Forward di-hadron back-to-back correlations in $\boldsymbol{pA}$ collisions from rcBK evolution

TL;DR

This work develops a state-of-the-art CGC-based description of forward di-hadron production in p+A collisions by deriving gluon TMDs from rcBK evolution and embedding them in a TMD factorization framework. Applied to RHIC energies, the approach describes the observed suppression of the away-side peak in forward d+Au and makes concrete predictions for p+Au at √s = 200 GeV, including a roughly factor-of-two suppression of the away-side yield. The authors compare rcBK evolution with the Kutak-Sapeta KS scheme to illustrate differences in rapidity dependence, proposing rapidity-differential observables as strong tests of small-x dynamics. They also highlight the need to incorporate Sudakov resummation to accurately capture the away-side width and outline future work to sharpen the saturation signal via rapidity measurements.

Abstract

We study the disappearance of the away-side peak of the di-hadron correlation function in p+A vs p+p collisions at forward rapidities, when the scaterring process presents a manifest dilute-dense asymmetry. We improve the state-of-the-art description of this phenomenon in the framework of the Color Glass Condensate (CGC), for hadrons produced nearly back-to-back. In that case, the gluon content of the saturated nuclear target can be described with transverse-momentum-dependent gluon distributions, whose small-$x$ evolution we calculate numerically by solving the Balitsky-Kovchegov equation with running coupling corrections. We first show that our formalism provides a good description of the disappearance of the away-side azimuthal correlations in d+Au collisions observed at BNL Relativistic Heavy Ion Collider (RHIC) energies. Then, we predict the away-side peak of upcoming p+Au data at $~\sqrt[]{s}=200$ GeV to be suppressed by about a factor 2 with respect to p+p collisions, and we propose to study the rapidity dependence of that suppression as a complementary strong evidence of gluon saturation in experimental data.

Figures (6)

• Figure 1: The $pA \rightarrow \pi^0\pi^0X$ process. See the text for details about the displayed quantities.
• Figure 2: This figure presents the $x_2$ evolution of three TMDs appearing in the cross section of Eq. (\ref{['eq:full']}), for a target proton. In panel (a), the initial conditions at $x_2=0.01$ are presented. We show $\mathcal{F}_{gg}^{(1)}$ (solid line), $\mathcal{F}_{gg}^{(1)}-\mathcal{F}_{gg}^{(2)}$ (dashed line), and $\mathcal{F}_{gg}^{(6)}$ (dot-dashed line). The vertical dotted lines represent the saturation scale at the given value of $x_2$. In the figure, $Y=\ln \bigl(0.01/x_2\bigr)$. The plotted quantities do not include the factor $S_{\perp}/\alpha_s$ in Eq. (\ref{['eq:dipgluontmd']}), common to all the gluon TMDs.
• Figure 3: The figure shows STAR data on azimuthal $\pi^0$ correlations at forward rapidity, in p+p collisions (circles) and central d+Au collisions (triangles) at $~\sqrt[]{s}=200~{\rm GeV}$. To remove fake two particle correlations which are essentially due to pileup effects, an arbitrary offset is added to push the STAR measurements close to 0 at the minimum of the correlation functions. Calculations of $CP(\Delta\phi)$ in our TMD+rcBK framework are shown as shaded bands. Light-shaded band: p+p collisions. Dark-shaded band: d+Au collisions. The meaning of the shaded bands is discussed in the text.
• Figure 4: In this figure we show predictions for azimuthal correlation of forward neutral pions in p+p (dashed line) and p+Au (dotted line) collisions at $~\sqrt[]{s}=200~{\rm GeV}$. Different panels correspond to different $p_t$ cuts applied to the cross section.
• Figure 5: The figure shows $\mathcal{F}_{gg}^{(1)}$ for a target nucleus divided by the same quantity for a target proton, as function of $k_t$. Results are shown within two different evolution schemes, namely rcBK [panel (a)] and KS approximation [panel(b)]. The ratio is taken at different values of $x_2$, indicated with different line styles. In the figure, $Y=\ln \bigl(0.01/x_2\bigr)$.