Magnetic Component of Strongly Coupled Quark-Gluon Plasma & QCD Phase Diagram from E-M Duality Perspective
Jinfeng Liao & Edward ShuryakSUNY Stony Brook
Aug. 14 , 2008 @ INT
INT QCDINT QCD--CPCP
OUTLINE
• E-M Duality for sQGP
• When Magnetic Scenario Meets Heavy Ion Data
• Pin Down the Parameters of Magnetic Component
• Discussions of QCD Phase Diagram
INT QCDINT QCD--CPCP
E-M Duality in General
• What E-M duality says:a) D+1 local field theory E, allowing D-dim. Topological
Excitations Mconvenient at E-coupling < 1 (M mass 1/E-coupling)
b) an eff. local field theory based on M with E non-local convenient at E-coupling > 1
c) further more the M-coupling ~ 1/ E-coupling !!!working examples ? YES !
• 2-D Ising model:
• 2-D sine-Gordon --- Thirring Model
• More nontrivial: \cal N=2 SYM Seiberg-Witten:
INT QCDINT QCD--CPCP
See:e.g. J. Harvey , hep-th/9603086
Minimal Lesson: D.o.F. in per. Spectrum may NOT be the D.o.F. at strong coupling !
New Quest for D.o.F
INT QCDINT QCD--CPCP
Very High TTc ~ 4 TcwQGPs-QGPHadronic World
???
quarks, gluons: EQPdominating thermodynamics pQCD calculable
non-pert. scale: e^2 TM-sector setting indim. reduction MQCDheavy, strongly correlated monopoles (Kolthas-Altes, Meyer, …)
hadrons: E-Compositeinteraction so strong quarks/gluons confined !however: hadrons are merely excitations of some more complicated stuff QCD vacuum: Magnetic
dual superconductor monopole condensation(`t Hooft -- Mandelstam)(lattice: Giacomo/Suzuki/Greensite/....)
Magnetic D.o.F: Lessons from S-W
• N=2 SYM: solved by Seiberg-Witten • Deg. vacua: complex higgs U
energy scale set by |U| (our analog: T) • confining point: monopole becomes
massless and forms condensate• on way to that: gluons more and more
heavy and strongly coupled • monopoles the OPPOSITE !!
INT QCDINT QCD--CPCP
From: Lerche, hep-th/9611190
Summarizing the E-component in sQGP• quarks/gluons from high-T down to Tc
become heavy and rare, gradually ceasing already about 1.5Tc
• hadrons from low-T do NOT necessarily melt right at Tc, instead they survive to about 1.5Tc and then dissolve into quarks and gluons at higher T
Q: what about M-component?q/g/H all heavy, who are ruling the bulk?
INT QCDINT QCD--CPCP
Very High TTc ~ 4 TcwQGPs-QGPHadronic World
quarks, gluons: EQP
non-pert. scale: e^2 TM-sector setting inheavy, strongly correlated monopoles
hadrons: E-Composite
QCD vacuum: Magnetic
dual superconductor, monopole ondensate
Magnetic Scenario for sQGP
1.5 Tc: e=g ?!
Magnetic Plasmamade of light and abundantmagentic monopoles
E-S-C
M-W-C M-S-C
E-W-C
JL & Shuryak, PRC75:054907,2007
• sQGP: a strongly-coupled plasma with both Electric and Magnetic charges
• What would be the transport properties of such a mixture plasma, e.g. viscosity, diffusion,…
• Strong constraints from heavy ion data !
• Also, is the magnetic component important for jet quenching ?
INT QCDINT QCD--CPCPWhen Magnetic Scenario
Meets Heavy Ion Data JL & Shuryak, PRC75:054907,2007 Also: JL & Shuryak, to appear
Warmup: Single Monopole Motion I
INT QCDINT QCD--CPCP
M/D
E
e
A. S. Goldhaber, et al, Am. J. Phys. 58(1990)429K. A. Milton, hep-ex/0002040
Charge-Monopole• studied in great details by many people, both classical and quantum
• Poincare cone: focusing & bouncing
Warmup: Single Monopole Motion II
INT QCDINT QCD--CPCP
eDipole-Monopole• Again : focusing
& bouncing• Now : even trapping• Important for transport !
+
-
M
V
E+
E-
E-M PING-PONG
Warmup: Single Monopole Motion III
INT QCDINT QCD--CPCP
A grain of salt :
• Very complicated trajectories• Cone-like structure near
the corners• Multi-bouncing before
eventually escaping
Warmup: Single Monopole Motion III
INT QCDINT QCD--CPCP
A Cage for Monopole :
Lorentz Trapping Effect• Enhance very much the
collision rate • Monopole can be trapped
locally for a time scale much longer than micro. time scale
Absent for E-charge in the same setting
MD for E-M Mixture Plasma
INT QCDINT QCD--CPCP
MD is a powerful tool :• QED Coulomb plasma extensively
studied• Non-Abelian Coulomb plasma studied
by Gelman, Shuryak, and Zahed• Extremely useful for calculating
transport properties
New Window -- 1st MD for E-M mixture• Lorentz force betwne E-M• ~1000 particles in a “cup”• Varying E/M ratio: M00,M25,M50• Varying Gamma as well• Measure viscosity, diffusion• Mapping to sQGP parameters
Transport: Diffusion INT QCDINT QCD--CPCP
• More mixing less diffusion• power law • the power is close to 0.47 (cube-
analysis) and the 0.5 (AdS/CFT)
Transport: Viscosity INT QCDINT QCD--CPCP
• More mixing less visicosity• rapid rising for Gamma < 1• tendency to rise again for Gamma~10
Transport Summary INT QCDINT QCD--CPCP
AdS/CFT predictions:(Kovtun,Son,Strainet;Casselderrey & Teaney)
Weakly coupled limit:both proportional to M.F.P.
RHIC Results:viscous hydro \eta/sheavy flaovr diffusion
Jet Quenching at RHIC
Nuclear Modification Factor:
Colorless Probe
Colorful Probe
R_aa = 1 : NO medium effect, just bunch of pp
Raa & V2 from Phenix
0 2.5 5 7.5 10 12.5 15
P_t0
0.1
0.2
0.3
0.4
0.5
_V2
H02-
04%
LMinBias 0-10%
20-30% 40-50%
60-70% 80-92%
PHENIX,PRC76:034904,2007arXiv:0801.4020
Large Azimuthal Asymmetry !
Jet Energy Loss
Probe dependence:
Medium dependence:
Entangled dependence:
All together :
Note: mid rapidityhigh Pt > 5GeV
E ~ Pt
Raa AND V2 of High Pt Hadron
Raa : well described by most models
V2 in non-central collisions : surprisingly large !no satisfactory model ; what’s thegeometric limit ?
Shuryak, PRC66:027902,2002• hard sphere nuclei with sharp edges• constant \kappa
even black limit can NOT produce enough v_2Drees & Feng & Jia, PRC71:034909,2005• Woods-Saxon + medium dilution + quadratic length• constant \kappa
only bring down the v_2 (except cylindrical geo. up ~10%)
PHENIX,PRC76:034904,2007arXiv:0801.4020
Possible improvement : CGC like initial 10% increase of the final v_2 !
Rethinking about the \kappa
From: PRD77:014511,2008.
S
The dependence could be very non-trivial !
From “almond” to “ONION”
Pantuev, JETP Lett.85:104-108,2007Jet absorption retarded by a “latent time” of about 2-3fm
Scanning the RHIC Fireball with Jet
The jet :ignited in x-y plane according to density of binary collisionrandomly escaping near \phi=0,\pi/2,\pi,3\pi/2 directions
The medium :initial profile Woods-Saxon with impact b & Npart. scalingevolution Bjorken dilution ~ 1/ \tau
Key idea of our geometric model:
Varying s_min & s_max to scan layer by layer :really a kind of jet tomography !
Black Limit Raa & V2
b=7 , N_part ~ 260 , \tau_0 = 1 fm
V2 with constrained Raa
b=7 , N_part ~ 260 , \tau_0 = 1 fm
R_aa is constrained by measurements : b=7fm R_aa ~ 0.33 (PHENIX 20-30%)
For each layer scan:
first adjust \kappa to fit the R_aa
then calculate the V_2
PHENIX V2 20-40%5-15 GeV: ~ 0.10-0.14
HG Near Tc QGP
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
entropy interval Hêfm^3L0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
_V2
Hhti
waa_R
dettifL
V2 with constrained Raa@ another centrality
b=10 , N_part ~ 120 , \tau_0 = 1 fm
R_aa is constrained by measurements : b=10fm R_aa ~ 0.52 (PHENIX 40-50%)
For each layer scan:
first adjust \kappa to fit the R_aa
then calculate the V_2
PHENIX V2 40-60%5-15 GeV: ~ 0.11-0.15
HG Near Tc QGP
The Near Tc Region
No wonder the Near Tc Region shall be special on general ground.However:Our study of azimuthal asymmetry in high Pt hadron yield suggest in Particular that ------Jet quenching happens mostly in this Near Tc Region !
Is there any independent evidence for such a conclustion ?Yes the conical flow created from interaction of away-side jet with the medium
True 3PC jet correlations
1~ 0.35, ~ 24sc
sη
π⎛ ⎞×⎜ ⎟⎝ ⎠
From: Roy Lacey at ICHP08
From: PRD77:014511,2008.
In light of \eta / s
From: Csernai, Kapusta, McLerran From: Lacey & Collaborators
Minimal viscosity around TcStrong dissipation/relaxation concentrated locally
Thanks to Larry for pointing out this to me .
Magnetic Quenching of Electric Jet
Why more quenching in the Magnetic Plasma near Tc rather than in the QGP at higher T ?• Time argument :
• Mass argument :
• Density argument :
• Transport cross-section argument :
• Lattice Gauge Theory (LGT) is another important way of studying sQGP
• LGT provides important support for the dual superconductivity scenario of color confinement
• Are there evidence for the magnetic component of sQGP from LGT?
• Further: can the parameters of magnetic component be measured or inferred ?
INT QCDINT QCD--CPCP
Pin Down the Parameters of Magnetic Component JL & Shuryak, arXiv: 0804.0255
INT QCDINT QCD--CPCP
Magnetic Monopoles on the Lattice
Chernodub & Zakharov , arXiv:0611228,0806.2874;Chernodub, et al, arXiv: 0710.2547
INT QCDINT QCD--CPCP
Monopole Density & Correlation
D'Alessandro & D’Elia , arXiv:0711.1266
M-anti-M , M-M equal-time spatial orrelation functions
INT QCDINT QCD--CPCP
The Correlation Teaches us sth.
Gas
Liquid
Solid
From: Gelman, Shuryak, & Zahed, nucl-th/0601029
INT QCDINT QCD--CPCP
From Correlation to M-Coupling JL & Shuryak, arXiv: 0804.0255
Our MD
Lattice
M-coupling runs to be large at high T !
INT QCDINT QCD--CPCP
Magnetic Component is a Good Liquid JL & Shuryak, arXiv: 0804.0255
Plasma coupling of M-component:
• a magnetic componentof sQGP made of dense monopoles;
• the magnetic coupling runs oppositely to the electric, crossing around 1.5Tc;
• the magnetic component should be a good liquid:
all these are supported by the lattice calculations need more1 1.5 2 2.5 3 5 63.5 4.5 5.54
T ê T C
1
1.5
0
0.5
2
2.5
5
5.5
3
3.5
4.5
4
citengaM
G
á
á
á
á
á
á
á
á GM*
GE*
High T end :
INT QCDINT QCD--CPCP
More E-M Crossing
A. Nakamura, et al, PRD69(2004)014506
Screening mass
M. Baker, PRD78(2008)014009
Dual QCD : vacuum & finite T<3T
Electric component of sQGP 1-2Tc• Susceptibilities quarks/gluons: heavy below 1.5Tc
• Potential model Q.M. hadrons: survive above 1.5TcThey are NOT the only players, nor the dominant !E-M duality
Magnetic component of sQGP 1-2Tc• A good liquid made of dense monopoles
• Condense at lower T while become dilute and stronger coupled at higher T, oppositely to the electric
• Using MD we showed a mixture plasma explains the transport properties of the RHIC measurements
• It helps us understand the geometry & physics of jet quenching
INT QCDINT QCD--CPCP
Summary
Magnetic Scenario (with time)a deeper theoretical understanding of sQGP
New Phase Diagram from E-M Duality
INT QCDINT QCD--CPCP
RHIC
LHC
FAIR
INT QCDINT QCD--CPCP
The Order of Transition ?
INT QCDINT QCD--CPCP
The Order-Disorder Transition ?
Is dual superconductivity the correct picture for QCD confinement ?
CROSSOVER !! ??[ real QCD vacuumis confining, for sure. ]
Symmetric Phase ---- deconfined< Magnetic U(1) > = 0
Asymmetric Phase ---- confined < Magnetic U(1) > NOT 0NO CROSSOVER
Pisa group (Di Giacomo and collaborators)
DISCLAIMER: I am not to be blamed for the results ☺1st ORDER ??
arXiv:0710.1174 & refs therein
Backup: QCD in General
• QCD & QCD-like theoriessimple Lagrangian, rich phenomena
• N_c : # of color N_f : # of flavor
• Asymptotic freedom (UV)IR : strongly coupled
• Color confinement• Chiral Sys. Breaking
INT QCDINT QCD--CPCP
D.o.F. in per. Spectrum is NOT the D.o.F. in QCD vacuum !
Backup: Quarks & Gluons Down Toward TcINT QCDINT QCD--CPCP
T M_q / T M_g / T1.5 T_c 3.9(2) 3.4(3)3.0 T_c 1.7(1) 1.2(1)
• What is the M/T for q,g in sQGP? Abundant or NOT ?
• Direct Info. from lattice:(P. Petreczky, et al, Nucl. Phys.
Proc. Suppl. 106 (2002) 513.)
Already at 1.5Tc, EQPs are very heavy !
They may become even heavier further down to Tc !
Indirect probe: thermodynamic variablese.g. baryonic & isospin succeptibilities
Liao & Shuryak, PRD73:014509,2006
1. Quarks dominate close to 2Tc2. Baryons dominate close to Tc
Q-only
B-only
Backup: Bound States Above TcINT QCDINT QCD--CPCP
Liao & Shuryak, Nucl.Phys.A775:224,2006
In sQGP 1-2 Tc:• EQPs are heavy • Binary interaction is strong
forming bound state !hadrons surviving above Tceven more exotic states (Shuryak & Zahed, PRC 70(2004)021901 PRD 70(2004)054507)
First studied and found robust multi-body bound states : • baryons (qqq) and glueballs (ggg)• polymer chains Q-g-g----g-antiQ
Backup: RHIC ResultsINT QCDINT QCD--CPCP
D. Molnar & M. Gyulassy, Nucl. Phys. A 697(2002)495
D. Teaney, Phys.Rev.C68:034913,2003.
• Large masses found at lattice for quasi-quarks/gluons
M_q / T M_g / T1.5 T_c 3.9(2) 3.4(3)3.0 T_c 1.7(1) 1.2(1)
P. Petreczky, et al, Nucl. Phys. Proc. Suppl. 106 (2002) 513.
INT QCDINT QCD--CPCP
Backup: Masses from Lattice
Backup: Baryonic SusceptibilitesINT QCDINT QCD--CPCP
From: Liao & Shuryak, PRD73:014509,2006.
Backup: Bound StatesINT QCDINT QCD--CPCP
From: Shuryak & Zahed; Liao & Shuryak
Backup: Bound StatesINT QCDINT QCD--CPCP
From: Shuryak & Zahed; Liao & Shuryak
O. Kaczmarek, et al : Prog.Theor.Phys.Suppl.153(2004)287
Backup: Polymer ChainsINT QCDINT QCD--CPCP
From: Liao & Shuryak.
Backup: Dirac MonopolesINT QCDINT QCD--CPCP
A. S. Goldhaber, et al, Am. J. Phys. 58(1990)429K. A. Milton, hep-ex/0002040
Backup: eDipole-MonopoleINT QCDINT QCD--CPCP
“Magnetic Bottle “(Budker)in controlled thermal nulcear fusion
Backup: eDipole-MonopoleINT QCDINT QCD--CPCP
Backup: Lorentz TrappingINT QCDINT QCD--CPCP
Backup: MD setting INT QCDINT QCD--CPCP
Backup: Transport from MDINT QCDINT QCD--CPCP
Backup: ’t Hooft-PolyakovINT QCDINT QCD--CPCP
Backup: MAP & Wrapped TrajectoryINT QCDINT QCD--CPCP
Maximal Abelian Projection: SU(2) example Monopole density counting
From wrapped trajectories
Chernodub & Zakharov , arXiv:0806.2874
Abelian Dominance & Monopole Dominance for IR properties in the QCD vacuum are well established.
More about the way to monopole:
Backup: E-M Equilibrium PointINT QCDINT QCD--CPCP
A. Nakamura, et al, PRD69(2004)014506Approaching Tc from above:• E-screening mass decrease
less E-charge E-charge getting heavier
• M-screening mass increasemore M-chargeM-charge getting lighter
Chernodub & Ilgenfritz, arXiv: 0805.3714
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