Inelastic photoproduction of polarised $J/ψ$

TL;DR

This work analyzes inelastic J/psi photoproduction within the NRQCD framework, focusing on the full polar and azimuthal decay angular distributions to distinguish colour-singlet and colour-octet production mechanisms across kinematic variables z and p_t. It combines direct and resolved photon contributions and employs a density-matrix formalism to connect short-distance production to long-distance NRQCD matrix elements. The study finds that colour-octet channels can dominate certain regions but predict a strong high-z peak not supported by data, while the azimuthal coefficient nu provides a robust discriminant between production mechanisms; endpoint-region effects require resummation/shape-function treatment. The results offer concrete observables for upcoming HERA measurements to test NRQCD factorisation and constrain colour-octet matrix elements in photoproduction.

Abstract

The comparison of $J/ψ$ photoproduction data in the inelastic region with theoretical predictions based on the NRQCD approach has remained somewhat ambiguous and controversial, in particular at large values of the inelasticity variable $z$. We study the polar and azimuthal decay angular distribution of $J/ψ$ mesons as functions of $z$ and transverse momentum $p_t$. Future measurements of decay angular distributions at the HERA $ep$ collider will provide a new test of theoretical approaches to factorisation between perturbation theory and quarkonium bound-state dynamics and shed light on the colour-octet production fraction in various regions of $z$ and $p_t$.

Figures (8)

• Figure 1: Colour-singlet (CS) and colour-octet (CO) contributions due to direct and resolved photons to the $J/\psi$ energy distribution $d\sigma/dz$ at the photon--proton centre-of-mass energy $\sqrt{s_{\gamma p}} =100\,$GeV in comparison with HERA data H1ZEUSinelastic averaged over the specified range of $\sqrt{s_{\gamma p}}$. The shaded area bounded by the solid lines represents the sum of all contributions according to scenarios I and II for the colour-octet matrix elements. The lines corresponding to separate colour-octet contributions are plotted for $\langle {\cal O}_8^{J/\psi}(^1\!S_0)\rangle= \langle {\cal O}_8^{J/\psi}(^3\!P_0)\rangle/m_c^2=0.008\,\hbox{GeV}^3$. The colour-singlet cross section is evaluated in leading order in $\alpha_s$. Other parameters: $m_c=1.5\,$GeV, renormalisation/factorisation scale $\mu=2 m_c$, GRV LO proton and photon parton distributions GRV, $\Lambda^{(4)}_{LO}=200\,$MeV.
• Figure 2: Colour-singlet (CS) and colour-octet (CO) contributions due to direct and resolved photons to the $J/\psi$ transverse momentum distribution $d\sigma/dp_t$ at the photon--proton centre-of-mass energy $\sqrt{s_{\gamma p}} =100\,$GeV; $z$ is integrated to its upper kinematic limit. Other specifications are as in Figure \ref{['sigmaz']}.
• Figure 3: Angular parameter $\lambda$ of the decay angular distribution as a function of $z$. Direct and resolved photons are included. The dashed line is the colour-singlet model prediction. The shaded area shows the NRQCD prediction bounded by the choice of parameters according to scenarios I and II. Other parameters are as in Figure \ref{['sigmaz']}.
• Figure 4: Angular parameter $\mu$ of the decay angular distribution as a function of $z$. Direct and resolved photons are included. The dashed line is the colour-singlet model prediction. The shaded area shows the NRQCD prediction bounded by the choice of parameters according to scenarios I and II. Other parameters are as in Figure \ref{['sigmaz']}.
• Figure 5: Angular parameter $\nu$ of the decay angular distribution as a function of $z$. Direct and resolved photons are included. The dashed line is the colour-singlet model prediction. The shaded area shows the NRQCD prediction bounded by the choice of parameters according to scenarios I and II. Other parameters are as in Figure \ref{['sigmaz']}.