Corona effect in AA collisions at LHC

TL;DR

This paper investigates the corona effect in AA collisions at LHC, proposing a finite formation time for produced media and explaining R_{AA} and v_2 behaviors with a parton energy loss model, contrasting with earlier flat R_{AA} predictions.

Contribution

It introduces a modified hypothesis accounting for a finite formation time and parton energy loss, explaining the rising R_{AA} and azimuthal anisotropy at LHC energies.

Findings

R_{AA} increases with p_t at LHC, contrary to previous flat predictions.

A fixed energy loss of about 7 GeV explains R_{AA} dependencies.

Predicted v_2 at high p_t aligns with observed data.

Abstract

Following our earlier finding based on RHIC data on the dominant jet production from nucleus corona region, we reconsider this effect in nucleus-nucleus collisions at LHC energy. Our hypothesis was based on experimental data, which raised the idea of a finite formation time for the produced medium. At RHIC energy and in low density corona region this time reaches about 2 fm/c. All observed high p_t particles are produced in the corona region and have a chance to escape during this 2 fm/c. After that, the formed high density matter absorbs all jets. Following this hypothesis, the nuclear modification factor R_{AA} should be independent on particle momentum and be flat versus p_t. At the same time, we describe the finite azimuthal anisotropy of high p_t particles, v_2. A separate prediction held that, at LHC energy, the formation time in the corona region should be two times smaller, about 1 fm/c. New data at LHC show that R_{AA} is not flat and is rising with p_t. We add to our original hypothesis an assumption that a fast parton traversing the produced medium loses the fixed portion of its energy. A shift of about 7 GeV (I would call it as a parton binding energy) from the original power law p^{-6} production cross section in pp explains well all the observed R_{AA} dependencies. The shift of about 7 GeV is also valid at RHIC energy, where the cross section follows a power law with about p^{-8} and this shift explains a very slow rise of R_{AA} seen for neutral pions with p_t above 15 GeV/c. We also show that the observed at LHC dependence of v_2 at high p_t and our previous predictions agree.

Figures

Equations

$$T(r)=T_0\cdot \sqrt{{\rho }_{periph}/\rho (r)},$$

Full text

Over the last 17 years of relativistic nucleus-nucleus collisions at RHIC and LHC, a set of observables was found which confirms the formation of high energy and high density matter. Among these features are the strong jet suppression manifested in particle suppression at high transverse momentum, $p_{t}$, and large particle anisotropy. There is also a long list of models and theoretical assumptions to explain these effects. In our view, when one talks about jet suppression, a significant effect of particle production from the nucleus corona region is often ignored or underestimated. In a previous publication based purely on experimental data at RHIC, a simple model was proposed [1] to explain the angular dependence in the reaction plane of the nuclear modification factor $R_{AA}$. The model nicely described the centrality and azimuthal dependence (or factor $v_{2}$ for high $p_{t}$) of $R_{AA}$ at RHIC energy. In the model, there is one free parameter of about 2.3 fm/$c$ which was interpreted as plasma formation time at the low density corona region. The physical meaning of this parameter is that fast partons have roughly this time to escape from the produced medium and, theafter, they are absorbed by the absolutely opaque central region. This value of $T_{0}$=2.3 fm/$c$ is not “crazy large” because the number of nuclear collisions, $N_{coll}$, near corona region is rather small, but it should be less than 0.8 fm/c in the core region of the produced matter [2]. Time, necessary to form the strongly interacting colored matter, should be proportional to the mean distance between the interaction or collision points with a color exchange. This distance, itself, should be inversely proportional to the square root of the density of such interactions. The picture in some sense is similar to the percolation scenario [3]. If the density of $N_{coll}$ in $x-y$ plane of colliding nuclei near the corona region is $\rho_{periph}$ then the formation time $T(r)$ versus density $\rho(r)$ will be:

[TABLE]

where $r$ is the distance from the center. In Fig. 1 we plot the evolution of the formation time versus the distance from the center of the region for the colliding Au+Au nuclei in the 0-5% centrality bin. For the $N_{coll}$ density distribution of colliding nucleons we used density profiles generated for our first publication [1]. To demonstrate how formation time works we show in Fig. 1 two extreme cases: when the fast parton is produced in the center of the colliding region, arrow 1, and near the surface at a depth of about 2 fm from the Woods-Saxon radius, arrow 2. The first parton moves with the speed of light along its world line 1 only for about 0.8 fm and then is stopped by the produced matter. The second parton will survive. The proposed model in [1] works well at RHIC energy.

In “The last call for prediction” published prior to the start of LHC we also proposed some features which should be observed at LHC if a similar picture with formation time is valid [4] (see pages 119–121 and figures 99–100 in the e-print version). As we already mentioned, the formation time should be proportional to the mean distance between interactions with the color exchange. It means also that only part of the nucleon-nucleon inelastic cross section will contribute to the process: single- and double diffractive and soft process with meson exchange will not be relevant here. If a relativistic rise of the total nucleon-nucleon, NN, cross section comes purely from the contribution from the colored parton hard scatterings, we can estimate the relative value of hard scatterings to the total nucleon-nucleon cross section. At $\sqrt{(}S_{NN})$=20 GeV the NN total cross section is at its minimum of 30 millibars - there is almost no hard scattering, but mostly soft nucleon-nucleon interactions with meson exchange. At 200 GeV the cross section rises by 13 mb, at 5500 GeV – by 49 mb. The formation time of the colored matter should be proportional to one over the square root of these numbers because the density of $N_{coll}$ is proportional to the cross section. If we get $T$=2.3 fm/$c$ at 200 GeV, then from the rise of the NN total cross section, we estimate T=1.2 fm/$c$ near the corona region at around 5 TeV of LHC energy. In the center of the collision zone it will be about three times shorter. Calculations show that such a value of $T$ should give a constant $R_{AA}$=0.1 for high $p_{t}$ particles in the most central collisions. We have to emphasize that the value of T around 1.2 fm/$c$ is valid within uncertainty of 5% in the LHC energy range of 2.7–5 TeV. It comes from a little change of $pp$ total cross section between 85 mb and 90 mb if one interpolates the existing $pp$ data [5], thus, and relative change of hard scattering contribution is on the level of 5 mb.

Predictions made in [4] assume that the core of the produced matter is opaque, but experimental data for Pb+Pb collisions obtained by ALICE, CMS and ATLAS [6, 7, 8] show that $R_{AA}$ is continuously rising at high $p_{t}$. It means that the core of the collision zone becomes more transparent for fast particles. It is natural to assume that the parton loses some portion of its energy. We found that a constant energy loss of 7 GeV describes well the data for $R_{AA}$ versus $p_{t}$. Particle, namely pion, production cross section at LHC energy follows a simple power law $p^{-6}$ [9] at high $p_{t}$. Thus, the energy drop by 7 GeV becomes less significant with increasing parton $p_{t}$. In Fig. 2 we present results for the $R_{AA}$ versus $p_{t}$ from CMS data [10] and our calculations for most central collisions. There are two contributions: a constant value of 0.1 for a particle from the corona region, as was predicted in ref. [4], and a new momentum dependent component when matter becomes more transparent for fast parton, which loses 7 GeV. This provides excellent agreement with the data. In Fig. 3 we show a similar plot for mid-central collisions. In this case the contribution to $R_{AA}$ from the corona region reaches 0.35 [4], but the penetrating parton contribution is about the same.

Out of curiosity we checked how this 7 GeV energy loss works at RHIC and added this component to the previous calculation with the corona region and absolutely black core, Fig. 4. The only difference here is that the production cross section at RHIC follows a more steep power law $p^{-8}$ [11]. Within the error bars our line follows the experimental points. Such a large energy loss (7 GeV) at RHIC explains why the assumption about the complete black core with some corona contribution worked so well – the loss is too big for produced particles at RHIC.

Our model worked well at RHIC for the observed large azimuthal of high $p_{t}$ particles or parameter $v_{2}$. Nearly 10 years ago we did a prediction for $v_{2}$ at LHC [4]. It seems that the prediction is valid. In Fig. 5 we compare our estimations with CMS results at $p_{t}$=15 GeV/$c$ [12]. The prediction of a large $v_{2}$ even at LHC is confirmed, the sensitivity to the collision geometry persists up to high $p_{t}$. There is a deviation at small $N_{part}$ but this is due to the well known effect of distortion by the initial geometry fluctuations (see for example, PHOBOS paper [13]). We also can explain the observed drop of $v_{2}$ with particle or jet momentum above 15 GeV/$c$. The corona effect for in- and out-of-plane particle production is diluted by penetrating partons with energy loss. For example, looking at Fig. 2 and Fig. 3, one can see that at $p_{t}$=40 GeV/$c$ particles from the corona region count for about one half of the total yield at this momentum. Thus, $v_{2}$ should drop to about a factor of 2. This what is qualitatively seen by the three experiments [12, 14, 15].

In conclusion, we demonstrate that in PbPb collisions at LHC the contribution from the corona region and the assumption of a finite formation time for the colored strongly interacting matter are the reasons for the observed centrality and momentum dependence of particle $R_{AA}$. At LHC energies, a fast parton escapes the interaction zone by losing about 7 GeV. Within our model this value does not depend on momentum, centrality, energy density, and, probably, on beam energy. The observed azimuthal angular asymmetry at a high transverse momentum is well described at RHIC and LHC energies.

This work was partially supported by the RFBR grant numbers 14-22-03069-ofi-m and 14-02-00570-a. We would like to thank Keith Guzik for help with the text.