PHYSICAL REVIEW C 101, 014910 (2020)
Temperature and fluid velocity on the freeze-out surface from π, K,andp spectra
in pp, p-Pb, and Pb-Pb collisions
Aleksas Mazeliauskas
*
Theoretical Physics Department, CERN, CH-1211 Genève 23, Switzerland
and Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
Vytautas Vislavicius
†
Niels Bohr Institutet, Københavns Universitet, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
(Received 12 September 2019; published 17 January 2020)
We present a new approach to take into account resonance decays in the blast-wave model fits of identified
hadron spectra. Thanks to precalculated decayed particle spectra, we are able to extract, in a matter of seconds,
the multiplicity dependence of the single freeze-out temperature T
fo
, average fluid velocity β
T
, velocity
exponent n, and the volume dV /dy of an expanding fireball. In contrast to blast-wave fits without resonance
feed-down, our approach results in a freeze-out temperature of T
fo
≈ 150 MeV, which has only weak dependence
on multiplicity and collision system. Finally, we discuss separate chemical and kinetic freeze-outs separated by
partial chemical equilibrium.
DOI: 10.1103/PhysRevC.101.014910
I. INTRODUCTION
The relativistic hadron collisions explore the properties
of dense nuclear matter at temperatures several times higher
than that of the pseudocritical QCD temperature T
c
= 156.5 ±
1.5MeV[1], i.e., the state of deconfined quarks and gluons.
Remarkably, the study of produced hadron and light nuclei
abundances indicates an apparent thermal particle production
at constant chemical freeze-out temperature T
chem
≈ T
c
,as
shown by fits of the statistical hadronization model (SHM)
[2]. Furthermore, phenomenological models based on viscous
fluid description of the quark-gluon plasma (QGP) expansion
successfully reproduce many soft hadronic observables [3–7].
Global fits to experimental data can then be used to extract the
model parameters and the transport properties of dense QCD
matter [8].
One of the earliest and simplest models of hadron produc-
tion from a flowing medium is the blast-wave model [9]. It
is based on calculating particle emission from a parametrized
freeze-out surface of temperature T
fo
and radial velocity pro-
file β
T
(r). The primary particle spectra are taken to be thermal
in the local rest frame of the fluid. Then the experimentally
observed hadrons, e.g., pions, kaons, or protons, are calculated
*
aleksas.mazeliauskas@cern.ch
†
vytautas.vislavicius@cern.ch
Published by the American Physical Society under the terms of the
Creative Commons Attribution 4.0 International license. Further
distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI. Funded
by SCOAP
3
.
by adding the decay feed-down from the short-lived primary
resonances to the initial thermal abundances. In general,
freeze-out with only direct decays gives a reasonably good
description of the data [10–12], but neglects possible rescat-
tering and regeneration of hadrons, which can be modelled
by hadronic after-burners [13,14]. The blast-wave model can
be simplified even further by using thermal spectra of pions,
kaons, and protons to directly fit the measured particle spectra.
As decay feed-down significantly modifies the magnitude and
momentum dependence of distributions, individual normal-
izations are introduced for each particle species and the mo-
mentum range for the fit is restricted [15]. In this case the ex-
tracted freeze-out temperature and radial velocity profiles are
interpreted as temperature and velocity at the kinetic particle
freeze-out. This is the routine analysis procedure performed
for measured identified particle spectra as a convenient way
to characterize and compare the soft particle production at
different centralities and collision systems [15–19].
In this paper we present a procedure for the blast-wave
model fits, which includes the feed-down from resonance
decays. We are certainly not the first to include resonance
decays in the blast-wave model, as it was done already in
[9] and other studies [10,20–22]. However, up to now the
generation of primary thermal hadrons and their decays were
two separate steps, the latter computed by either Monte Carlo
generators [23–26], or semianalytic treatments of decay in-
tegrals [27,28]. This amounts to considerable computational
costs, as for each set of model parameters a large number
of primary hadron spectra need to be generated and then
decayed through thousands of decay channels [29]. Instead
we use a recently published method of efficient calculation of
direct resonance decays [30,31]. The technique is based on
first calculating the resonance decays in the fluid rest frame
2469-9985/2020/101(1)/014910(8) 014910-1 Published by the American Physical Society