Prompt photon-jet angular correlations at central rapidities in $p+A$ collisions

Photon-jet azimuthal correlations in proton-nucleus collisions are a promising tool for gaining information on the gluon distribution of the nucleus in the regime of nonlinear color fields. We compute such correlations from the process $g\to q\overline{q}\gamma$ in the rapidity regime where both the projectile and target light-cone momentum fractions are small. By integrating over the phase space of the quark which emits the photon, subject to the restriction that the photon picks up most of the transverse momentum (to pass an isolation cut), we effectively obtain a $g+A\to q\gamma$ process. For nearly back-to-back photon-jet configurations we find that it dominates over the leading-order process $q+A\to q\gamma$ by two less powers of $Q_{\perp }/Q_S$, where ${\mathit{Q}}_{\perp }$ and $Q_S$ denote the net photon-jet pair momentum and the saturation scale of the nucleus, respectively. We determine the transverse-momentum-dependent gluon distributions involved in $g+A\to q\gamma$ and the scale where they are evaluated. Finally, we provide analytic expressions for $⟨\cos n\varphi ⟩$ moments, where $\varphi$ is the angle between ${\mathit{Q}}_{\perp }$ and the average photon-jet transverse momentum ${\tilde{\mathit{P}}}_{\perp }$, and first qualitative estimates of their transverse momentum dependence.

Figure 1

Example for a LO diagram for photon production in the high-energy limit. The blob contains multiple (eikonal) scatterings on the dense target with momentum exchange $k$. The complete LO contribution includes photon emission before the interaction with the nucleus (not shown).

Figure 2

Examples for NLO diagrams for photon production in the high-energy limit. In the left diagram the gluon from the proton emits a $q\overline{q}$ pair which then scatters on the dense nucleus. In the right diagram the gluon scatters on the nucleus and then produces a $q\overline{q}$ pair and a photon. The complete NLO contribution includes diagrams where the photon is emitted from the antiquark line, or from a virtual quark-antiquark state (not shown) in the case of single-inclusive photon production.

Figure 3

$a_1$ for $g\to q\gamma$ to order $Q_{\perp }^2/{\tilde{P}}_{\perp }^2$ for the MV model with two different saturation scales. We take $Q_{\perp }/{\tilde{P}}_{\perp }=0.1$, $z=3/4$ and $\zeta =1$.

Figure 4

$a_2$ for $g\to q\gamma$ to order $Q_{\perp }^2/{\tilde{P}}_{\perp }^2$ for the MV model with two different saturation scales. We take $Q_{\perp }/{\tilde{P}}_{\perp }=0.1$, $z=3/4$ and $\zeta =1$.

Figure 5

$a_1$ for $g\to q\gamma$ to order $Q_{\perp }^2/{\tilde{P}}_{\perp }^2$ as a function of the photon isolation cut for the MV model with two different saturation scales. We take $Q_{\perp }/{\tilde{P}}_{\perp }=0.1$, ${\tilde{P}}_{\perp }=15Q_S$ and $\zeta =1$.