# Multi-quark matrix elements in the proton and three gluon exchange for exclusive $\eta_c$ production in photon-proton diffractive scattering

## TL;DR

This paper develops a theoretical framework for exclusive $ ext{eta}_c$ production in photon-proton scattering, analyzing multi-gluon exchanges and their relation to proton structure, with implications for experimental measurements of GPDs.

## Contribution

It formulates a high-energy dipole scattering approach for $ ext{eta}_c$ production, including new expressions for ${
m C}$-odd amplitudes and their relation to multi-quark correlators and GPDs.

## Key findings

- Single photon exchange dominates at low momentum transfer.
- Three gluon exchange becomes dominant at higher momentum transfer.
- Proposed models suggest measurable GPDs in specific kinematic regimes.

## Abstract

Exclusive production of a $\eta_c$ pseudo-scalar meson in $\gamma^{(*)} + p \to \eta_c + p$ scattering at high energies involves a ${\cal C}$-odd exchange in the $t$-channel. We formulate the description of this process within the high-energy framework of eikonal dipole scattering. We obtain expressions for the light-cone wave function of the $\eta_c$ required in this framework as well as for the ${\cal C}$-odd amplitudes due to exchange of a single photon, of a photon plus two gluons, and of three gluons. We relate these amplitudes to correlators of the $+$ component of the quark current in the light-cone wave function of the proton. For high transverse momenta these correlators correspond to Generalized Parton Distributions (GPDs) given by diagrams where all exchanged gauge bosons attach to a single quark in the proton. Diagrams involving multi-quark matrix elements potentially sensitive to correlations, screen infrared singularities. Moreover, they are numerically important for configurations where the exchanged bosons nearly share the total momentum transfer. Using two simple models for the three quark Fock state of the proton at $x\simeq0.1$, we find that single photon exchange dominates for $|t|<1.5$~GeV$^2$. Here, the quark GPD could be measured cleanly in $\gamma^{(*)} + p \to \eta_c + p$ via single photon exchange. For higher momentum transfer three gluon (`Odderon') exchange is dominant.