANCe and $W$ denotes WHIZARD.
• Figure 5: Differential cross section distributions of process (\ref{['ccA']}) in femtobarns as a function of the photon scattering angle cosine, $\cos\theta_{\gamma}$, at a center-of-mass energy of 24 GeV for the helicity combination $\chi_{1} = +$, $\chi_{2} = +$, and photon helicity $\chi_{4} = \pm$. $R$ denotes ReneSANCe and $W$ denotes WHIZARD.