Confronting anomalous kaon correlations measured in Pb-Pb collisions atpsNN 276 TeV Joseph I. Kapusta1Scott Pratt2and Mayank Singh1

2025-04-27 0 0 502.31KB 12 页 10玖币

侵权投诉

Confronting anomalous kaon correlations measured in Pb-Pb collisions at √sN N = 2.76

TeV

Joseph I. Kapusta,1Scott Pratt,2and Mayank Singh1

1School of Physics & Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

2Department of Physics and Astronomy and Facility for Rare Isotope Beams

Michigan State University, East Lansing, MI 48824 USA

Measurements of the dynamical correlations between neutral and charged kaons in central Pb-Pb

collisions at √sNN = 2.76 TeV by the ALICE Collaboration display anomalous behavior relative

to conventional heavy-ion collision simulators such as AMPT, EPOS, and HIJING. We consider

other conventional statistical models, none of which can reproduce the magnitude and centrality

dependence of the correlations. The data can be reproduced by coherent emission from domains

which grow in number and volume with increasing centrality. We show that the energy released by

condensation of strange quarks may be suﬃcient to explain the anomaly.

I. INTRODUCTION

High energy heavy-ion collision experiments help us ex-

plore the deconﬁned state of QCD matter. The Quark-

Gluon Plasma (QGP) created in these experiments ex-

pands and cools to form hadrons on timescales on the

order of ten fm/c. We infer the properties of the QGP

from the yields and correlations of these hadrons.

The ALICE Collaboration has measured the correla-

tion function νdyn(K0

S, K±) as a function of multiplic-

ity and transverse momentum in Pb-Pb collisions at

√sNN = 2.76 TeV [1]. These measurements stand in

contrast to the predictions made using standard heavy-

ion simulators [2], including AMPT, EPOS, and HIJING.

The purpose of this paper is to construct a simple model,

based on the condensation of strange quark and anti-

quark pairs, in an attempt to reproduce the data, and

to explore the degree to which other, less exotic, physics

might explain the ALICE results. The proposed disor-

dered chiral condensate (DCC) [3] state is expected to

give anomalaous values of νdyn(K0

S, K±) which could ex-

plain the data, though we show in this work that an

ordinary strange condensate will give a similar result.

The νdyn(A,B) measures the degree to which the obser-

vation of particles of types Aand Bare more correlated

with themselves than with each other,

νdyn(A, B) = RAA +RBB −2RAB,

RAB =hNANBi−hNAiδAB

hNAihNBi−1,(1)

where the symbols h···i refer to averages over events.

The second term, proportional to δAB , subtracts the con-

tribution of a particle with itself. If particles were uncor-

related with one another, one would have RAA =RBB =

RAB = 0, and νdyn would vanish. That is the reason

for referring to this correlation function as dynamical. If

νdyn(A, B)>0, it implies that the observation of an Aor

Btype particle more strongly biases a second particle to-

ward being the same type. For the ALICE measurement

the two types of particles were charged kaons, either K+

or K−, and neutral kaons, i.e. K0

Smesons. Positive val-

ues of νdyn(K0

S, K±) can result from decays, such as the

φmeson, which decays into either two charged kaons or

two neutral kaons. Other sources can be charge conser-

vation, or anomalously strong Bose enhancement from

condensation or coherent emission.

Background sources of correlation, such as decays and

charge conservation, largely correlate two particles with

one another. In such cases νdyn scales inversely with

the multiplicity. For this reason, ALICE multiplied νdyn

by a factor 1/α, which is inversely proportional to the

multiplicity

1/α =NK±NK0

NK±+NK0

,(2)

where NK±and NK0

Srefer to the average number of

charged and K0

Smesons observed per event. If one cor-

rects for multiplicity, and if the number of charged and

neutral kaons were equal, 1/α would become one sixth

the total number of kaons.

We present a phenomenological model with coherent

emission in Sec. II. We ﬁnd that the data can be repro-

duced if a suﬃcient fraction of the kaons were to origi-

nate from coherent sources of suﬃcient size. Section III

considers simple systems to illustrate the eﬀects of de-

cays, charge conservation, and Bose symmetrization. We

ﬁnd that generating large correlations requires that many

kaons are in the same quantum state, as occurs in Bose

condensation. Section IV shows results of a purely ther-

mal model with charge conservation. The resulting corre-

lation from this model also comes well short of the data.

Section V calculates the energy available from strange

quark condensation in several versions of the linear sigma

model. Conclusions from this study, along with prospects

and suggestions for future study, are given in Sec. VI.

II. ISOSPIN FLUCTUATIONS FROM

CONDENSATES

The observable which isolates isospin ﬂuctuations is

νdyn as discussed earlier. The ALICE Collaboration

measured the number of short-lived kaons K0

Sand the

number of positively and negatively charged kaons K+

arXiv:2210.03257v1 [hep-ph] 6 Oct 2022

and K−to construct νdyn(K0

S, K±) [1]. Table I shows

some of the experimental data. The numbers marked

with an asterix were interpolated from 966.0 in the

10-20% bin. From the data there is a best ﬁt rela-

tion where dNch/dη = 1.317N1.19

part. Conversely Ntot

K≈

0.113 dNch/dη as one would expect from an isothermal

freeze-out model. In either case the 60-80% bin appears

anomalous and has been excluded from these ﬁts. The

quantity αwas deﬁned as

α=1

NK0

NK±

.(3)

For a ﬁrst analysis we assume that kaons of all four kinds

are produced in equal numbers despite the fact that K0

was measured in a slightly diﬀerent range in momentum

space than the charged kaons.

Centrality νdyn νdyn/α 1/α NK0

S≡3/2αNK±≡3/α dNch/dη Npart

0-5 % 0.006827 ±0.00068 0.213 ±0.021 31.20 46.80 93.60 1601.0 382.8

5-10 % 0.006927 ±0.00069 0.169 ±0.017 24.40 36.60 73.20 1294.0 329.7

10-15 % 0.006993 ±0.0007 0.141 ±0.014 20.16 30.24 60.48 1075.0* 281.1

15-20 % 0.007226 ±0.0007 0.113 ±0.011 15.64 23.46 46.92 857.0* 238.6

20-40 % 0.008307 ±0.0008 0.080 ±0.010 9.630 14.45 28.89 537.50 157.2

40-60 % 0.016430 ±0.00167 0.066 ±0.007 4.02 6.03 12.06 205.0 68.56

60-80 % 0.025130 ±0.0022 0.053 ±0.005 2.11 3.17 6.33 55.50 22.52

TABLE I. Summary of the relevant νdyn experimental data from Table 2 of Ref. [1]. The charged particle pseudo-rapidity

densities are taken from [4] and the number of participants from [5].

ALICE found that the correlations are spread across

pseudo-rapidity but are restricted in transverse momen-

tum. This indicates that the coherent kaons likely orig-

inate in diﬀerent domains which extend to at least 1.5

units in pseudo-rapidity and are moving at diﬀerent ve-

locities depending on their transverse position in the pro-

duced matter. In the language of DCC, the data favors

the domains picture [6] as opposed to the “Baked Alaska”

picture where there is a single DCC at the center with

the expanding ﬁreball on the outside [7].

A simple formula for νdyn was derived in Ref. [8]. It is

νdyn = 4βKβK

3Nd−1

Ntot

K(4)

where βKis the fraction of all kaons coming from con-

densates, Ndis the number of domains, and Ntot

Kis the

total number of kaons regardless of their charge or source.

This formula is based on several assumptions. (1) There

are two sources for each domain. One is a coherent source

which, by deﬁnition, has a distribution of the fraction f

of neutral kaons which is equal to one (which is the case

for strange DCC [9]) while the other (random) source is

a Gaussian with a width determined by the number of

kaons. (2) Domains are independent of each other. (3)

The number of domains is greater than two.

The fraction of kaons from condensates can be esti-

mated as

βK=ζVd

mKNtot

(5)

where ζis the energy density of condensation which is

converted to kaons and Vdis the total volume of all such

domains.

In the DCC picture domain size should be limited by

causality, and that is related to the lifetime of the system.

In order to estimate the latter, we use results from Pb-

Pb collisions at √sNN = 2.76 TeV as simulated by the

relativistic 2nd order viscous hydrodynamic code MU-

SIC, with IP-Glasma initial conditions and initial proper

time τ0= 0.4 fm/c [10]. For a given event, the ﬂuid cell

with the highest initial temperature was followed until

it expanded and cooled to some temperature of inter-

est, and the proper time duration (not including τ0) was

recorded. Averaged over events in a given multiplicity

window yielded a numerical value τav. The results are

shown in the Table II, with τav in units of fm/c. If the

expansion is primarily one dimensional then one would

expect Nd/Vdto scale as 1/τav. Being an intensive quan-

tity, Nd/Vdshould be independent of the total charged

particle multiplicity dNch/dη. On the other hand, both

Vdand Ndshould be proportional to dNch/dη. Taken

together it means that νdyn will depend on centrality.

The experimental data for νdyn(K±, K0

S)/α is plotted as

a function of dNch/dη in Fig. 1(a) and as a function of

time in Fig. 1(b). In both cases the data exhibits greater

than linear growth.

To reproduce the data, we assume that the number

of domains scales with the total kaon multiplicity which

Centrality T= 160 MeV T= 150 MeV T= 140 MeV

0-5 % 11.56 13.27 14.93

5-10 % 10.84 12.48 14.39

10-15 % 10.22 11.78 13.84

15-20 % 9.81 11.52 12.98

20-25 % 9.31 10.72 12.10

25-30 % 9.05 10.15 11.89

30-35 % 8.47 9.69 11.11

35-40 % 7.88 8.81 10.53

40-45 % 7.24 8.61 9.83

45-50 % 6.88 7.51 8.94

TABLE II. Proper time elapsed in fm/c beginning at the start

of hydrodynamic ﬂow and ending at the indicated tempera-

ture using the hydrodynamic code MUSIC with IP Glasma

initial conditions [10]. Chemical equilibration happens at

about 160 MeV.

scales with dNch/dη so that

Nd=aNtot

Vd=v0Ntot

Kτav

10τ0,(6)

where the factor of 10 is inserted simply as a matter of

numerical convenience. Then

βK=bτav

10τ0(7)

where

b=ζv0

(8)

which results in

νdyn = 4bτav

10τ0 b

3aτav

10τ0−11

Ntot

νdyn

α=2

3bτav

10τ0 b

3aτav

10τ0−1.(9)

A ﬁt to the ﬁve highest multiplicity bins yields b=

0.1044 ±0.0380 and b2/a = 0.2187 ±0.0458 as shown in

Fig. 2. We assume that chemical freeze-out occurs at

T= 160 MeV. The ﬁt only determines the product of ζ

with v0. Using as a reference ζ= 25 MeV/fm3we have

v0= 2.07 25 MeV/fm3

ζfm3.(10)

Table III shows the results with the reference ζ= 25

MeV/fm3. We use the extrapolated value of τav for the

20-40% bin to be 8.62 fm/c and for the 40-60% bin to be

6.60 fm/c so that we can ﬁll in the table. If, for example,

ζ= 50 MeV/fm3instead, the number of sources Nddoes

not change but the volume Vdis halved.

FIG. 1. The correlation νdyn(K±, K0

S)/α from the ALICE

Collaboration is plotted against the charged multiplicity, also

measured by ALICE (a) and against the duration of the col-

lision in the deconﬁned phase, as estimated by hydrodynamic

calculations (b). Times are shown for three choices of de-

conﬁnement temperatures: 140, 150 and 160 MeV. The cor-

relation increases roughly linearly with the multiplicity, and

stronger than linear with the collision duration.

Centrality NdVd(fm3)βK

0-5 % 9.32 1120 0.302

5-10 % 7.29 821 0.283

10-15 % 6.02 640 0.267

15-20 % 4.67 476 0.256

20-40 % 2.88 258 0.225

40-60 % 1.20 82 0.172

TABLE III. The number of domains Ndand the total volume

Vdoccupied by them. The two parameter ﬁt was made to the

ﬁve highest multiplicity bins. This assumes ζ= 25 MeV/fm3.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

ConfrontinganomalouskaoncorrelationsmeasuredinPb-PbcollisionsatpsNN=2:76TeVJosephI.Kapusta,1ScottPratt,2andMayankSingh11SchoolofPhysics&Astronomy,UniversityofMinnesota,Minneapolis,MN55455,USA2DepartmentofPhysicsandAstronomyandFacilityforRareIsotopeBeamsMichiganStateUniversity,EastLansing,MI48824USAM...

展开>> 收起<<

Confronting anomalous kaon correlations measured in Pb-Pb collisions atpsNN 276 TeV Joseph I. Kapusta1Scott Pratt2and Mayank Singh1.pdf

共12页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Confronting anomalous kaon correlations measured in Pb-Pb collisions atpsNN 276 TeV Joseph I. Kapusta1Scott Pratt2and Mayank Singh1

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: