Towards the Test of Saturation Physics Beyond Leading Logarithm

TL;DR

The first next-to-leading-order (NLO) numerical analysis of forward hadron production in pA and dA collisions in the small-x saturation formalism provides a precise test of saturation physics beyond the leading logarithmic approximation.

Abstract

We present results from the first next-to-leading order (NLO) numerical analysis of forward hadron production in pA collisions in the small-x saturation formalism. Using parton distributions and fragmentation functions at NLO, as well as the dipole amplitude from the solution to the Balitsky-Kovchegov equation with running coupling, together with the NLO corrections to the hard coefficients, we obtain a good description of the available RHIC data in dAu collisions. We also comment on the results in the large p_T region beyond the saturation scale. Furthermore, we make predictions for forward hadron production in pPb collisions at the LHC. This analysis not only incorporates the important NLO corrections for all partonic channels, but also reduces the renormalization scale dependence and therefore helps to significantly reduce the theoretical uncertainties. It therefore provides a precise test of saturation physics beyond the leading logarithmic approximation.

Figures (4)

• Figure 1: Comparisons of BRAHMS Arsene:2004ux ($h^-$) and STAR Adams:2006uz ($\pi^0$) yields in $\text{dAu}$ collisions to results of the numerical calculation with the rcBK gluon distribution, both at leading order (tree level) and with NLO corrections included. The edges of the solid bands were computed using $\mu^2 = \text{\SIrange{10}{50}{GeV^2}}$.
• Figure 2: Comparisons of BRAHMS data Arsene:2004ux at $\eta=3.2$ with the theoretical results for four choices of gluon distribution: GBW, MV with $\Lambda=0.24GeV$, BK solution with fixed coupling at $\alpha_s = 0.1$, and rcBK with $\Lambda_\textrm{QCD}=0.1GeV$. The edges of the solid bands show results for $\mu^2=\text{\SIrange{10}{50}{GeV^2}}$. As in other figures, the crosshatch fill shows LO results and the solid fill shows NLO results.
• Figure 3: Predictions for the yields at the LHC energy $\sqrt{s_\text{NN}}=5.02TeV$ in $\text{pPb}$ collisions, both at LO and with NLO corrections included, using the rcBK gluon distribution. On the left, we show results for $\pi^-$ yields at $\eta = 6.375$ ($Y_\text{CM} = 5.91$ in the center of mass frame) which falls in the range of pseudorapidities detected by TOTEM, and on the right, for $\pi^0$ yields at $\eta = 8.765$ ($Y_\text{CM} = 8.3$) which falls in the range detected by LHCf. The edges of the solid bands were computed using $\mu^2 = \text{\SIrange{20}{100}{GeV^2}}$ on the left and $\mu^2 = \text{\SIrange{2}{10}{GeV^2}}$ on the right.
• Figure 4: $\mu$-dependence of the calculated cross sections at $p_\perp = 2GeV$. The NLO results for fixed coupling ($\alpha_s=0.2$) and one-loop running coupling are both presented, where the $\alpha_s$ here is referred to the one in front of the NLO hard coefficients in Eq. (\ref{['eq:master']}). The dramatic drop of the NLO curve with the running coupling at low $\mu^2$ is simply due to the breakdown of perturbative calculations at large $\alpha_s (\mu)$. Nevertheless, these two NLO curves almost overlap with each other at large values of $\mu^2$.