Forward inclusive dijet production and azimuthal correlations in pA collisions

TL;DR

The paper develops a first-principles framework for forward inclusive dijet production in dilute-hadron–dense-target collisions within the Color Glass Condensate, including multiple scatterings and small-x evolution via the BK equation. It derives the qT -> qgX cross-section in terms of 2-, 4-, and 6-point Wilson-line correlators and expresses target averages using a Gaussian CGC with BK evolution, ultimately obtaining a compact all-twist formula involving an unintegrated gluon distribution F_{x_A} and x_A-dependent functions G_{x_A}, H_{x_A}, and I^{λ}_{αβ}. The formalism is applied to azimuthal correlations in forward hadron production (hT -> h1h2X), revealing a partial suppression and broadening of the away-side Δφ peak as x_A decreases, with stronger effects at LHC energies. Limitations include the omission of gluon-initiated dijet channels at high energy and the need to handle higher-point correlators for complete phenomenology, motivating future extensions that couple CGC evolution with additional small-x dynamics.

Abstract

We derive forward inclusive dijet production in the scattering of a dilute hadron off an arbitrary dense target, whose partons with small fraction of momentum x are described by a Color Glass Condensate. Both multiple scattering and non-linear QCD evolution at small-x are included. This is of relevance for measurements of two-particle correlations in the proton direction of proton-nucleus collisions at RHIC and LHC energies. The azimuthal angle distribution is peaked back to back and broadens as the momenta of the measured particles gets closer to the saturation scale.

Figures (4)

• Figure 1: Inclusive quark-gluon production cross-section in the high-energy scattering of a quark off a Color Glass Condensate. $p\!=\!(p^+,p_\perp):$ momentum of the incoming quark; $q\!=\!(q^+,q_\perp)$ and $k\!=\!(k^+,k_\perp):$ momentum of the outgoing quark and gluon. The vertical wavy lines represent the interaction with the target CGC, each line carries a factor $g_S{\cal A}$ and multiple gluon exchanges must be resummed. The black points represent the emission of the produced gluon by the quark, it is emitted before the interaction or after the interaction in which case the contribution comes with a minus sign, as explained in the text.
• Figure 2: Left plot: the dimensionless unintegrated gluon distribution $\Delta^2\ F_{x_A}(\Delta)$ as a function of $\Delta^2$ (see formula \ref{['funcF']}). Right plot: the dimensionless quantity $1\!-\!k_\perp\cdot G_{x_A}(k_\perp)$ as a function of $k_\perp^2$ (see formula \ref{['nomass']}, in the massless case). The curve for $x_A\!=\!x_0\!=\!0.01$ is obtained from the MV initial condition \ref{['mvmod']}. The evolution towards smaller values of $x_A$ is obtained with the BK equation \ref{['bk']}, and is shown over 6 units of $\ln(x_0/x_A).$
• Figure 3: The $\Delta\phi$ spectrum \ref{['obs']} in two situations for the RHIC energy $\sqrt{s}\!=\!200\ \hbox{GeV/nucleon}.$ Fig.3a: $p_{T_1}\!=\!3.5\ \hbox{GeV},$$p_{T_2}\!=\!2\ \hbox{GeV},$$y_1\!=\!3.5$ and $y_2$ is varied from $1.5$ to $2.5.$ Fig.3b: $p_{T_1}\!=\!5\ \hbox{GeV},$$y_1\!=\!3.5,$$y_2\!=\!2$ and $p_{T_2}$ is varied $1.5\ \hbox{GeV}$ to $3\ \hbox{GeV}.$ In both cases, the correlation in azimuthal angle is suppressed as the value of $x_A$ probed in the process decreases. Varying $p_{T_2}$ at fixed $y_2$ is much more efficient as the ratio $p_{T_2}/Q_s$ varies over a larger range.
• Figure 4: The $\Delta\phi$ spectrum \ref{['obs']} in the two situations studied in Fig.3, but for the LHC energy $\sqrt{s}\!=\!5.5\ \hbox{TeV/nucleon},$ resulting in probing much smaller values of $x_A.$ In both cases, the correlation in azimuthal angle varies as a function of $y_2$ and $p_{T_2}$ as in Fig.3, but globally the azimuthal correlation is more suppressed (see the vertical axis) and the peak is less pronounced.