Core-corona interplay in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV

TL;DR

This paper presents a simple Glauber Monte-Carlo based model separating wounded nucleons into core and corona categories to explain the centrality dependence of light flavor hadron production in Pb-Pb collisions at 2.76 TeV, highlighting the corona's significant role.

Contribution

The study introduces a core-corona separation approach that accounts for the corona's influence on collision observables at LHC energies, improving understanding of centrality dependence.

Findings

Corona contribution is significant at LHC energies.

The model reproduces centrality dependence of hadron yields.

Limitations in reproducing detailed transverse momentum distributions.

Abstract

A simple approach based on the separation of wounded nucleons in an A-A collision in two categories, those suffering single collisions - corona and the rest - core, estimated within a Glauber Monte-Carlo approach, explains the centrality dependence of the light flavor hadrons production in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV. The core contribution does not include any dependence of any process on the fireball shape as a function of the impact parameter. Therefore, the ratios of the $p_T$ distributions to the one corresponding to the minimum bias pp collisions at the same energy, each of them normalised to the corresponding charged particle density, the $\langle p_T\rangle$ and transverse energy per unit of rapidity are reproduced less accurate by such an approach. The results show that the corona contribution plays an important role also at LHC energies and it has to be considered in order to evidence the centrality dependence of different observables related to the core properties and dynamics.

Figures

a the percentage of wounded nucleons which scatter only once, for head-on collisions of two identical nuclei is represented as a function of their mass at two incident energies, i.e. $\sqrt{s_{NN}}$=200 GeV and 2.76 TeV. The percentage of nucleons scattered only once is decreasing with the increasing mass of the colliding nuclei and the centre of mass energy, the value for Pb-Pb collisions at the LHC energy being very small. However, for peripheral and mid-central collisions their contribution becomes important and a good scaling is evidenced as a function of the number of participating nucleo

a the percentage of wounded nucleons which scatter only once, for head-on collisions of two identical nuclei is represented as a function of their mass at two incident energies, i.e. $\sqrt{s_{NN}}$=200 GeV and 2.76 TeV. The percentage of nucleons scattered only once is decreasing with the increasing mass of the colliding nuclei and the centre of mass energy, the value for Pb-Pb collisions at the LHC energy being very small. However, for peripheral and mid-central collisions their contribution becomes important and a good scaling is evidenced as a function of the number of participating nucleo

Tables

Table 1. Table 1: Centrality, impact parameter Alcen ⟨ N p ​ a ​ r ​ t ⟩ delimited-⟨⟩ subscript 𝑁 𝑝 𝑎 𝑟 𝑡 \langle N_{part}\rangle and the percentage of wounded nucleons with more than one collision estimated for the corresponding centrality, based on the Glauber Monte-Carlo approach, for Pb-Pb at s N ​ N subscript 𝑠 𝑁 𝑁 \sqrt{s_{NN}} =2.76 TeV collisions.

$Cen$ (%)	b (fm)		$⟨N_{part}⟩$		$f_{core}$
0 - 5	0.00 - 3.50		382.5$\pm 3.1$		0.942$\pm 0.003$
5 - 10	3.50 - 4.95		329.4$\pm 4.9$		0.900$\pm 0.002$
10 - 20	4.95 - 6.98		259.9$\pm 2.9$		0.861$\pm 0.002$
20 - 30	6.98 - 8.55		185.4$\pm 3.9$		0.814$\pm 0.002$
30 - 40	8.55 - 9.88		128.1$\pm 3.3$		0.764$\pm 0.002$
40 - 50	9.88 - 11.04		84.2$\pm 2.6$		0.703$\pm 0.002$
50 - 60	11.04 - 12.09		52.1$\pm 2.0$		0.626$\pm 0.002$
60 - 70	12.09 - 13.05		29.5$\pm 1.3$		0.536$\pm 0.004$
70 - 80	13.05 - 13.97		14.9$\pm 0.6$		0.431$\pm 0.005$
80 - 90	13.97 - 14.96		6.3$\pm 0.2$		0.325$\pm 0.003$

Equations

$$\rho (r)=\frac{1}{1+exp(\frac{r-R_A}{a})}$$

$${\left(\frac{dN}{dy}\right)}_i^{cen}=N_{part}[(1-f_{core})M_i^{ppMB}+f_{core}{M}_i^{core}]$$

$$\begin{gathered} ⟨p_T{⟩}_i^{cen}= \\ \frac{f_{core}⟨p_T{⟩}_i^{core}{M}_i^{core}+(1-f_{core})⟨p_T{⟩}_i^{ppMB}{M}_i^{ppMB}}{f_{core}{M}_i^{core}+(1-f_{core})M_i^{ppMB}} \end{gathered}$$

$$\frac{d{E}_T}{dy}\approx 3{\left(\frac{d{E}_T}{dy}\right)}_{{\pi }^{+}}+4{\left(\frac{d{E}_T}{dy}\right)}_{K^{+},p,{\Xi }^{-}}+2{\left(\frac{d{E}_T}{dy}\right)}_{\Lambda ,{\Omega }^{-}}$$

Full text

I

I.1

I.1.1

At ultra-relativistic energies the initial energy density distribution within the fireball is highly non-homogeneous Dre . This non-homogeneity is directly correlated with the distribution of nucleons suffering a given number of collisions (the thickness of nuclear matter to which a nucleon is exposed) which can be estimated in a simple Monte-Carlo Glauber approach. The non-homogeneous distribution of the initial state has a direct consequence on the fluctuations of different observables and the dynamics of the initial state up to the freeze-out moment. At a given collision energy, the amount of energy transferred into the fireball increases with centrality, i.e. the volume of the overlapping zone, and is correlated with the measured charged particle multiplicity. Therefore, the charged particle multiplicity dependence was extensively studied for many observables. It is mandatory to understand how much of this dependence on centrality or system size is due to the initial high energy density state and its subsequent dynamics and how much is due to a simple interplay between core-corona contributions.

Extensive studies of the core-corona separation effects on the centrality dependence of the strangeness production, average transverse momenta, elliptic flow or $p_{T}$ spectra in heavy-ion collisions at SPS and RHIC energies were done Bec0 ; Boz ; Wer ; Stei ; Bec ; Aich ; Boz1 ; Gem ; Schr . The core-corona interplay estimated by parametrizing the core-mantle contributions such as to reproduce the density of charged particles produced in Au-Au collisions Boz was confirmed by more consistent approaches, based on string density before hadronization within the EPOS model using some global parameters Wer or on quark number density within the UrQMD transport+hydrodynamics hybrid model Stei . Approaches based on separating the participating (wounded) nucleons $N_{part}$, in two classes, those which scatter only once, coined corona, which would correspond to a minimum-bias pp collision and the rest which contribute to the fireball, called core, both estimated within the geometrical Glauber model, were equally successful in explaining the experimental trends Bec ; Aich . A very good agreement between the percentage of nucleons undergoing single collisions and the percentage taken as a fit parameter in a core-corona scenario was evidenced Boz1 . Based on this and due to its simplicity, in the present paper we consider the approach from Aich in order to explore to which extent it can explain the centrality dependence of different observables in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV.

The number of participating nucleons and the percentage of wounded nucleons which scatter more than once, $f_{core}$, were estimated using the Monte-Carlo Glauber approach Gla ; Fra ; San . For the nuclear density profile of the colliding Pb nuclei a Woods-Saxon distribution was used:

[TABLE]

with a=0.546 fm and $R_{A}$=6.62 fm. The nucleons of the two Pb nuclei are colliding if the transverse distance between them is smaller than the distance estimated from the inelastic nucleon-nucleon cross section of 64 mb at $\sqrt{s}$=2.76 TeV Alcen ; Al5 . The correlation between the centrality and impact parameter is taken from Alcen .

These values, $\langle N_{part}\rangle$ and the percentage of nucleons suffering more than a single collision are presented in Table I.

In Fig.1a the percentage of wounded nucleons which scatter only once, for head-on collisions of two identical nuclei is represented as a function of their mass at two incident energies, i.e. $\sqrt{s_{NN}}$=200 GeV and 2.76 TeV. The percentage of nucleons scattered only once is decreasing with the increasing mass of the colliding nuclei and the centre of mass energy, the value for Pb-Pb collisions at the LHC energy being very small. However, for peripheral and mid-central collisions their contribution becomes important and a good scaling is evidenced as a function of the number of participating nucleons for Au-Au and Pb-Pb collisions at the respective energies, as could be followed in Fig.1b.

We start with integrated values, i.e. the yields of light flavor hadrons per unit of rapidity measured in the mid-rapidity region Al3 ; Al1 ; Al2 ; Al14 . Within a core-corona approach, the yield of a given species $i$, at a given centrality, per unit of rapidity can be written as:

[TABLE]

where $M_{i}^{ppMB}$=$\frac{1}{2}(dN/dy)_{i}^{ppMB}$ at the same energy and $M_{i}^{core}$ is the multiplicity per core participant. A similar decomposition can be done for the double differential $p_{T}$ distributions. $(dN/dy)_{i}^{ppMB}$ values for $\mathrm{\pi}$, K, p were reported in Al13 . The values for hyperons and $\phi$ mesons were obtained following the same receipt as the one used by the ALICE Collaboration Al7 ; Al10 ; Al2 ; Al14 ; Al16 and reported values Al20 , respectively. Eq.(2) for 0-5$\%$ centrality was used to extract the core contribution for each species.

The estimated light flavor hadrons yields as a function of the average number of participants $\langle N_{part}\rangle$ from Eq.(2) and the published experimental values are presented in Fig.2 by open and full symbols, respectively. As it is observed, the enhancement of light flavor hadrons production with increasing centrality is reproduced rather well by a pure geometrical approach, a superposition of the single nucleon-nucleon (corona) contribution and the contribution due to nucleons which scatter more than once (core) whose relative weights were estimated within the Glauber approach. This approach is also applied for the ratio of double differential cross sections normalised to the charged particle densities, i.e.: $\left(\frac{\frac{d^{2}N}{dydp_{T}}}{\langle\frac{dN_{ch}}{d\eta}\rangle}\right)_{i}^{cen}/\left(\frac{\frac{d^{2}N}{dydp_{T}}}{\langle\frac{dN_{ch}}{d\eta}\rangle}\right)_{i}^{ppMB}$. The numerator and denominator of $\left(\frac{\frac{d^{2}N}{dydp_{T}}}{\langle\frac{dN_{ch}}{d\eta}\rangle}\right)_{i}^{cen}$ were estimated separately as a superposition of corona and core contributions. Similar to the integrated yield, the core contributions are obtained from the experimental spectra for the most central collisions. In Fig.3 left column (a,b,c), the ratios of the normalised $p_{T}$ distributions Pet2 based on $p_{T}$ spectra measured by the ALICE Collaboration Al9 ; Al11 are represented. The results using the core-corona scenario can be followed in the second column (d,e,f) while the ratios between experimental $p_{T}$ distributions and the ones estimated within the core-corona approach are shown in the third column (g,h,i). The trends observed in the experiment are qualitatively reproduced. Quantitatively, as could be seen in the last column of Fig.3, there are some differences between the estimates based on the core-corona ansatz and the experimental values. This is the consequence of not including any dependence of different phenomena on the core shape as a function of centrality. At RHIC energies, the PHENIX Collaboration has done detailed studies on the azimuthal dependence of the in-plane/out-of-plane transverse expansion Phe2 and $R_{AA}$ Phe1 for Au-Au collisions at $\sqrt{s_{NN}}$=200 GeV. A clear $N_{part}$ and azimuthal angle dependence of these two phenomena was evidenced. This is the explanation of the observed deviations in the last column of Fig.3 in the region of $p_{T}$ where the expansion and suppression have the main contribution to the spectra shapes. Therefore, a deviation from a simple core-corona approach where the core contribution scales only with the number of participants colliding more than once, not including any dependence on the fireball shape, is expected. Being aware of these effects, one can investigate to which extent the $\langle p_{T}\rangle$ dependence as a function of centrality is predicted in the simple core-corona approach by the formula:

[TABLE]

$\langle p_{T}\rangle_{i}^{ppMB}$ for $\mathrm{\pi}$, K, p in pp collisions at 2.76 TeV were reported by the ALICE Collaboration Al13 .

The values for $\Lambda$ and $\Xi$ were obtained via interpolation using the values at $\sqrt{s}$=900 GeV and 7 TeV Al16 ; CMS . The values for the $\phi$ meson were taken from Al20 .

The $\langle p_{T}\rangle_{i}^{cen}$ estimated using Eq.(3) are presented in Fig.4 by open symbols for light flavor hadrons as a function of $\langle\frac{dN_{ch}}{d\eta}\rangle$. $\langle p_{T}\rangle$ values for $\Lambda$ and $\Xi$ for different centralities were obtained by fitting the $p_{T}$ spectra Al1 ; Al2 with the expression from Bil and extrapolating the measured spectra in the unmeasured regions using the fit results. The experimental results are presented by full symbols. As in the case of normalised $p_{T}$ distributions ratios, the $\langle\frac{dN_{ch}}{d\eta}\rangle$ dependence of $\langle p_{T}\rangle_{i}^{cen}$ is qualitatively reproduced by a core-corona interplay. The quantitative difference, larger than the one for the yields (Fig.2), as it was already mentioned, could be due to the fireball shape dependence of the $\frac{d^{2}N}{dydp_{T}}$ distribution as a function of $\langle\frac{dN_{ch}}{d\eta}\rangle$ (centrality). Based on these results and the following approximation for the transverse energy:

[TABLE]

where $\frac{d{E_{T}}}{dy}=\langle m_{T}\rangle\frac{dN}{dy}$ and $\langle m_{T}\rangle=\sqrt{\langle{p_{T}}\rangle^{2}+m^{2}}$, the influence of the interplay between core and corona contributions on the $\langle\frac{dE_{T}}{dy}\rangle/\langle\frac{N_{part}}{2}\rangle$ can be also estimated.

As could be noticed, Eq.(4) does not include the contribution of $\Sigma^{+}$, $\Sigma^{-}$ and the corresponding anti-baryons. The estimate of their contribution to $\langle\frac{dE_{T}}{dy}\rangle$, based on different assumptions and model predictions Al15 ; Al21 , is $\sim 2.75\%$, well within the experimental errors and model dependent predictions. As far as this does not change the conclusion on the $\langle N_{part}\rangle$ dependence of $\langle\frac{dE_{T}}{dy}\rangle$ in the core-corona approach and the experimental $\Sigma$ spectra are not yet available, we decided to not include the contribution of $\Sigma$ baryons in the present study. The results are presented in Fig.5 by open circles. The $\frac{dE_{T}}{dy}$ values estimated within the core-corona approach follow the trend obtained using in Eq.(4) the experimental values - red triangles. This estimate is in a very good agreement with the $\langle\frac{dE_{T}}{dy}\rangle$ values from Ref. Al15 - green squares.

In Fig.6 the ratio $\langle\frac{dE_{T}}{d\eta}\rangle$/$\langle\frac{dN_{ch}}{d\eta}\rangle$ as a function of $\langle N_{part}\rangle$ is represented. The ratio obtained based on the core-corona estimate - open symbols agrees with the experimental values within the error bars. This shows that in such a representation the $\langle N_{part}\rangle$ dependence of $\langle\frac{dE_{T}}{d\eta}\rangle$ and $\langle\frac{dN_{ch}}{d\eta}\rangle$ has a similar trend due to the interplay between core and corona contributions, therefore it cancels in the ratio.

In conclusion, the centrality dependence of the light flavor hadrons yields at mid-rapidity is well reproduced by a simple core-corona assumption where the corona represents the percentage of the wounded nucleons which scatter only once and the core represents the rest of wounded nucleons at a given collision centrality. The difference between the experimental ratio of normalised $p_{T}$ distributions to the average charged particle densities for Pb-Pb and minimum bias pp collisions at the same energy, the average transverse momenta and the transverse energy at mid-rapidity, as a function of centrality and the estimates using the core-corona approach can be attributed to the core shape dependence of different phenomena, like flow and suppression, which depends on the collision geometry and is not included in the present approach. The broad distribution of $N_{part}$ for a given experimentally selected centrality is also not considered in the present estimates. The results show that the corona contribution plays an important role also at energies available at the Large Hadron Collider and it has to be separated in order to evidence the centrality dependence of different observables related to the core properties and dynamics.

Acknowledgements.

This work was carried out within the 44/05.10.2011 and 2/03.01.2012 projects sponsored by Ministry of Research and Inovation via CNCSI and IFA coordinating agencies.