Revealing “flickering” of the interaction strength in $pA$ collisions at the CERN LHC

Using the high-energy color fluctuation formalism to include inelastic diffractive processes and taking into account the collision geometry and short-range nucleon-nucleon correlations in nuclei, we assess various manifestations of “flickering” of the parton wave function of a rapid proton in $pA$ interactions focusing at energies available at the CERN Large Hadron Collider (LHC) in soft QCD processes and in the special soft QCD processes accompanying hard processes. We evaluate the number of wounded nucleons, $N_{\text{coll}}$—the number of inelastic collisions of projectiles—in these processes and find a nontrivial relation between the hard collision rate and centrality. We study the distribution over $N_{\text{coll}}$ for a hard trigger selecting configurations in the nucleon with the strength larger or smaller than the average one and argue that the pattern observed in the LHC $pA$ measurements by CMS and ATLAS for jets carrying a large fraction of the proton momentum, $x_p$, is consistent with the expectation that these configurations interact with the strength which is significantly smaller than the average one, a factor of two smaller for $x_p\sim 0.5$. We also study the leading twist shadowing and the European Muon Collaboration effects for superdense nuclear matter configurations probed in the events with a larger-than-average number of wounded nucleons. We also argue that taking into account energy-momentum conservation does not change the distribution over $N_{\text{coll}}$ but suppresses hadron production at central rapidities.

Figure 1

The probabilities $P_N$ of having $N=N_{\text{coll}}$ wounded nucleons, averaged over the global impact parameter $b$, as a function of $N_{\text{coll}}$ for the Glauber model (${\omega }_{\sigma }=0$) and in the CF model with ${\omega }_{\sigma }=0.1$ (our base value used in the current analysis) and ${\omega }_{\sigma }=0.2$. The inset is in the log scale.

Figure 2

Comparison of the distributions over $N=N_{\text{coll}}$ for the Glauber model and for the CF model with ${\omega }_{\sigma }=0.1$ with the Gaussian [Eq. (5)] and exponential [Eq. (10)] large-$\sigma$ behavior.

Figure 3

Sketch of the transverse geometry of collisions.

Figure 4

Ratio $R_{\mathrm{HT}}$ [Eq. (12)] of the rates of hard collisions in the Glauber and the CF models to those in the optical model as a function of $N=N_{\text{coll}}$.

Figure 5

The distribution over the number of collisions for a hard trigger using (a) the full calculation and (b) the approximation $R_{\mathrm{HT}}=1$.

Figure 6

Ratio of the probabilities $P_N$ of having $N=N_{\text{coll}}$ wounded nucleons for configurations with different $\langle \sigma \left(x\right)\rangle$ and $P_N$ for $\sigma ={\sigma }_{\mathrm{tot}}$ at LHC [panels (a) and (b)] and RHIC [panels (c) and (d)] energies. The ratio is averaged over the global impact parameter $b$ and plotted as a function of $N=N_{\text{coll}}$. The solid and dashed curves neglect the dispersion of $\sigma$, while the dotted and dot-dashed curves show the results obtained with a Gaussian distribution around $\langle \sigma \left(x\right)\rangle$ with the variance equal to 0.1. Panels (a) and (c) show results for $NN$ interaction cross sections smaller than average, while panels (b) and (d) show results for $NN$ interaction cross sections larger than average.

Figure 7

Ratio of the probabilities $P_N$ of having $N=N_{\text{coll}}$ wounded nucleons for configurations with different $\langle \sigma \left(x\right)\rangle$ and $P_N$ for $\sigma ={\sigma }_{\mathrm{tot}}$ for LHC (a) and RHIC (b) energies. The ratio is averaged over the global impact parameter $b$ and plotted as a function of $N=N_{\text{coll}}$. The dashed curve is also shown in Fig. 6; see text for the definition of the two-state model shown by the dotted curve.

Figure 8

Fractional contributions to the quark (left panel) and gluon (right panel) PDFs at $x=0.1$, 0.3, and 0.5 and $Q^2={10}^4{\mathrm{GeV}}^2$ originating from the interval $[x,x_{\mathrm{cut}}]$ at the input scale $Q_0^2=4$ ${\mathrm{GeV}}^2$. The solid curves correspond to the quark contribution and the dotted curves are for the gluon contribution.

Figure 9

Ratio of the nuclear gluon conditional distribution for given $N_{\text{coll}}$ and the inclusive gluon density normalized to their values at $x=0.2$ as a function of $x$ for different values of $Q^2$ and $k$. See text for details.

Figure 10

The ${\overline{u}}_A$ quark superratio $({\overline{u}}_A(x,Q^2,N_{\text{coll}})/{\overline{u}}_A(x,Q^2))/({\overline{u}}_A(x=0.2,Q^2,N_{\text{coll}})/{\overline{u}}_A(x=0.2,Q^2))$ as a function of $x$ for different values of $Q^2$ and $k$. See Fig. 9 for comparison and text for details.