Photon-jet ridge at RHIC and the LHC

We investigate long-range rapidity correlations of pairs of prompt photons and jets in the color glass condensate framework in proton-proton and proton-nucleus collisions at RHIC and the LHC. We show that photon-jet correlations exhibit long-range azimuthal collimation at the near side for low transverse momenta of the produced photon and jet in high-multiplicity events. These ridge-like features are strikingly similar to the observed ridge effect for dihadron correlations at RHIC and the LHC. We show that correlations in the relative rapidity and the relative azimuthal angle between pairs of prompt photons and jets strongly depend on the gluon saturation dynamics at small-$x$ kinematics and such measurements can help to understand the true origin of the observed dihadron ridge in $p+A$ collisions, and address whether the ridge is a universal phenomenon for all two-particle correlations at high-energy and high-multiplicity events. We also investigate whether there is a ridge-like structure for photon-hadron pair correlations at RHIC and the LHC. We find that the hadronization of jets has nontrivial effects on the photon-jet correlations.

Figure 1

Transverse momentum dependence of photon-jet azimuthal correlations $CP$ defined via the coincidence probability in Eq. (14) as a function of the angle between the photon and jet $\mathrm{\Delta }\varphi$ at fixed rapidities of the produced photon ${\eta }^{\gamma }=3$ and jet ${\eta }^{\text{jet}}=1$ (with $\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}=2$) at the RHIC energy 0.2 TeV. Transverse momentum bins of the triggered photon $p_T^{\text{trig}}$ and associated jet $p_T^{\text{asc}}$ are given in the plot. All results are obtained from the rcBK solutions with an initial saturation scale $Q_{0A}^2=15Q_{0p}^2$ (with $Q_{0p}^2=0.168{\mathrm{GeV}}^2$) corresponding to a high-multiplicity event in $p+p(A)$ collisions.

Figure 2

Left: Transverse momentum dependence of the function $p^2{N}_F(p_T,x_g)$ at a fixed $x_g={10}^{-4}$ for different initial saturation scales of nuclei. Right: The ratio of photon-jet to single prompt photon cross sections $r_2$ defined in Eq. (15) as a function of transverse momentum of the triggered photon or associated jet for $p_T^{\text{trig}}=p_T^{\text{asc}}$ with rapidity interval $\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}=3$ in $p+A$ collisions at th 5.02 TeV LHC. In both panels results are obtained from the rcBK solutions with different initial saturation scales $Q_{0A}^2=N_{\text{part}}^{\mathrm{Pb}}{Q}_{0p}^2$, with $N_{\text{part}}^{\mathrm{Pb}}=5$, 15, 20 and $Q_{0p}^2=0.168{\mathrm{GeV}}^2$.

Figure 3

Left: $\gamma$-jet correlations $CP(\mathrm{\Delta }\varphi )$ defined via the coincidence probability in Eq. (14) within two transverse momentum bins at two rapidity intervals $\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}=2$, 3 in $p+A$ collisions at RHIC. Right: Initial saturation scale $Q_{0A}$ dependence of $CP(\mathrm{\Delta }\varphi )$ in a fixed transverse momentum bin and rapidity interval $\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}=2$ (with ${\eta }^{\text{jet}}=1$) in $p+A$ collisions at RHIC. In the right panel, the results are obtained with the rcBK solutions with different initial saturation scales $Q_{0A}^2=N_{\text{part}}^{\mathrm{Pb}}{Q}_{0p}^2$, where $N_{\text{part}}^{\mathrm{Pb}}=5$, 15, 20 is the number of nucleon participants on the lead (or gold) side. In the left panel, all results are obtained with a fixed $N_{\text{part}}^{\mathrm{Pb}}=15$. The initial saturation scale of the proton is $Q_{0p}^2=0.168{\mathrm{GeV}}^2$.

Figure 4

Top left: Rapidity-interval $|\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}|$ dependence of the photon-jet azimuthal correlation $C_2(\mathrm{\Delta }\varphi )$ defined in Eq. (16) as a function of the angle between the produced photon and jet $\mathrm{\Delta }\varphi$ in $p+A$ collisions at 0.2 TeV. Top right: Initial saturation scale $Q_{0A}$ dependence (or multiplicity dependence) of $C_2(\mathrm{\Delta }\varphi )$ for a fixed rapidity interval $|\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}|=3$ at RHIC obtained from the rcBK solutions with different initial saturation scales $Q_{0A}^2=N_{\text{part}}^{\mathrm{Pb}}{Q}_{0p}^2$, with $N_{\text{part}}^{\mathrm{Pb}}=5$, 15, 20 and $Q_{0p}^2=0.168{\mathrm{GeV}}^2$. Lower: Energy dependence of $C_2(\mathrm{\Delta }\varphi )$ at a fixed rapidity interval $|\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}|=3$ at different energies (0.2, 5.02 and 63 TeV) in $p+A$ collisions. In the top left and lower panels all results are obtained with a fixed $N_{\text{part}}^{\mathrm{Pb}}=15$. In all panels, we take the transverse momenta of the produced photon and jet at $k_T=q_T=1\mathrm{GeV}$ and the rapidity of the produced jet at ${\eta }^{\text{jet}}=1$.

Figure 5

Left: Azimuthal photon-hadron ($\gamma -{\pi }^0$) correlation $C_2$ as a function of the angle between the produced hadron and prompt photon $\mathrm{\Delta }\varphi$ at two rapidity intervals of $\mathrm{\Delta }{\eta }^{\gamma -h}=-3$ (corresponding to ${\eta }^{\gamma }=1$ and ${\eta }^h=4$) and $\mathrm{\Delta }{\eta }^{\gamma -h}=3$ (corresponding to ${\eta }^{\gamma }=4$ and ${\eta }^h=1$) in $p+A$ collisions at RHIC. Right: Average total transverse momentum defined by $⟨p_T^{\text{total}}=|{\mathbf{k}}_T+{\mathbf{q}}_T^h/z_h|⟩$ at $\mathrm{\Delta }\varphi =0$ as a function of $\mathrm{\Delta }{\eta }^{\gamma -h}={\eta }^{\gamma }-{\eta }^h$ for two cases: with a fixed rapidity of the photon ${\eta }^{\gamma }=1$, and with a fixed rapidity of the hadron ${\eta }^h=1$. In both panels, the results are obtained from the rcBK evolution solutions assuming the initial saturation scale of the target to be $Q_{0A}^2=15Q_{0p}^2$, corresponding to a high-multiplicity event with the number of nucleon participants on the lead side of $N_{\text{part}}^{\mathrm{Pb}}=15$. In both panels, we take the transverse momenta of the produced photon and hadron at $k_T=q_T^h=1\mathrm{GeV}$.

Figure 6

Left: Rapidity-interval dependence of the photon-hadron azimuthal correlation $C_2(\mathrm{\Delta }\varphi )$ as a function of the angle between the produced photon and jet $\mathrm{\Delta }\varphi$ in $p+A$ collisions at 0.2 TeV. Right: Initial saturation scale $Q_{0A}$ dependence (or multiplicity dependence) of the photon-hadron $C_2(\mathrm{\Delta }\varphi )$ at a fixed rapidity interval $\mathrm{\Delta }{\eta }^{\gamma -\text{jet}}=-3$ in $p+A$ collisions at 0.2 TeV, obtained from the rcBK solutions with different initial saturation scales $Q_{0A}^2=N_{\text{part}}^{\mathrm{Pb}}{Q}_{0p}^2$, with $N_{\text{part}}^{\mathrm{Pb}}=5$, 15, 20 and $Q_{0p}^2=0.168{\mathrm{GeV}}^2$. In the left panel the results are obtained with a fixed $N_{\text{part}}^{\mathrm{Pb}}=15$. In both panels, we take the transverse momenta of the produced photon and hadron at $k_T=q_T^h=1\mathrm{GeV}$ and the rapidity of the hadron at ${\eta }^h=1$.