guiding principles for search femtoscopic
TRANSCRIPT
1Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Outline
Introduction
Phase Diagram & HIC
Search strategy for the CEP
Theoretical guidance
Guiding principles for search
The probe
Femtoscopic
โsusceptibilityโ
Analysis
Finite-Size-Scaling
Dynamic Finite-Size-Scaling
Summary
Epilogue
2
Characterizing the phases of matter
The location of the critical End point and the phase coexistence regions are
fundamental to the phase diagram of any substance !
The properties of each
phase is also of
fundamental interest
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
p
3Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Known unknowns
Location of the critical point (CEP)? Order of the phase transition? Value of the critical exponents?
Location of phase coexistence regions?
Detailed properties of each phase?
All are fundamental to charting the phase diagram
Known knownsSpectacular achievement:
Validation of the crossover transition leading to the QGP Initial estimates for the transport properties of the QGP
(New) measurements, analysis techniques and theory efforts which probe
a broad range of the (T, ๐๐)-plane, are essential to fully unravel the unknowns!
The QCD Phase Diagram
4Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
RHIC
First collisions 2000
p+p, d+Au, Cu+Cu, Cu+Au, Au+Au, U+U
sNN ~ 7 โ 200 GeV
LHC
First collisions 2010
p+p, Pb+Pb, p+Pb
sNN =2.76 TeV
(5.5 TeV in 2015-16)
The RHIC and LHC are two major experimental facilities currently
used to study the QCD phase diagram
5Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Heavy ion collisions are used to produce the hot and dense
matter used to probe the QCD phase diagram
# participants
Npart
6Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
The particles produced in collision events are used to
study the produced medium
A Typical Event RHIC
LHC
7Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Essential Question
What new insights do we have on:
The CEP โlandmarkโ?
Location (๐๐๐๐, ๐๐ต๐๐๐
) values?
Static critical exponents - ๐, ๐พ?
Static universality class?
Order of the transition
Dynamic critical exponent โ z?
Dynamic universality class?
The QCD Phase Diagram
All are required to fully characterize the CEP
& drives the ongoing search
8Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Theoretical Guidance
Experimental verification and characterization
of the CEP is a crucial ingredient
Theory consensus on the static
universality class for the CEP3D-Ising Z(2)
๐ ~ 0.63 ๐พ ~ 1.2
M. A. Stephanov
Int. J. Mod. Phys. A 20, 4387 (2005)
Dynamic Universality class
for the CEP less clear
One slow mode
z ~ 3 - Model HSon & Stephanov
Phys.Rev. D70 (2004) 056001
Moore & Saremi ,
JHEP 0809, 015 (2008)
Three slow modes
zT ~ 3
zv ~ 2
zs ~ -0.8
Y. Minami - Phys.Rev. D83
(2011) 094019
The predicted location (๐๐๐๐ฉ, ๐๐๐๐๐ฉ
) of
the CEP is even less clear!
M. A. Stephanov
Int. J. Mod. Phys. A 20, 4387 (2005)
9Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
The critical point is characterized by several (power law) divergences
Central idea use beam energy scans to vary ๐๐ & T to search for the
influence of such divergences!
We use femtoscopic measurements to perform our search
Anatomy of search strategy
๐๐O
๐น๐ ~ ๐๐ search for โcriticalโ
fluctuations in HICStephanov, Rajagopal, Shuryak, PRL.81, 4816 (98)
~ -v
cT T
~pC
~T
10Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
2
0(q) (q) (1 4 ) 1 (( , ) )KR C q rd r rr S
Source function(Distribution of pair
separations)
Encodes FSICorrelation
function
Inversion of this integral
equation Source Function
(๐ ๐ฟ, ๐ ๐๐, ๐ ๐๐ )
3D Koonin Pratt Eqn.
)/)(/(
/)(
2111
212
pp
ppq
ddNddN
dddNC
Interferometry as a susceptibility probe
Hanbury Brown & Twist (HBT) radii
obtained from two-particle
correlation functions
S. Afanasiev et al. (PHENIX)
PRL 100 (2008) 232301
In the vicinity of a phase transition or the CEP, the divergence of ๐ฟleads to anomalies in the expansion dynamics
2 1sc
The expansion of the emitting
source (๐ ๐ฟ, ๐ ๐๐, ๐ ๐๐ ) produced in HI collisions
is driven by cs
Susceptibility ()
of the order parameter
diverges at the CEP
Strategy
Search for non-monotonic patterns for HBT radii
combinations that are sensitive to the divergence of ๐ฟ
11Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Interferometry signal
)/)(/(
/)(
2111
212
pp
ppq
ddNddN
dddNC
A. Adare et. al. (PHENIX)
arXiv:1410.2559
Strategy
Search for non-monotonic patterns for HBT radii
combinations that are sensitive to the divergence of ๐ฟ
12Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
2
2
2
2
2 2 2
2
2 2
1
( )
1
geo
sideT
T
geo
out TT
T
long
T
RR
m
T
RR
m
T
TR
m
Chapman, Scotto, Heinz, PRL.74.4400 (95)
(R2out - R2
side) sensitive to the ๐ฟ
Specific non-monotonic patterns expected as a function of โsNN
A maximum for (R2out - R2
side)
A minimum for (Rside - Rinitial)/Rlong
Interferometry Probe
Hung, Shuryak, PRL. 75,4003 (95)
Makhlin, Sinyukov, ZPC.39.69 (88)
2 1sc
The measured HBT radii encode
space-time information for
the reaction dynamics
The divergence of the susceptibility ๐ฟ โsoftensโโ the sound speed cs
extends the emission duration
(Rside - Rinit)/ Rlong sensitive to cs
emission
duration
emission
lifetime
13
โ๐๐ต๐ต dependence of interferometry signal
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30,
2015
The measurements validate the expected non-monotonic patterns!
Reaction trajectories spend a fair amount of time near a
โsoft pointโโ in the EOS that coincides with the CEP!
longR
2 2 2
out sideR R
/
2
side i long
initial
R R R u
R R
Finite-Size Scaling (FSS) is used for further
validation of the CEP, as well as to characterize
its static and dynamic properties
Lacey QM2014.
Adare et. al. (PHENIX)
arXiv:1410.2559
** Note that ๐๐ฅ๐จ๐ง๐ , ๐๐จ๐ฎ๐ญ and ๐๐ฌ๐ข๐๐ [all] increase with โ๐ฌ๐๐ **
14Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Basis of Finite-Size Effects
Only a pseudo-critical point is observed shifted
from the genuine CEP
~ - Lv
cT T
note change in peak heights,
positions & widths
A curse of Finite-Size Effects (FSE)
T > Tc
T close to Tc
L characterizes the system size
Illustration large L
small L
15Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Finite-size shifts both the pseudo-critical point
and the transition line
A flawless measurement, sensitive to FSE, can not give
the precise location of the CEP
The curse of Finite-Size effectsE. Fraga et. al.
J. Phys.G 38:085101, 2011
Displacement of pseudo-first-order transition lines and CEP due to finite-size
16Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
The Blessings of Finite-Size
Finite-size effects have specific identifiable
dependencies on size (L) The scaling of these dependencies give access
to the CEPโs location and itโs critical exponents
/ 1/( , ) ( ) /c cT L L P tL t T T T
~ -v
cT T L
M. Suzuki,
Prog. Theor. Phys. 58, 1142, 1977
Finite-size effects have a specific
L dependence
L scales
the volume
17
๐บ๐๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐ ๐๐ ๐ฏ๐ฉ๐ป ๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30,
2015
The data validate the expected patterns for Finite-Size Effects
Max values decrease with decreasing system size
Peak positions shift with decreasing system size
Widths increase with decreasing system size
Data from L. Adamczyk et al. (STAR)
Phys.Rev. C92 (2015) 1, 014904Roy A. Lacey
Phys.Rev.Lett. 114 (2015) 14, 142301
Large L
small L
18Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan,
Sept. 30, 2015
I. Use (๐น๐๐๐๐ -๐น๐๐๐ ๐
๐ ) as a proxy for the susceptibility
II. Parameterize distance to the CEP by ๐๐ต๐ต๐๐= ๐ โ ๐๐ช๐ฌ๐ท / ๐๐ช๐ฌ๐ทcharacteristic patterns signal
the effects of finite-size
2 2
2 2 2 2
2 2
( )
side geom
out geom T
long
T
R kR
R kR
TR
m
2 1s
S
c
III. Perform Finite-Size Scaling analysis
with length scale L R
๐บ๐๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐ ๐๐ ๐ฏ๐ฉ๐ป ๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐
19
Length Scale for Finite Size Scaling
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
ฯx & ฯy RMS widths of density distribution
scales the full RHIC and LHC data sets R
, ,out side longR R R R
is a characteristic length scale of the
initial-state transverse size,R
scales
the volumeR
20
๐ญ๐๐๐๐๐ โ ๐บ๐๐๐ ๐บ๐๐๐๐๐๐
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30,
2015
~ 0.66~ 1.2
The critical exponents validate
the 3D Ising model (static) universality class
2nd order phase transition for CEP
~ 165 MeV, ~ 95 MeVcep cep
BT
~ 47.5 GeVCEPs
( ๐ฌ๐๐๐ & chemical freeze-out
systematics)
** Same ๐ value from analysis of the widths **
From slope
From intercept
max
2 2
out sideR R R
1
( ) ( ) RNN NNs V s k
21Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept.
30, 2015
~ 0.66 ~ 1.2
2nd order phase transition
3D Ising Model (static)
universality class for CEP
~ 165 MeV, ~ 95 MeVcep cep
BT
Use ๐๐๐๐ฉ, ๐๐๐๐๐ฉ
, ๐ and ๐
to obtain Scaling
Function ๐๐
**A further validation of
the location of the CEP and
the (static) critical exponents**
๐ช๐๐๐๐๐๐๐ ๐๐๐๐ ๐๐๐ ๐ญ๐บ๐บ
/ 1/( , ) ( )T L L P tL
M. Suzuki,
Prog. Theor. Phys. 58, 1142, 1977
๐ ๐๐ง๐ ๐๐ are from โ๐ฌ๐๐
22
A ๐ญ๐จ๐ธ
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept.
30, 2015
What about Finite-Time Effects (FTE)?
๐๐๐ diverges at the CEP
so relaxation of the order parameter could be anomalously slow
~ z
z > 0 - Critical slowing down
Multiple slow modes?zT ~ 3, zv ~ 2, zs ~ -0.8
z < 0 - Critical speeding up
Y. Minami - Xiv:1201.6408eg. ๐น๐ ~ ๐๐ (without FTE)
๐น๐ โช ๐๐ (with FTE)
Significant signal attenuation for
short-lived processes
with zT ~ 3 or zv ~ 2
Dynamic Finite-Size Scaling (DFSS) is used to
estimate the dynamic critical exponent z
dynamic
critical exponentAn important consequence
The value of the dynamic critical exponent/s is crucial for HIC
23
๐ซ๐๐๐๐๐๐ ๐ญ๐๐๐๐๐ โ ๐บ๐๐๐ ๐บ๐๐๐๐๐๐
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept.
30, 2015
DFSS ansatz
2nd order phase transition
~ 165 MeV, ~ 95 MeVcep cep
BT
at time ๐ when T is near Tcep
/ 1/, , , z
TL T L f L t L
/, , z
cL T L f L
For
T = Tc
Rlong L-z (fm
1-z)
2.5 3.0 3.5 4.0
(R-
)(R
2
ou
t - R
2
sid
e)
(fm
2-
0
1
2
3
4
5
Rlong fm
3 4 5 6 7
(R2
ou
t - R
2
sid
e)
fm2
2
4
6
8
10
12 00-0505-1010-2020-3030-4040-50
(%)
z ~ 0.87
The magnitude of z is similar to
the predicted value for zs but
the sign is opposite
**Experimental estimate of the
dynamic critical exponent**
longR M. Suzuki,
Prog. Theor. Phys. 58, 1142, 1977
~ 0.66 ~ 1.2
24
Epilogue
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
Strong experimental indication for the CEP
and its location
New Data from RHIC (BES-II)
together with theoretical
modeling, will provide crucial
validation tests for the
coexistence regions, as well
as to firm-up characterization
of the CEP!
~ 0.66
~ 1.2
3D Ising Model (static)
universality class for CEP
2nd order phase transition
~ 165 MeV, ~ 95 MeVcep cep
BT
(Dynamic) Finite-Size Scalig analysis
Landmark validated
Crossover validated
Deconfinement
validated
(Static) Universality
class validated
Model H Universality
class invalidated?
Other implications!
z ~ 0.87
Much additional
work required to
get to โthe end of
the lineโ
End
25Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30, 2015
26
๐ญ๐๐๐๐๐ โ ๐บ๐๐๐ ๐บ๐๐๐๐๐๐ Analysis
Roy A. Lacey, Stony Brook University; TGSW workshop, Tsukuba Japan, Sept. 30,
2015
Locate (๐ป, ๐๐) position of
deconfinement transition and
extract critical exponents
Determine Universality Class
Determine order of the phase
transition to identify CEP
(only two exponents
are independent )
Note that is not strongly dependent on V ,f f
B T