Exclusive photoproduction of a di-meson pair with large invariant mass

TL;DR

This work analyzes exclusive photoproduction of a di-meson pair in the framework of collinear factorisation, focusing on the γN → N' M1M2 channel with M1,M2 as pions or rhos and in a kinematic regime where the di-meson invariant mass is large. The authors develop a fully automated approach to compute the leading-twist, leading-order amplitude, factorising it into a perturbative hard part and non-perturbative Generalised Parton Distributions (GPDs) and Distribution Amplitudes (DAs), with GPDs modeled via Radyushkin's Double Distribution Ansatz and DAs taken in their asymptotic form. They generate and classify thousands of diagrams, map them onto GPD/DA structures, and perform a robust numerical integration over $x$, $v$, and $z$ using partial fractions and the Sokhotski–Plemelj formula, including a folding procedure to avoid spurious divergences. Numerical results for $S_{\gamma N}=20$ GeV$^2$ and $M_{12}^2=3$ GeV$^2$ show sizeable fully differential cross sections, illustrating the potential of these exclusive $2\to 3$ channels for accessing both chiral-even and chiral-odd GPDs and guiding future experimental explorations at JLab, LHC UPC, and the EIC.

Abstract

We consider the exclusive photoproduction of a di-meson pair with large invariant mass, $γN \rightarrow N' M_1M_2$, in the framework of collinear factorisation. The mesons considered $M_1$ and $M_2$ are either pions or rho mesons, charged or neutral. We consider the kinematic regime characterised by a large invariant mass of the two-meson system, and a small deflection of the nucleon in the centre-of-mass frame. In this kinematic domain, the amplitude factorises into a perturbative hard part and non-perturbative parts described by Generalised Parton Distributions (GPDs) and Distribution Amplitudes (DAs). We automate the calculation of the fully differential cross section at leading twist and leading order, and we present some numerical results at JLab 12 GeV kinematics. This class of processes provides yet more exclusive $2 \to 3$ channels that can be used to extract GPDs.

Figures (5)

• Figure 1: The projection of a diagram obtained with FeynArts and FeynCalc onto the GPD and DAs.
• Figure 2: Five ways of connecting the fermion lines, giving five topologies. The unmarked blobs correspond to places where the internal gluons and/or incoming photon could attach to.
• Figure 3: Fully differential cross section as a function of $-u'$ for the photoproduction of $\pi^-\rho^0_L$ (top-left), $\pi^-\rho^0_T$ (top-right), $\pi^+\rho^0_L$ (bottom-left) and $\pi^+\rho^0_T$ (bottom-right) at $S_{\gamma N}= 20GeV^2$ and $M^2_{12}=3GeV^2$.
• Figure 4: Fully differential cross sections as a function of $-u'$ for the photoproduction of $\pi^0\rho^+_L$ (top-left), $\pi^0\rho^+_T$ (top-right), $\pi^0\rho^-_L$ (bottom-left) and $\pi^0\rho^-_T$ (bottom-right) at $S_{\gamma N}= 20GeV^2$ and $M^2_{12}=3GeV^2$.
• Figure 5: Fully differential cross sections for the photoproduction of $\rho^0_L\rho^0_L$ (top-left), $\rho^0_T\rho^0_T$ (top-right) and $\pi^0\pi^0$ (bottom) on a proton target at $S_{\gamma N}= 20GeV^2$ and $M^2_{12}=3GeV^2$. For the two first processes, the range of $-u'$ has been extended beyond the kinematically allowed range (given the cuts $-u'>1 \;\hbox{GeV}^2$ and $-t'>1 \;\hbox{GeV}^2$, see main text) in order to observe the reflection symmetry of the cross section about the line $-u' = M_{12}^2/2$.