exotics hadrons in heavy ion collisionshim.phys.pusan.ac.kr/pds_him/him/2012/2012-02/03_him2012...1)...

Exotics hadrons

in heavy ion collisions

Heavy Ion Meeting

2012 - 02

Feb. 20-22 2012

Alpensia Resort, Pyungchang

Sungtae Cho

Institute of Physics and Applied Physics

Yonsei University

Outline

− Introduction

− Statistical model

− Coalescence model

− Production yields of exotics

− Results

− Conclusion

Feb. 20-22 2012

Alpensia, Pyungchang Heavy Ion Meeting 2012-02 2

− This talk is based on

Identifying multiquark Hadrons from heavy ion collisions,

ExHIC Collaboration, Phys. Rev. Lett., 106, 212001 (2011)

Exotic hadrons in heavy ion collisions,

ExHIC Collaboration, Phys. Rev. C, 84, 064910 (2011)

Feb. 20-22 2012


− Normal hadrons : Mesons and Baryons

− Multiquark hadrons

1) H dibaryon and scalar tetra quark (1976)

hadronic molecule (1990)

2) Hadronic molecules & multiquark states

Belle (2003)

BaBar (2003)

Feb. 20-22 2012

Alpensia, Pyungchang Heavy Ion Meeting 2012-02

)980(0f

)3872(X

)2317(sJD

KK

Introduction

4

− Normal hadrons : Mesons and Baryons

− Multiquark hadrons

1) H dibaryon and scalar tetra quark (1976)

hadronic molecule (1990)

2) Hadronic molecules & multiquark states

Belle (2003)

BaBar (2003)

Feb. 20-22 2012


)980(0f

)3872(X

)2317(sJD

KK

ccqqDDDD ,, **scqqscDK ,,

Introduction

5

− Exotic hadrons considered in this work

Feb. 20-22 2012


− The purpose of this work

1) To estimate the possibility of observing predicted exotics

with/without heavy quarks in heavy ion collision experiment

2) To find a possible solution to a problem of identifying hadronic

molecular states and/or hadrons with multiquark components

− We focus on hadron production yields

1) Normal hadron (light quark hadrons) production yields are well

described by the statistical model

2) Many aspects of the heavy ion collision experimental results

have been explained by the coalescence model

Feb. 20-22 2012


P. Braun-Munzinger, J. Stachel, J. P. Wessels, N. Xu, Phys. Lett. B344, 43 (1995)

1) In a chemically and thermally equilibrated system of non-

interacting hadrons and resonances, the particle production

yield is given by

Take the incomplete strangeness and charm equilibration into

account

2) The hadronization temperature and the chemical potential

are determined from the experimental data

Feb. 20-22 2012


ssBBcc nnnn

c e

0

/1

2

2 12 Hi TE

i

iHi

e

dppgVN

22

iii pmE

Statistical model

8

− Time evolution of quark-gluon plasma

J. D. Bjorken, Phys. Rev. D 27, 140 (1983)

i. Collision

ii. Pre-equilibrium : QGP

iii. Hadronization : Mixed phase

iv. Freeze-out : Hadron gas Feb. 20-22 2012


22 zt

9

3) The temperature obtained from the analysis of the yield

ratios reflects the stage of the freeze-out

A. Andronic, P. Braun-Munzinger, and J. Stachel, Nucl. Phys. A 772, 167 (2006)

Feb. 20-22 2012


4) The energy dependence of experimental hadron yields at

mid-rapidity in central nucleus-nucleus collisions

Feb. 20-22 2012


5) The energy dependence of hadron ratios

: The yield is the convolution of two

competing contribution as a

function of energy

i. The decreasing net light quark

ii. The increasing production of

quark-antiquark pairs

Feb. 20-22 2012


− Yields of hadrons with n constituents

describe the dynamic process of converting constituents to a bound state in the presence of a partonic matter 1) Wigner function, the coalescence probability function depends on Lorentz-invariant combinations of the relative coordinates between the particles and parametrizes the overlap integral between the particle wave functions

Feb. 20-22 2012


),,:,,(),()2(

111

1

3

3 nn

Wn

i

ii

i

iii

i

Coal ppxxfpxfE

pddp

ggN

Coalescence model

),,:,,( 11 nn

W ppxxf

n

i

nn

nn

yp

i

yx

yx

yx

yxedy ii

1

11

11

*

2,,

22,,

2

13

2) Covariant phase space density involves a Lorentz-invariant

phase space integration of a space-like hyper-surface,

which counts the number of particles contained in the system

: The hyper-surface for the spatial integration is the same for all

particles involved in the coalescence process.

− Hadron and quark coalescence

1) Confirmation of hadron mechanism, quark recombination or

quark coalescence is one of the evidences of the formation of

quark-gluon plasma in relativistic heavy ion collisions

Feb. 20-22 2012


iii

i

iii Npxf

E

pddp ),(

)2( 3

3

14

− Hadron coalescence

1) A covariant coalescence model for relativistically expanding

fireball formed in high-energy nucleus collisions is developed

and is applied to predict the formation rate of hadrons like

deuteron, or pentaquark

2) The cluster distribution factorizes for arbitrary parent rapidity

distributions : Coalescence is basically a nonrelativistic

phenomenon

Feb. 20-22 2012

Alpensia, Pyungchang Heavy Ion Meeting 2012-02 dy

dN

dy

dNC

dy

dNC 2121NCNNC

15

3) Momentum spectra of the clusters are studied to find

i. whether the transverse mass spectra of the clusters can

still be thermally parametrized if one starts with thermal parent

distribution

ii. how the longitudinal momentum distribution of the clusters is

influenced by the longitudinal expansion

4) Some details

i. A free parameter in Gaussian wave packets for the coalescence

factor is proportional to the inverse size of the cluster to be formed

ii. The coalescence rate is proportional to a volume factor which

for small clusters approaches the ratio (cluster volume/reaction

zone volume) : this dependence can be used to determine the

reaction zone volume from the coalescence yield

Feb. 20-22 2012


− Quark coalescence

or quark recombination V. Greco, C. M. Ko, and P. Levai, Phys. Rev. Lett. 90, 202302 (2003)

R. J. Freis. B. Muller, C. Nonaka, and S. Bass, Phys. Rev. Lett. 90, 202303 (2003)

1) Fragmentation picture

: A parton spectrum relates

the probability for a parton

to hadronize into a hadron, carrying a fraction z<1 of

the momentum of the

parent parton

i. The puzzle in antiproton

/pion ratio Requires a rescaling for a

fraction z for all hadrons

Feb. 20-22 2012


ii. There must be a competition between two particle

production mechanisms

: A fragmentation dominates at large transverse momenta and

a coalescence prevails at lower transverse momenta

vs.

2) Quark number scaling of the elliptic flow Denes Molnar and Sergei A. Voloshin, Phys. Rev. Lett 91, 092301 (2003)

Assumption : partons have elliptical anisotropy

Feb. 20-22 2012


z

pp

h

TFrag

T n

pp

h

TCoal

T

2

2

2

2

2

2cos

2cos)(

T

T

pT

dp

Ndd

dp

Ndd

pvT

)2cos()(212

1,2

Tq

TT

q

TT

qpv

dpp

dN

ddpp

dN

18

Coalescence model predicts

3) The coalescence model

also nicely explains the yield

of antihyperons recently

discovered in heavy ion

collision at RHIC

STAR Collaboration, Science

328, 58 (2010)

Feb. 20-22 2012


)(,2 TB pv

)2/(21

)2/(2)(

2

,2

,2

,2

Tq

Tq

TMpv

pvpv

)3/(61

)3/(3)3/(32

,2

3

,2,2

Tq

TqTq

pv

pvpv

TqTh p

nnvpv

1)( ,2,2

19

1) Evaluate the yields of exotic hadrons for all possible structure

configurations

; normal hadrons, multiquark hadrons, hadronic molecules

Feb. 20-22 2012


Production yields of exotics

),,:,,(),()2(

111

1

3

3 nn

Wn

i

ii

i

iii

i

Coal ppxxfpxfE

pddp

ggN

20

1) Evaluate the yields of exotic hadrons for all possible structure

configurations

; normal hadrons, multiquark hadrons, hadronic molecules

2) It is expected that the probability to combine n quarks into

a compact region is suppressed as n increases

Feb. 20-22 2012


),,:,,( 11 nn

W ppxxf

gN Coal

X )3872(

ccccqq*DD

Production yields of exotics

21

3) The internal structure of hadrons produced is considered

s-wave

p-wave

d-wave

4) Final results

Feb. 20-22 2012


360.0~)21(

)4(2

2/32

ii

i

i

i

TVg

N

093.0~)21(

2

3

2

)21(

)4(2

2

2

2/32

ii

ii

ii

i

i

i

T

T

TVg

N

029.0~)21(

2

15

8

)21(

)4(2

2

2

2

2/32

ii

ii

ii

i

i

i

T

T

TVg

N

n

j

ln

i ii

ii

i

i

ii

i

i

iCoal

h

i

T

T

l

l

TVg

NgN

1

1

12

2

2

2/32

)21(

2

!)!12(

!)!2(

)21(

)4(

i

i

1

i

j

jii m

m

111

1

22

− Free parameters 1) Quark coalescence :

: Reference hadrons -

2) Hadron coalescence

: The relation between the binding energy and the root mean

square radius

Feb. 20-22 2012


),1115( )2286(c

StatStatStattotalStat

CCCCNNNN )2520()2455()2286(

,

)2286(

)(67.0 ,

)2286()2625( c

totalCoalStat

CCNN

,519MeVs MeVc 385

2

0

2

2..

aEB

2

2

02 ar

22

3

r

)1405(

2

)1405(

)1405(2

3

r

MeV5.20

23

1) Summary of exotic hadrons considered (Mesons & Baryons)

Feb. 20-22 2012


Results

24

2) Estimated exotic hadron yields at RHIC and LHC

Feb. 20-22 2012


3) The loosely bound exotic hadron molecules are more produced

Normal hadron zone

The exotic multiquark

hadrons become

suppressed

Feb. 20-22 2012


Stat

i

Coal

moleculei

N

N ,2

22.0,

Stat

i

Coal

normali

N

N

2.0,

Stat

i

Coal

multiquarki

N

N

26

3) The loosely bound exotic hadron molecules are more produced

Normal hadron zone

The exotic multiquark

hadrons become

suppressed

The yield of a hadron in

relativistic heavy ion collision

reflects its structure!!

Feb. 20-22 2012


Stat

i

Coal

moleculei

N

N ,2

22.0,

Stat

i

Coal

normali

N

N

2.0,

Stat

i

Coal

multiquarki

N

N

27

4) Comparison to experimental data

: Fortunately, STAR Collaboration has a preliminary measurement

for P. Fachini [STAR Collaboration], Nucl. Phys. A 715, 462 (2003)

Can we say whether

is a tetraquark

hadron or a hadronic

molecule?

:

Feb. 20-22 2012


)980(0f

KK

2.0~

0

0 )980(

N

N f

)980(0f

28

4) Comparison to experimental data

: Fortunately, STAR Collaboration has a preliminary measurement

for P. Fachini [STAR Collaboration], Nucl. Phys. A 715, 462 (2003)

Can we say whether

is a tetraquark

hadron or a hadronic

molecule?

: At least, must

not be a tetraquark

hadron

Feb. 20-22 2012


)980(0f

KK

2.0~

0

0 )980(

N

N f

)980(0f

)980(0f

8)980( fN

29

Conclusion − The models for hadron production yields

1) Normal hadron yields are well described by the statistical model

2) Many aspects of the heavy ion collision experimental results

have been explained by the coalescence model

− Production yields of exotic hadrons from

heavy ion collisions

1) The yields of exotic hadrons are large enough to be measurable

in experiments

2) The probability to combine n quarks into a compact region is

suppressed as n increases 3) The yield of a hadron in relativistic heavy ion collision reflects is

strongly dependent on its structure

Feb. 20-22 2012


exotics hadrons in heavy ion collisionshim.phys.pusan.ac.kr/pds_him/him/2012/2012-02/03_him2012...1)...

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