Quenching of high-$p_T$ hadrons: Energy loss versus color transparency

High-$p_T$ hadrons produced in hard collisions and detected inclusively bear peculiar features: (i) they originate from jets whose initial virtuality and energy are of the same order and (ii) such jets are rare and have a very biased energy sharing among the particles, namely the detected hadron carries the main fraction of the jet energy. The former feature leads to an extremely intensive gluon radiation and energy dissipation at the early stage of hadronization, either in vacuum or in a medium. As a result, a leading hadron must be produced on a short length scale. Evaluation within a model of perturbative fragmentation confirms the shortness of the production length. This result is at variance with the unjustified assumption of long production length, made within the popular energy-loss scenario. Thus, we conclude that the main reason of suppression of high-$p_T$ hadrons in heavy-ion collisions is the controlled-by-color-transparency attenuation of a high-$p_T$ dipole propagating through the hot medium. Adjusting a single parameter, the transport coefficient, we describe quite well the data from the Large Hadron Collider and the Relativistic Heavy Ion Collider for the suppression factor $R_{AA}$ as function of $p_T$, collision energy, and centrality. We observe that the complementary effect of the initial-state interaction causes a flattening and even fall of $R_{AA}$ at large $p_T$. The azimuthal anisotropy of hadron production, calculated with no further adjustment, also agrees well with data at different energies and centralities.

Figure 1

Space-time development of hadronization of a highly virtual quark producing a leading hadron, which carries the main fraction $z_h$ of the initial quark light-cone momentum.

Figure 2

The path length taken by a parton (quark or gluon) of energy $E$ and virtuality $Q^2=E^2$ to radiate a fraction $\delta =\Delta E\left(t\right)/\Delta E_{\mathrm{tot}}$ of the total vacuum energy loss. The curves correspond to different jet energies, $E=10,20,50$, and 100 GeV.

Figure 3

Sudakov suppression factor caused by the ban for radiation of gluons with fractional energy higher than $1-z_h$, during the time interval $t<t_p=l_p$. Calculations are done for jet energies, $E=Q=k_T=10,100$ GeV, and several fractional hadron momenta, $z_h=0.6$–0.9.

Figure 4

The differential fragmentation function Eq. (12) (in arbitrary units) at $Q^2=E^2$ as function of $l_p$ for quark jets with energies $E=k_T=10,20$, and 100 GeV (from top to bottom) and $z_h=0.7$.

Figure 5

The mean production length as function of energy for quark (solid curves) and gluon (dashed curves) jets. In both cases, the curves are calculated at $z_h=0.5,0.7$, and 0.9 (from top to bottom).

Figure 6

$p_T$ dependence of pion production in $pp$ collisions at $\sqrt{s}=200$ GeV (a) and charged hadron production at 7 TeV (b). The contributions of quark and gluon jets are shown by dashed and dotted curves, respectively. Data points are from the PHENIX [31] and CMS [32] experiments.

Figure 7

The mean fraction $\langle z_h\rangle$ of the jet energy carried by a hadron detected with transverse momentum $p_T$. The calculations are performed as described in the text for collision energies $\sqrt{s}=200$, 2760, and 7000 GeV.

Figure 8

The suppression factor $R_{AA}$ for central (0–5$\%$) lead-lead collisions at $\sqrt{s}=2.76$ TeV. The dashed line is calculated within the path-integral approach [Eq. (31)] with the space- and time-dependent transport coefficient Eq. (20), where the adjusted parameter ${\widehat{q}}_0=2$ GeV${}^2$/fm. The solid curve also includes the effects of initial state interactions in nuclear collisions [10, 51], as is described in Sec. 4b. Data for $R_{AA}$ are from the ALICE [47] and CMS [48, 49] experiments.

Figure 9

Centrality dependence of the suppression factor $R_{AA}(p_T,b)$ measured in the ALICE experiment [47]. The intervals of centrality are indicated in the plot. The meaning of the curves is the same as in Fig. 8.

Figure 10

The same as in Fig. 9, with data from the CMS experiment [48, 49].

Figure 11

Nuclear attenuation factor $R_{dAu}\left(p_T\right)$ as function of $p_T$ of ${\pi }^0$ mesons produced in central (0–20$\%$) $d$-Au collisions at $\sqrt{s}=200$ GeV and $\eta =0$. The solid and dashed curves represent the model predictions calculated with and without the ISI corrections. Isotopic effect is included. The data are from the PHENIX experiment [56].

Figure 12

Nuclear attenuation factor $R_{AA}\left(p_T\right)$ for neutral pions produced in central gold-gold collisions at $\sqrt{s}=200$ GeV. The solid and dashed line are calculated with or without ISI corrections. PHENIX data are from Refs. [57] (triangles) and [60] (squares).

Figure 13

Centrality dependence of the suppression factor $R_{AA}(p_T,b)$ measured in the PHENIX experiment [57] in gold-gold collisions at $\sqrt{s}=200$ GeV. The intervals of centrality are indicated in the plot.

Figure 14

The same as in Fig. 13 but at $\sqrt{s}=62$ GeV. Data are from Ref. [61].

Figure 15

Nuclear factor $R_{AA}\left(p_T\right)$ for charge hadrons in lead-lead collisions at $\sqrt{s}=2.76$ TeV at different centralities indicated on the figure. ALICE data [58] and our calculations with Eq. (31) are divided into two classes: in-plane ($3\pi /4<\left|\varphi \right|<\pi$ and $\left|\varphi \right|<\pi /4$) and out-of-plane ($\pi /4<\left|\varphi \right|<3\pi /4$).

Figure 16

$R_{AA}\left(p_T\right)$ for charge hadrons in gold-gold collisions at $\sqrt{s}=200$ GeV at centralities 0–20$\%$. PHENIX data [57] and our calculations with Eq. (31) are divided into two classes of events: in-plane ($11\pi /12<\left|\varphi \right|<\pi$ and $\left|\varphi \right|<\pi /12$) and out-of-plane ($5\pi /12<\left|\varphi \right|<7\pi /12$).

Figure 17

ALICE data [58] for azimuthal anisotropy, $v_2$, vs $p_T$ for charge hadron production in lead-lead collisions at midrapidity at $\sqrt{s}=2.76$ TeV and at different centralities indicated in the figure. The curves present the results of calculation with Eq. (37).

Figure 18

The same as in Fig. 17 but displaying data from the CMS experiment [59].

Figure 19

The same as in Fig. 17 but displaying data from the PHENIX experiment [62].