Hadron production in pA collisions at the LHC from the Color Glass Condensate

TL;DR

This paper addresses how saturation physics in the Color Glass Condensate controls hadron production in proton-nucleus collisions at high energies. It develops a hybrid formalism that includes both elastic and inelastic contributions to single inclusive hadron production, with dipole amplitudes evolved via the running-coupling BK equation from MV initial conditions. The authors show that inelastic terms steepen the mid-rapidity $p_T$ spectra and raise $R_{pA}$ with $p_T$, while being small at forward rapidity, and they provide LHC predictions that are sensitive to the initial saturation scales $Q_{0s}$ and to $\alpha_s$ in the inelastic piece. Forward-rapidity measurements at the LHC are identified as robust tests of gluon saturation and can constrain low-$x$ dynamics, reducing theoretical uncertainties in CGC-based predictions.

Abstract

We investigate the contribution of inelastic and elastic processes to single inclusive hadron production in proton-proton and proton (deuteron)-nucleus collisions at RHIC and the LHC. Using the hybrid formulation which includes both elastic and inelastic contributions, supplemented with the running-coupling Balitsky-Kovchegov equation, we get a good description of RHIC data. It is shown that inclusion of the inelastic terms makes the transverse momentum dependence of the production cross section steeper in the mid-rapidity region but does not affect the cross section in the very forward region. The inelastic processes also lead to a sharper increase of the nuclear modification factor R_{pA} with increasing p_T. We also make predictions for the nuclear modification factor in proton-nucleus collisions at the LHC (\sqrt{s}=4.4 and 8.8 TeV) at various rapidities using the Color Glass Condensate framework.

Figures (5)

• Figure 1: Single inclusive hadron production in proton-proton (upper panel) and deuteron-gold (lower panel) collisions at different pseudo-rapidities at RHIC obtained by the solution of the running-coupling BK equation, the so-called rcBK (right) and the DHJ (left) dipole model. Right: dashed and full lines refer to the results coming from the rcBK equation corresponding to two different initial values for the saturation scale at $x_0=0.01$. We have taken $\alpha_s=0.1$ in Eq. (\ref{['final']}) for all curves. Left: dashed and full lines refers to the results when $\alpha_s=0$ (the DHJ term or the elastic contribution) and $\alpha_s=0.1$ (for the inelastic term), respectively. We have taken $K=1$ in all panels. The experimental data are from Ref. exp.
• Figure 2: Right: nuclear modification factor $R_{pA}$ for inclusive charged hadrons $h^{+}+h^{-}$ production at the LHC $\sqrt{s}=4.4$ TeV and $\eta=4$ coming from the solutions of the rcBK with different initial values for the saturation scale (at $x_0=0.01$) for proton and nucleus. The dashed and full lines refer to the cases when the cross-section in both pp and pA collisions was obtained via Eq. (\ref{['final']}) by taking $\alpha_s=0$ (only elastic contribution) and $\alpha_s=0.1$ respectively. Left: the scaled unintegrated gluon distribution $N_A(x,p_T) \times p_T^4$ as a function of transverse momentum $p_T$ at a fixed $x=10^{-5}$ obtained from the rcBK equation with two different initial values for the saturation scale $Q_{0s} (x_0=0.01)$.
• Figure 3: Nuclear modification factor $R_{pA}$ for $h^{+}+h^{-}$ production in proton-nucleus collisions at the LHC ($\sqrt{s}=4.4$ TeV) at different rapidities (from top to bottom: $\eta=4,6, 7$) obtained from the solution of rcBK equation assuming two different initial nuclear saturation scales $Q_{0s}^2=0.5~\text{GeV}^2$ (left) and $Q_{0s}^2=0.67~\text{GeV}^2$ (right). In both panels the initial saturation scale for proton was taken $Q_{0s}^2=0.168~\text{GeV}^2$. The effect of different value for the strong coupling $\alpha_s$ in Eq. (\ref{['final']}) is also shown.
• Figure 4: Right: $R_{pA}$ for inclusive charged hadron production at different rapidities at the LHC obtained from the DHJ parameterization of the dipole profile Eq. (\ref{['dhj-d']}), with different values for the strong coupling in Eq. (\ref{['final']}). $R_{pA}$ for inclusive charged hadron production for various values of the strong coupling constant $\alpha_s$ in Eq. (\ref{['final']}) at the LHC ($\sqrt{s}=4.4$ TeV and $\eta=5$) obtained by the rcBK equation Eq. (\ref{['bk1']}).
• Figure 5: Right: nuclear modification factor $R_{pA}$ for $h^{+}+h^{-}$ production in proton-nucleus collisions at the LHC ($\sqrt{s}=8.8$ TeV) at different rapidities obtained from the solution of rcBK dipole evolution equation (\ref{['bk1']}) with different values for the strong coupling constant in Eq. (\ref{['final']}). Left: $R_{pA}$ for $h^{+}+h^{-}$ production in proton-nucleus collisions at the LHC in midrapidity ($\sqrt{s}=4.4$ TeV, $\eta=0$) for two different initial nuclear saturation scales of $Q_{0s}^2 = 0.5, 0.67\, \text{GeV}^2$ extracted from RHIC data. The initial saturation scale for proton is taken to be $Q_{0s}^2 = 0.168~\text{GeV}^2$. The theoretical error bars mainly show the uncertainties associated with the choice of $\alpha_s$.