the thermal model for the light quark (u,d,s) hadrons
Post on 09-Jul-2022
4 Views
Preview:
TRANSCRIPT
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)
A.Andronic@GSI.de
“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
A.Andronic@GSI.de
...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.
A.Andronic@GSI.de
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
A.Andronic@GSI.de
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
A.Andronic@GSI.de
...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)
A.Andronic@GSI.de
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
A.Andronic@GSI.de
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
A.Andronic@GSI.de
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)
A.Andronic@GSI.de
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?
A.Andronic@GSI.de
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)A.Andronic@GSI.de
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
A.Andronic@GSI.de
“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
A.Andronic@GSI.de
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
A.Andronic@GSI.de
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
A.Andronic@GSI.de
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
A.Andronic@GSI.de
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) 334A.Andronic@GSI.de
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
A.Andronic@GSI.de
top related