Transcript Third Moments in Heavy Ion Collisions - uni

xQCD, Bad Honnef, June 22, 2010
Third Moments of Conserved Charges
as Probes of QCD Phase Structure
Masakiyo Kitazawa
(Osaka Univ.)
M. Asakawa, S. Ejiri and MK,
PRL103, 262301 (2009).
Phase Diagram of QCD
T
Quark-Gluon Plasma
QCD critical point
Hadrons
Color SC
m
0
How can we map these components of phase
diagram in heavy-ion collision experiments?
Third moments of conserved charges
(including skewness) would smartly do this!
Fluctuations at QCD Critical Point
Stephanov, Rajagopal, Shuryak ’98,’99
2nd order phase transition at the CP.
baryon # susceptibility
divergences of fluctuations of
•pT distribution
•freezeout T
•baryon number,
proton, chage, …
However,
•Region with large fluctuations may be narrow.
•Fluctuations may not be formed well due to critical slowing down.
•Fluctuations will be blurred by final state interaction.
Asakawa, Heinz, Muller, ’00
Jeon, Koch, ’00
(Net-)Charge Fluctuations
D-measure: D  4
( N Q ) 2
NQ
N ch
Dy
NQ: net charge # / Nch: total #
hadrons:

values of D:

0


D ~ 3-4


0




quark-gluon:
u
g d
g
d
s d
largesmall
s
g
u
g
u
g
D~1
When is experimentally measured D formed?
•Conserved charges can remember fluctuations
at early stage, if diffusions are sufficiently slow.
Experimental Results for D-measure
RHIC results: D ~ 3
PHENIX ’02, STAR ’03
•hadron gas: D ~ 3-4
•free quark-gluon gas: D ~ 1
•Failure of QGP formation?
•Is the diffusion so fast?
STAR, ’10
NO! The result does not contradict these statements.
Large uncertainty in Nch. Bialas(’02), Nonaka, et al.(’05)
Higher Order Moments
Ratios between higher order
moments (cumulants)
RBC-Bielefeld ’09
Ejiri, Karsch, Redlich, ’05
Gupta, ’09
4th/2nd at m =0 reflects the charge
of quasi-particles
Hadrons:1
Quarks:1/32
Higher order moments increase much faster near the CP.
Stephanov, ’09
We want much clearer signals to map
the phase diagram, such as changing signs.
Take a Derivative of cB
cB has an edge along the phase boundary
c B
changes the sign at
m B QCD phase boundary!
Note:
( N B ) 2
1  2
cB  

2
V m B
VT
( N B )3
c B
1  3


 m3 (BBB)
3
2
m B
V m B
VT
•m3(BBB) can be measured by event-by-event
analysis if NB in Dy is determined for each event.
: third moment
of fluctuations
NB
Dy
Impact of Negative Third Moments
Once negative m3(BBB) is established, it is evidences that
(1) cB has a peak structure in the QCD phase diagram.
(2) Hot matter beyond the peak is created in the collisions.
•No dependence on any specific models.
•Just the sign! No normalization (such as by Nch).
Third Moment of Electric Charge
Experimentally,
•net baryon # in Dy : difficult to measure
•net charge # in Dy : measurable!
m3 (QQQ) 
( N Q )3
VT
2
1  3

V mQ3
mQ : chemical potential
associated to NQ
Third Moment of Electric Charge
Experimentally,
•net baryon # in Dy : difficult to measure
•net charge # in Dy : measurable!
m3 (QQQ) 
( N Q )3
VT
2
1  3

V mQ3
mQ : chemical potential
associated to NQ
Under isospin symmetry,
m3 (QQQ) 
1   1

c

c
B
I 

8 mB  27

singular @CEP
isospin susceptibility
(nonsingular)
Hatta, Stephanov ’02
cB
cI/9
The Ridge of Susceptibility
Region with m3(BBB)<0 is limited near the critical point:
= 0 at mB=0
m3(BBB)
(C-symmetry)
is positive for small mB (from Lattice QCD)
~ mB at mB>>LQCD (since ~mB4 for free Fermi gas)
T
m
The Ridge of Susceptibility
Region with m3(BBB)<0 is limited near the critical point:
= 0 at mB=0
m3(BBB)
(C-symmetry)
is positive for small mB (from Lattice QCD)
~ mB at mB>>LQCD (since ~mB4 for free Fermi gas)
Analysis in NJL model:
T
m3(BBB)<0
m3(QQQ)<0
m
Proton # Skewness @STAR
STAR, 1004.4959
Measurement of the skewness
of proton number @STAR
shows that ( N P )3  0
for 19.6-200GeV.
Proton # Skewness @STAR
STAR, 1004.4959
Measurement of the skewness
of proton number @STAR
shows that ( N P )3  0
for 19.6-200GeV.
Remark: Proton number, NP, is not a conserved charge.
No geometrical connection b/w 2nd & 3rd moments.
( N P )3
VT 2


( N P ) 2
m P
VT
m3 (BBB) 
c B
mB
Derivative along T Direction
T

T

T

mˆ

m
 m 

T T m
mˆ  m / T
m
m3 (BBE) 
m3 (QQE) 
( N B ) 2  E
VT 3
( NQ ) 2  E
VT 3
1  (T c B )

T T mˆ
1  (T c Q )

T T mˆ
E : total energy in a subvolume
measurable experimentally
Signs of m3(BBE) and m3(QQE)
change at the critical point, too.
mˆ  m / T
More Third Moments
m3 (EEE) 
m3 (BEE ) 
m3 (QEE ) 
( E )
1  (T Cmˆ )
 3
T
T
mˆ
3
2
VT 5
 N B ( E ) 2
VT 4
 N Q ( E ) 2
VT 4
1 Cmˆ

T m B
V T

2
mˆ
VT 2

T

T

m
mˆ
m
1 Cmˆ

2T m B
“specific heat” at constant mˆ
2
2
(

E
)
T 
Cmˆ  
T
•diverges at critical point
•edge along phase boundary
mˆ  m / T
More Third Moments
m3 (EEE) 
m3 (BEE ) 
m3 (QEE ) 
( E )
2
VT 5
 N B ( E ) 2
VT 4
 N Q ( E ) 2
VT 4
V T

2
mˆ

T

T

m
1 Cmˆ

T m B
mˆ
m
1 Cmˆ

2T m B
“specific heat” at constant mˆ
2
2
(

E
)
T 
Cmˆ  
T
1  (T Cmˆ )
 3
T
T
mˆ
3
•diverges at critical point
•edge along phase boundary
VT 2
Signs of these three moments change, too!
Model Analysis
2-flavor NJL;
G=5.5GeV-2, mq=5.5MeV, L=631MeV
•Regions with m3(*EE)<0 exist even on T-axis.
 This behavior can be checked •on the lattice
•at RHIC and LHC energies
Trails to the Edge of Mountains
m3(EEE) on the T-axis
•Experimentally: RHIC and LHC
1 (T 2C ) 1  T 3S
 3
•On the lattice: m3 (EEE)  3
T
T
T T T
Trails to the Edge of Mountains
m3(EEE) on the T-axis
•Experimentally: RHIC and LHC
1 (T 2C ) 1  T 3S
 3
•On the lattice: m3 (EEE)  3
T
T
T T T
m3(QQQ), etc. at mB>0
•Experimentally: energy scan at RHIC
•On the lattice: ex.) Taylor expansion
  c2 mB2  c4 mB4  c6 mB6 
c4
c6
m3 (BBB) ~ c4 mB  5c6 mB3 
Cheng, et al. ‘08
Summary 1
Seven third moments
m3(BBB), m3(BBE), m3(BEE), m3(EEE),
m3(QQQ), m3(QQE), and m3(QEE)
all change signs at QCD phase boundary near the critical point.
To create a contour map of the third moments on the QCD
phase diagram should be an interesting theoretical subject.
Negative moments would be measured and confirmed both
in heavy-ion collisions and on the lattice. In particular,
(1) m3(EEE) at RHIC and LHC energies,
are interesting!
(2) m3 (QQQ)=0 at energy scan,
Summary 2
Critial Point
Let’s go see the scenery over the ridge!
But, do not forget to first draw a map
for a safe expedition.
Loreley, photo by MK, 2005
Derivative along T direction
simple T-derivative:
c B

T
c I

T
( N B ) 2  E  m ( N B )3  T ( N B ) 2
VT 3
( N Q ) 2  E  m ( N Q )3  T ( N Q ) 2
VT 3
E : total energy in a subvolume
measurable experimentally
mixed 3rd moments:
m3 (QQE) 
( NQ )2  E
VT
3
, m3 (BBE) 
( N E )2  E
VT 3
Problem: T and m can not be determined experimentally.
Further Possibility
•If measured moments originate from a narrow
region in the T-m plane, and
•if experimental resolution is sufficiently fine,
 (T 2Cmˆ )
T
lattice

( E )3  m  N B ( E ) 2
VT
 m3 (EEE) 
exp.
m
T
3
m3 (BEE)
This formula is
used to determine
m/T experimentally.
exp.
Moreover, third moments provide
the divergence vector of c and Cm .
These information may enable us to
pin down the initial state of fireballs.

T

T
mˆ

m
Loreley