Rapidity dependence of the average transverse momentum in hadronic collisions

The energy and rapidity dependence of the average transverse momentum $\langle p_T\rangle$ in $pp$ and $pA$ collisions at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) are estimated using the color glass condensate (CGC) formalism. We update previous predictions for the $p_T$ spectra using the hybrid formalism of the CGC approach and two phenomenological models for the dipole-target scattering amplitude. We demonstrate that these models are able to describe the RHIC and LHC data for hadron production in $pp, d\mathrm{Au}$, and $p\mathrm{Pb}$ collisions at $p_T\le 20$ GeV. Moreover, we present our predictions for $\langle p_T\rangle$ and demonstrate that the ratio $\langle p_T\left(y\right)\rangle /\langle p_T(y=0)\rangle$ decreases with the rapidity and has a behavior similar to that predicted by hydrodynamical calculations.

Figure 1

Comparison between the (a) BUW and (b) DHJ predictions for the transverse momentum $p_T$ spectra of charged particles produced in $p\mathrm{Pb}$ collisions and the ALICE data [59]. For the new version of the BUW model we assume $K=3.7$ for all pseudorapidity bins and for the new DHJ model $K=3.0$, 3.0, and 3.7 for $\langle \eta \rangle =0$, 0.55, and 1.05, respectively.

Figure 2

Predictions of the DHJ and BUW models for the $p_T$ spectra of charged particles in $pp$ collisions. (a) Comparison with the ALICE data [65]. The corresponding $K$ factors are the following: $K=2.47$ ($K=2.3$), 2.07 (1.85), and 1.77 (1.6) for the BUW (DHJ) model for $\sqrt{s}=0.9$, 2.76, and 7 TeV. (b) Comparison with the ATLAS data [66]. In this case we have assumed $K=3.3$, 2.5, and 2.3, respectively, for both models. (c) Comparison with the CMS data [67]. In this case we assume for both models $K=3.0$, 2.5, and 2.3 for $\sqrt{s}=0.9$, 2.36, and 7 TeV. (d) Predictions of the DHJ and BUW models for the $p_T$ spectra of neutral pions. Comparison with the ALICE data [68] for $\sqrt{s}=0.9$ and 7 TeV. For both models we have $K=1.2$ and 2.0.

Figure 3

(a) Predictions of the DHJ and BUW models for the $p_T$ spectra of neutral pions in $pp$ collisions. For the BUW model $K=1.5$ for $\langle \eta \rangle =0.5$ and $K=1.2$ for $\langle \eta \rangle =1.4$, 3.25, 3.7, and 3.925. For the DHJ model $K=1.2$ for $\langle \eta \rangle =3.25,3.7,3.925$. The experimental data are from [69]. (b) Predictions of the DHJ and BUW models for the $p_T$ spectra of hadron production in $d\mathrm{Au}$ collisions. For the BUW model we have $K=2.9$, 2.5, 2.0, 1.0, and 1.0 for $\eta =0$, 1, 2.2, 3.2, and 4, respectively. For the DHJ model we have $K=2.5$, 2.4, and 1.5 for $\eta =2.2$, 3.2, and 4, respectively. The experimental data are from [70]. (c) Comparison between the BUW predictions and the $ep$ HERA data for the total ${\gamma }^{*}p$ cross section [71].

Figure 4

Dependence of the ratio $\langle p_T(y,\sqrt{s})\rangle /\langle p_T(0,\sqrt{s})\rangle$ in the model used for the forward scattering amplitude in $pp$ and $p\mathrm{Pb}$ collisions. In panels (a) and (c) parton fragmentation is disregarded, while in (b) and (d) fragmentation is included.

Figure 5

Dependence of the ratio $\langle p_T(y,\sqrt{s})\rangle /\langle p_T(0,\sqrt{s})\rangle$ in the minimum transverse momentum $p_{T,\min }$ considering (a) the GBW and (b) the BUW model for the forward scattering amplitude.

Figure 6

Rapidity dependence of the ratio $R=\langle p_T(y,\sqrt{s})\rangle /\langle p_T(0,\sqrt{s})\rangle$ in (a) $pp$ and (b) $p\mathrm{Pb}$ collisions for different energies. The BUW (DHJ) predictions are represented by blue (red) lines.

Figure 7

Rapidity dependence of the ratio between the predictions for the $R=\langle p_T(y,\sqrt{s})\rangle /\langle p_T(0,\sqrt{s})\rangle$ in $pp$ collisions and those for $p\mathrm{Pb}$ collisions considering (a) the DHJ and (b) the BUW models.