Using the -meson elliptic flow to map the strength of partonic interaction
A compilation of recently measured STAR data for elliptic flow () of mesons in RHIC Beam Energy Scan program and comparison with a multiphase transport model (AMPT) has been presented. The experimental data at 19.6 GeV agrees well with string melting version of the AMPT model. The model includes partonic interactions and quark coalescence as a mechanism of hadronization. This indicates that there is a substantial contribution to collectivity from partonic interactions at 19.6 GeV. The measured -meson at = 7.7 and 11.5 GeV are found to be smaller than those obtained from AMPT model without partonic interactions. This indicates negligible contribution of partonic collectivity to the observed -meson at 11.5 GeV.
One of the main goals of the high energy heavy-ion collision experiments is to study the various aspects of the
QCD phase diagram whitepapers (). With this purpose the Relativistic Heavy Ion
Collider (RHIC) has finished the first phase of the Beam Energy Scan (BES)
program bes_res1 (); v2_BES_prc (); v2_BES_prl (). The aim of the BES program was to look for changes in
observation of various measurements as a function of beam energy to
establish transition region between the partonic and/or hadronic
dominant interactions in the QCD phase diagram bes_moti ().
The elliptic flow parameter is a good tool for studying the system formed in the early stages of high energy collisions at RHIC hydro (); hydro1 (); hydro2 (); hydro3 (); hydro4 (). It describes the azimuthal momentum anisotropy of particle emission in heavy-ion collisions. It is defined as the second harmonic coefficient of the azimuthal Fourier decomposition of the momentum distribution with respect to the reaction plane angle () and can be written as
where is emission azimuthal angle method ().
According to hydrodynamical description is an early time phenomenon and sensitive to the
equation of state of the system formed in the collision hydro (); hydro1 (); hydro2 (); hydro3 (); hydro4 (); early_v2 ().
The results from Relativistic Heavy Ion Collider (RHIC) on as a
function of transverse momentum () shows
that at low elliptic flow of identified
hadrons follows mass ordering (lower for heavier hadrons than that of
lighter hadrons) whereas at intermediate all
mesons and all baryons form two different groups.
When and are scaled by number of constituent
quarks of the hadrons, the measured values are consistent with
each other as the parton coalescence or recombination models
predicted ncq1 (); ncq1a (); ncq_phi (). This observation, is known as
number of constituents quark scaling (NCQ scaling). This effect has been interpreted as
collectivity being developed at the partonic stage of the evolution
of the system in heavy-ion collision ncq2 ().
Although the parton coalescence or recombination model can successfully explain the observed quark scaling in experimental data but one can not say that only NCQ scaling of identified hadrons ncq2 () is sufficient signature for the formation of de-confined matter. The study of NCQ scaling of identified hadrons from UrQMD model shows that the pure hadronic medium can also reproduced such scaling in ncq_urqmd1 (); ncq_urqmd2 (); ncq_urqmd3 (). This is due to modification of initially developed by later stage hadronic interactions ncq_urqmd2 (). So the of those particles which do not interact with hadronic interaction will be the clean and good probe for early dynamics in heavy-ion collisions. The meson, which is the bound state of and quark, has small interaction cross-section with other hadrons smallx () and freezes out early whitepapers (). Due to small hadronic interaction cross-section, -mesons are almost unaffected by later stage interaction and it will have negligible value if mesons are not produced via and quark coalescence NBN (); BN (). Therefore, it is very important to study the -meson in BES program at RHIC.
The paper is organized in the following way. In the section II, AMPT model has been briefly discussed. Section III describe the comparison of experimentally measured -meson with the corresponding results from the AMPT model (version 1.11). Finally the summary and conclusion has been discussed in section IV.
Ii The AMPT Model
The AMPT model, which is a hybrid transport model, has four main stages: the initial conditions,
partonic interactions, the conversion from the partonic to
the hadronic matter, and hadronic interactions ampt (). It uses the same initial conditions from HIJING hijing ().
Scattering among partons are modelled by Zhangâs parton cascade ZPC (), which calculates two-body parton scatterings
using cross sections from pQCD with screening masses. In the default
AMPT model, partons are recombined
with their parent strings and when they stop interacting,
the resulting strings fragment into hadrons according to the Lund
string fragmentation model lund (). However
in the string melting scenario (labeled as AMPT-SM), these strings are converted
to soft partons and a quark coalescence
model is used to combine parton into hadrons. The
evolution dynamics of the hadronic matter is described
by A Relativistic Transport (ART) model. The interactions between the minijet partons in the AMPT Default model and those between partons in the
AMPT-SM could give rise to substantial . Therefore, agreement between the data
and the results from AMPT-SM would indicate the contribution of
partonic interactions to the measured . The parton-parton interaction cross section
in the string-melting version of the AMPT is taken to be 3mb and 10
mb. In this study,
approximately 1.5 million events for each configuration were
generated for minimum-bias Au+Au collisions.
Iii Results and Discussion
In this section, the -meson measured by STAR experiment
at mid-rapidity ( 1.0) for = 7.7 - 200 GeV v2_BES_prc (); v2_BES_prl () has been compared with AMPT model.
mesons are identified from the and decay
channel, the same method as used in experimental analysis.
Figure 1 shows the comparison of elliptic flow of mesons in 0-80 minimum-bias Au+Au collisions at mid-rapidity ( 1.0) for = 7.7, 11.5, 19.6, 27, 39 and 62.4 GeV with the corresponding results from the AMPT model v2_BES_prc (); v2_BES_prl (). The measured data points are compared with both AMPT String Melting (3 mb and 10 mb parton-parton cross-section) and AMPT Default version. At = 62.4 GeV experimental data are in a good agreement with AMPT String Melting model with 10 mb parton-parton cross-section. This is also true for = 200 GeV as reported in Ref. NBN (). The measured , for GeV/c, lie between 3 mb and 10 mb for the energy range 39 GeV, but in order to explain the measurements for GeV/c, a parton-parton cross-section of the oder of 10 mb is required. None of the above model can explain the trend of -mesons at = 7.7 and 11.5 GeV where the event statistics for data is also small. As we expect that the -meson mostly reflect the collectivity from the partonic phase, therefore from the comparison of experimental data with AMPT model one can conclude that the partonic collectivity has been developed for 19.6 GeV at RHIC. Whereas the contribution from the partonic collectivity to the final collectivity seems negligible at 11.5 GeV.
iii.2 Integrated Elliptic Flow ()
The integrated elliptic flow , which is also an interesting observable, can be defined as:
i.e. the folds the measured versus with the distribution () of that particle.
The -averaged may have a better statistical precision than the differential measurements. To calculate the of mesons, each distribution was fitted with function (shown in Fig. 2): a order polynomial function and a function of the form
where , , and are free parameters and is the number of constituent quarks. This function was inspired by parameterizations of quark number scaling ncq_fit_xin (). The distribution of mesons has been fitted with Levy function as shown in panel (b) of Fig. 2. The functional form of Levy function is given by
where is known as the inverse slope parameter, is the -meson yield
per unit rapidity, is the rest mass of meson and is the Levy function
The for each choice of parameterization is given by the
integral of the corresponding distributions normalized by integral of
the distribution. In addition, the has
been calculated directly from measured data points of
with corresponding yield obtained from the fit function to the distribution. The final was
obtained by calculating the mean of the three
results and the systematic error was estimated from maximum deviation
from the mean value. There are two sources for the statistical error, one is error on
distribution and other is error on . Since the error on
is very small compared to that on , one can
simply neglect the error of . Hence, only errors on
are taken care for calculation of final statistical error on . The errors on are parameterized as a function of and extrapolated
to low and high as shown in panel (c) of
Fig. 2. Figure 2 is repeated for all the energies studied.
For calculation in data, the final
mesons spectra and at 62.4 and 200 GeV published by STAR has been
used phi_200_prc (). For the other energies, the STAR preliminary spectra xp_QM () and final
v2_BES_prc () has been used.
The integrated -meson for Au+Au minimum-bias collisions at mid-rapidity( 1.0 ) are compared to the corresponding AMPT model calculation at various beam energies in Fig. 3. In contrast to observations from the data, the values from model remain constant for all the energies for a given parton-parton interaction cross-section. The of mesons for 19.6 can be explained by the AMPT with string melting depending on parton-parton cross-section. The AMPT-SM model with 10mb parton-parton cross-section explain the data very well at =62.4 and 200 GeV, where as 3mb parton-parton cross-section is sufficient to describe the data at = 19.6, 27 and 39 GeV. On the other hand, both the AMPT-SM and AMPT Default model over predict data at = 11.5 GeV, indicating negligible contribution of the partonic collectivity to the final collectivity. Due to very small statistics at = 7.7 GeV, are not shown here. The observation that different parton-parton cross sections are needed to explain the data within the transport model framework indicates that the / changes with beam energy. Higher the cross section, smaller is the / expected for the system. This qualitative observation of variation in the value of / with beam energy is consistent with the expectations from various calculations as reported in eta_by_s ().
From the Fig. 3 , one can conclude that as the energy decrease contribution to the collectivity from the partonic phase also decreases and for 11.5 GeV, the hadronic interaction plays a dominant role in experimentally observed data.
Iv Summary and Conclusion
In summary, a compilation of the available data for elliptic flow of
mesons has been presented. The implications of these results on the quark-hadron phase
transition has been discussed by comparing experimental data with
AMPT model. The AMPT model with string melting scenario
quantitively explain the data at 19.6 GeV by
varying parton-parton interaction cross-section from 3mb to 10mb.
AMPT Default model under predict that experimental data for
19.6 GeV. This tells that there is a substantial
contribution of partonic collectivity to the final collectivity for 19.6 GeV.
However, both the AMPT-SM and AMPT Default can not explain the trend of
-meson as function of at = 7.7
and 11.5 GeV. Also the from AMPT default
over-predicts the data at = 11.5 GeV. This indicates
that possible turn off of partonic interaction starts at
11.5 GeV. Due to large statistical error on at
= 7.7 GeV, it is not possible to make any conclusions.
The comparison of the experimental data on the beam energy dependence
of the average elliptic flow of meson with the corresponding results from a transport model calculation with varying parton-parton cross section suggests that the partonic contribution to the collectivity decreases and possibly the value of the / of the system increases as the beam energy decreases.
The -meson measurement should be one of the main focuses
in the proposed BES phase II program and also in FAIR experiment at
GSI to explore the phase diagram further.
I thank Dr. Bedangadas Mohanty for useful discussions and help in the preparation of the manuscript. Financial support from DST SwarnaJanti project, Government of India is gratefully acknowledged.
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