Deeply virtual meson production at HERA and at the EIC within the Color Glass Condensate EFT

Abstract

Continuing our previous study of Deeply Virtual Meson Production (DVMP) at twist-3 accuracy, we derive compact expressions for all helicity amplitudes. We perform a phenomenological analysis of the helicity-amplitude ratio $\mathcal{A}^{11}/\mathcal{A}^{00}$ and of the spin-density matrix element $r_{00}^{04}$ within the Color Glass Condensate framework. Small-$x$ evolution is incorporated by numerically solving the running-coupling-and-collinearly-improved Balitsky-Kovchegov and Balitsky-Fadin-Kuraev-Lipatov equations with the McLerran-Venugopalan model as the initial condition. By capturing a relevant subset of next-to-leading order corrections, we provide the most theoretically accurate description of these observables to date. Our results are compared to HERA data, and predictions are presented for electron-lead collisions at the future Electron-Ion Collider. We discuss the impact of non-linear effects at low photon virtuality and the role of genuine higher-twist contributions associated with light vector meson distribution amplitudes, corresponding to higher-Fock-state components of the projectile.

Figures (4)

• Figure 1: Predictions for the helicity-amplitude ratio $R_{11}$ (left) and for the spin-density matrix element $r_{00}^{04}$ (right), as a function of $Q^2$ at fixed $W=100$ GeV, are compared to the data of H1 Aaron:2009xp. The red curves denote predictions obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the non-linear BK evolution. The dashed and dashed-dot blue lines are both obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the linear BFKL evolution; the dashed-dot one is rescaled by a constant factor in order to match the BK prediction at high $Q^2$. The error bands around the non-linear prediction show only the uncertainty due to the non-perturbative parameters of the DAs.
• Figure 2: Predictions for the helicity amplitudes ratio $R_{11}$ (left) and for the spin-density matrix element $r_{00}^{04}$ (right), as a function of $Q^2$ at fixed $W=100$ GeV, are compared to the data of H1 Aaron:2009xp. Both curves are obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the non-linear BK evolution. The error bands around the non-linear prediction show only the uncertainty due to the non-perturbative parameters of the DAs.
• Figure 3: Predictions for the helicity amplitudes ratio $R_{11}$ (left) and for the spin-density matrix element $r_{00}^{04}$ (right), as a function of $Q^2$ at fixed $W=140$ GeV. The red curves denote the predictions obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the non-linear BK evolution. The dashed-dot blue line is obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the linear BFKL evolution and by rescaling a constant factor to match the BK prediction at high $Q^2$. The error bands around the non-linear prediction show only the uncertainty due to the non-perturbative parameters of the DAs.
• Figure 4: Predictions for the helicity amplitudes r atio $R_{11}$ (left) and for the spin-density matrix element $r_{00}^{04}$ (right), as a function of $W$ for different values of $Q^2$: 1.3 GeV$^2$, 3 GeV$^2$ and 15 GeV$^2$. The red curves denote the predictions obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the non-linear BK evolution. The dashed-dot blue line is obtained by evolving the initial condition in eq. (\ref{['Eq:MV']}) through the linear BFKL evolution and by rescaling a constant factor to match the BK prediction at high $Q^2$. The error bands around the non-linear prediction show only the uncertainty due to the non-perturbative parameters of the DAs.