The thermal model for the light quark (u,d,s) hadrons

The thermal model on the verge of the ultimate test:the LHC data

A.Andronic – GSI Darmstadt

• The thermal model for the light quark (u,d,s) hadrons

• Charmonium in the statistical hadronization model

• Summary and outlook

AA, P. Braun-Munzinger, K. Redlich, J. Stachel, PLB 678 (2009) 350

AA, P. Braun-Munzinger, J. Stachel, PLB 673 (2009) 142

AA, P. Braun-Munzinger, J. Stachel, H. Stocker, PLB 697 (2011) 203

QM11 – Annecy, 23-28 May, 2011

Thermal fits of hadron abundances

ni = Ni/V = −TV

∂ lnZi∂µ

=gi

2π2

∫ ∞

0

p2dp

exp[(Ei − µi)/T ] ± 1

quantum no. conservation:µi = µbBi + µI3I3i + µSSi + µCCi

Latest PDG hadron mass spectrum(up to 3 GeV, 485 species)

Minimize: χ2 =∑i

(Nexpi −N therm

i )2

σ2i

Ni: hadron yield ⇒ (T , µb, V )dN

/dy

-110

1

10

210

Data

STAR

PHENIX

BRAHMS

=31.6/12df/N2χModel, 3= 24 MeV, V=1950 fmbµT=164 MeV,

=200 GeVNNs

+π -π +K-

K p p Λ Λ -Ξ+

Ξ Ω φ d d K* *Σ *Λ He3/He3

only STAR data: T=162 MeV, µb=24 MeV, V=2400 fm3, χ2/Ndf=17.5/15

Hadron abundances are in agreement with a thermally equilibrated system

Energy dependence of T , µb (central collisions)

40

60

80

100

120

140

160

180

1 10 102

√sNN (GeV)

T (

MeV

)

new fits (yields)

dN/dy

parametrization

4π

0

100

200

300

400

500

600

700

800

900

1 10 102

√sNN (GeV)µ b

(MeV

)

ratios

2005 fits, dN/dy data

yields

thermal fits exhibit a limiting temperature: Tlim = 164 ± 4 MeV

T = Tlim1

1+exp(2.60−ln(√sNN (GeV))/0.45)

, µb[MeV] = 13031+0.286

√sNN (GeV)

PLB 673 (2009) 142

Volume in central collisions

10 2

10 3

10 102

103

104

√sNN (GeV)

dNch

/dy

Npart=350

148⋅√s0.30

(hep-ph/0402291)

AGS SPS RHIC LHC

E895, E877

NA49,NA44

NA50,NA60

PHOBOS,BRAHMS

ALICE

(GeV)NNs10 210 310

)3V

olum

e (f

m

0

1000

2000

3000

4000

5000 y=1)∆ (chemV=0.3 GeV/c)

T (kHBTV

central collisions

Vchem(∆y = 1) = dNch/dy|y=0/nthermch

VHBT = (2π)3/2R2sideRlong ...data from ALICE, PLB 696, 328 (2011)

[email protected]

“Birds-eye” view of some ratios

(GeV)NNs10 210 310

dN/d

y ra

tio

-410

-310

-210

-110

1

10

+πp/-π/p

symbols: data, lines: thermal model

(GeV)NNs10 210 310

dN/d

y ra

tio

0

0.05

0.1

0.15

0.2

0.25

0.3

+π/+K-π/-K

symbols: data, lines: thermal model

good agreement data-model ...but not free of some “tensions”

p,p data of STAR ad-hoc “corrected” by -25% for feed-down

[email protected]

...and the state of other “horns”

0

0.05

0.1

0.15

0.2

Λ /

π-

E895 E896NA49

STARNA57,NA44

thermal model

0

0.05

0.1

0.15

0.2

10 x

Ξ /

π-

0

0.05

0.1

0.15

0.2

10 102

103

100

x Ω

/ π-

√sNN (GeV)

0

0.05

0.1

0.15

0.2

0.25

10 102

103

√sNN (GeV)φ

/ K-

E917,E802NA49STAR PHENIX

thermal model

overall agreement model-data

Acta Phys. Pol. 40 (2009) 1005

(Hyper-)nuclei predictions

(GeV)NNs10 210 310

eve

nts

6Y

ield

(dN

/dy)

for

10

-510

-410

-310

-210

-110

1

10

210

310

410

510

610 He3He, 3

He4He, 4

H3Λ

H5ΛΛ

He6ΛΛ

He7ΞΛΛ

RHIC (√sNN=200 GeV):

T=164 MeV, µb = 24 ± 2 MeV

Ratio Exp. (STAR) Model3He/3He 0.45±0.02±0.04 0.42±0.033ΛH/3

ΛH 0.49±0.18±0.07 0.45±0.033ΛH/

3He 0.82±0.16±0.12 0.35±0.0033ΛH/3He 0.89±0.28±0.13 0.37±0.003

...discrepancy for 3ΛH/

3He?

could be resolved if an excited state of3ΛH exists

Phys.Lett.B697,203(2011)

STAR, Science 328 (2010) 58.

[email protected]

The phase diagram of QCD

0

20

40

60

80

100

120

140

160

180

200

0 200 400 600 800 1000

µb (MeV)

T (

MeV

)

E/N=1.08 GeVs/T3=7percolation

Cleymans et al.

Becattini et al.

Andronic et al.

is chemical freeze-out a determina-tion of the phase boundary?if yes, how is thermalizationachieved?

• for SPS energies and higher:

driven by the deconfinement tran-sition

PBM, Stachel, Wetterich, PLB 596 (2004) 61

• for lower energies (SIS100):

is the quarkyonic phase transitionthe “thermalizer”?McLerran, Pisarski, NPA 796 (2007) 83

AA et al., NPA 837 (2010) 65

[email protected]

The phase diagram of QCD

0

20

40

60

80

100

120

140

160

180

200

1 10 102

µb (MeV)

T (

MeV

)

thermal fits

E/N=1.08 GeV

Becattini et al.

Andronic et al.

STAR

Tc[1-0.013(µb/Tc)2], Tc=164 MeV

LQCD, Kaczmarek et al.

what will we find at LHC?

relevance for LQCD(µs = µI3 = 0)O. Kaczmarek et al., PRD 83, 014504 (2011)

does freeze-out curve follow the chiral phase

transition or crossover line at µb 6= 0?

J. Cleymans, K. Redlich PRL 81, 5284 (1998)

P. Braun-Munzinger, J. Stachel, arXiv:1101.3167

[email protected]

...and here are the predictions- π

Yie

ld r

elat

ive

to

-410

-310

-210

-110

1

T=164 MeVT=160 MeVT=166 MeV

=2.76 TeVNNsPb-Pb +π -π

+K -K

p pΛ Λ

-Ξ+

Ξ

-Ω -Ω

d d

φ

K*

++∆

*Σ*Λ

Yie

ld r

atio

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Data (STAR)

=2.76 TeVNNsPb-Pb,

=0.2 TeVNNsAu-Au,

/pp /dd He3 /He3 He4 /He4

RHIC: T=164 MeV, µb=24 MeV

LHC: T=164 MeV, µb=1 MeV

4He discovery: STAR,Nature 473, 353 (2011)

[email protected]

Statistical hadronization of heavy quarks: assumptions

P.Braun-Munzinger, J.Stachel, PLB 490 (2000) 196

• all charm quarks are produced in primary hard collisions (tcc ∼ 1/2mc ≃ 0.1 fm/c)

• survive and thermalize in QGP (thermal, but not chemical equilibrium)

• charmed hadrons are formed at chemical freeze-out together with all hadronsstatistical laws, quantum no. conservation; stat. hadronization 6= coalescence

is freeze-out at(/the?) phase boundary?

...we believe yes ...based on data in the light-quark sector (support from LQCD?)

• no J/ψ survival in QGP (full screening)

can J/ψ survive above Tc? ...not settled yet (LQCD)

Asakawa, Hatsuda, PRL 92 (2004) 012001; Mocsy, Petreczky, PRL 99 (2007) 211602

if all this supported by data, J/ψ looses status as “thermometer” of QGP...and gains status as a powerful observable for the phase boundary

[email protected]

Statistical hadronization of charm: method and inputs

• Thermal model calculation (grand canonical) T ,µB: → nthX

• Ndircc = 1

2gcV (∑i nthDi

+ nthΛi) + g2

cV (∑i nthψi

+ nthχi)

• Ncc << 1 →Canonical (J.Cleymans, K.Redlich, E.Suhonen, Z. Phys. C51 (1991) 137):

Ndircc = 1

2gcNthocI1(gcN

thoc )

I0(gcN thoc )

+ g2cN

thcc → gc (charm fugacity)

Outcome: ND = gcV nthDI1/I0 NJ/ψ = g2

cV nthJ/ψ

Inputs: T , µB, V∆y=1(= (dNexpch /dy)/nthch), Ndir

cc (pQCD or exp.)

Minimal volume for QGP: V minQGP=400 fm3

[email protected]

The “null hypothesis”

0

0.05

0.1

0.15

0.2

0.25

10 102

103

104

√sNN (GeV)

σ ψ, /

σ J/ψ

Statistical model

pApp(p

–)Data

PbPb

dataaverage

charmonium in pp(A) collisions

...is far from thermalized(model is for AA)

...while a thermal value isreached in central PbPb(NA50, SPS)

[email protected]

The “null hypothesis” for bottonium

10-2

10-1

10 102

103

104

√sNN (GeV)

Rel

ativ

e cr

oss

sect

ion

Statistical model Y,/Y

Y,,/Y

Y,/Y

Y,,/Y

bottonium in pp(A) collisions

...is far from thermalized(model is for AA)

...will we find a thermal valueat LHC?

[email protected]

J/ψ production: the ultimate test at the LHC

partN0 50 100 150 200 250 300 350 400

ψJ/ A

AR

0

0.2

0.4

0.6

0.8

1

1.2

=0.2 TeV (PHENIX)NNsData,

/dy=0.065 mb)cc

σ=0.2 TeV (dNNsModel,

=2.76 TeVNNsModel,

mid-rapidity

/dy=0.4 mbcc

σd

/dy=0.3 mbcc

σd

partN0 50 100 150 200 250 300 350 400

ψJ/ A

AR

0

0.2

0.4

0.6

0.8

1

1.2=0.2 TeV (PHENIX)NNsData,

/dy=0.030 mb)cc

σ=0.2 TeV (dNNsModel,

=2.76 TeVNNsModel,

forward y

/dy=0.25 mbcc

σd

/dy=0.15 mbcc

σd

i) less generation (more suppr.) at forward rapidity; ii) less suppression at LHC

“generic” predictions validated by data (despite uncertainty of σcc input)[email protected]

Summary and outlook

• The thermal model quite successful for light-quark hadrons (central collisions)

despite imperfect fits at SPS and RHIC (and more data at low energies needed)

• It works also for heavy quarks(...produced exclusively in hard collisions, survive and thermalize in QGP)

Good agreement with J/ψ (and ψ′) data at SPS and RHIC

(...with a smallish σcc tough)

main uncertainty is charm cross section ... experiments will provide more precisemeasurements, in particular in AA (shadowing)

The thermal model ready to be confronted with the LHC data

...while compatibility to (new) RHIC data is further scrutinized

A. Andronic - QM2011, Annecy

Backup slides

The hadron mass spectrum as of 2008

Particle Data Group, Phys. Lett. B 667 (2008) 1

Additions (compared to 2005):

Many new resonances up to 3 GeV+(86)4 (non)strange mesons+(36)30 (non)strange baryons

σ meson (f0(600)):mσ=484±17 MeV,Γσ=510±20 MeVGarcıa-Martın, Pelaez, Yndurain, Phys. Rev. D 76

(2007) 074034

(in total 485 hadron species, incl. com-posites)

relative increase of calc. dens.

0.95

1

1.05

1.1

1.15

1.2

1.25

10 102

103

104

√sNN (GeV)

Rel

ativ

e pr

oduc

tion

π+

with high-mass resonances

with res. and σ(484,510)

50

100

150

200

250

300

350

400

450

T (

MeV

)

Temperature

PLB 673 (2009) 142

[email protected]

“The horn” as of 2009

0

0.05

0.1

0.15

0.2

0.25

K+ /

π+

E866,E895E802,E866NA49STAR

NA44PHENIX

thermal model

60

80

100

120

140

160

T (

Me

V)

T

0

0.025

0.05

0.075

0.1

0.125

0.15

0.175

0.2

10 102

103

Λ /

π-

E895 E896NA49

STARNA57,NA44

thermal model

0

100

200

300

400

500

600

700

800

µ b (

Me

V)

µb

√sNN (GeV)

much better explained by the model

...as due to detailed features of thehadron mass spectrum...which leads to a limiting temperature(“Hagedorn”, T < TH)...and contains the QCD phase transition

the horn’s sensitivity to the phase bound-ary is determined (via strangeness neu-trality condition) by the Λ abundance(determined by both T and µb)

PLB 673 (2009) 142

[email protected]

J/ψ: ”core” and ”corona”

realistic nuclei: ”core” (QGP, apply stat. hadr.) and ”corona” (NN coll.)

N coreJ/ψ

= g2cnthJ/ψ

V core

gc ∼ Ndircc = N core

coll σppcc /σ

ppinel

N coronaJ/ψ

= N coronacoll σ

ppJ/ψ

/σppinel

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350

Npart

Cor

ona

fract

ion

Au+Au

⇒ NJ/ψ = N coreJ/ψ

+ N coronaJ/ψ

[email protected]

Timescales for charm(onium) production

Karsch & Petronzio, PLB 193 (1987) 105, Blaizot & Ollitrault, PRD 39 (1989) 232

• QGP formation time, tQGP

– SPS (FAIR): tQGP ≃ 1 fm/c ∼ tJ/ψ– RHIC, LHC: tQGP . 0.1 fm/c ∼ tcc

survival of initially-produced J/ψ at SPS/FAIR energies? (Td ∼ Tc)

• collision time, tcoll = 2R/γcm

– SPS (FAIR): tcoll & tJ/ψ– RHIC: tcoll < tJ/ψ, LHC: tcoll << tJ/ψ

cold nuclear suppression (breakup by initial nucleons) important at SPS/FAIRenergies but not at RHIC and LHC

shadowing is yet another (cold nuclear) effect - important at LHC (RHIC?)

NB: the only way to distinguish: measure σcc in pA and AA

[email protected]

J/ψ at RHIC: rapidity dependence, RAA

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-2 -1 0 1 2

Au+Au 0-20% (Npart=280)R

AAJ/

ψ

-2 -1 0 1 2

Au+Au 20-40% (Npart=140)

y

model reproduces data (PHENIX, nucl-ex/0611020) very well (pQCD σcc)

direct indication of J/ψ generation at hadronization (enhanced at y=0)

(constant RAA expected within Debye screening model)

Phys. Lett. B 652 (2007) 259

J/ψ at RHIC: effect of shadowing

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-2 -1 0 1 2

σcc: pQCD FONLLσcc: PHENIX+shadowing(dAu)

Au+Au 0-20% (Npart=280)

RA

AJ/ψ

-2 -1 0 1 2

Au+Au 20-40% (Npart=140)

y

model describes data with PHENIX σcc (lower error plotted)J. Phys. G 35 (2008) 104155

[email protected]

J/ψ production relative to charm

0

0.2

0.4

0.6

0.8

1

1.2

50 100 150 200 250 300 350

Npart

100

x (d

NJ/

ψ /d

y) /

(dN

cc /d

y)

SPS (dσcc/dy=5.7 µb)

RHIC (dσcc/dy=63.1 µb)

LHC (dσcc/dy=639 µb)

pp, PHENIX data • ...the most ”solid” observable

...with similar features as RAA

• similar values at RHIC and SPS

...with differences in fine details

...determined by canonical sup-pression of open charm

• enhancement-like at LHC

can. suppr. lifted, quadratic termdominant

Nucl. Phys. A 789 (2007) [email protected]

J/ψ at LHC

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

50 100 150 200 250 300 350

Npart

100

x (d

NJ/

ψ /d

y) /

(dN

cc /d

y)

dσcc/dy (mb)

0.32

0.43

0.64

0.85

1.28

J. Phys. G 35 (2008) 104155

solid expectations for LHC

...providing we know well (from mea-surements) the charm productioncross section in Pb-Pb

agreement that (re)generation is thegame at LHC?

Liu, Qu, Xu, Zhuang, arXiv:0907.2723Song, Park, Lee, arXiv:1002.1884

“2-component” (kinetic, coales-cence) models

...as Grandchamp, Rapp, PLB 523 (2001) 60, NPA

709 (2002) 415

[email protected]

Documents

The thermal model for the light quark (u,d,s) hadrons