Ágnes Mócsy, Bad Honnef 08 1 Quarkonia from Lattice and Potential Models Characterization of QGP...
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Ágnes Mócsy, Bad Honnef 08 1
Quarkonia from Lattice and Potential Models
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Characterization of QGP with Heavy Quarks
Bad Honnef Germany, June 25-28 2008
Ágnes Mócsy
based on work with Péter Petreczky
Ágnes Mócsy, Bad Honnef 08 2
Confined Matter
Ágnes Mócsy, Bad Honnef 08 3
Deconfined Matter
Ágnes Mócsy, Bad Honnef 08 4
Deconfined Matter
Screening
Ágnes Mócsy, Bad Honnef 08 5
Deconfined Matter
Screening
J/ melting
Ágnes Mócsy, Bad Honnef 08 6
Deconfined Matter
Screening
J/ melting
J/ yield suppressed
Ágnes Mócsy, Bad Honnef 08 7
T/TC 1/r [fm-1]
(1S)
J/(1S)
c(1P)
’(2S)
b’(2P)
’’(3S)
Sequential suppression
QGP thermometer QGP thermometer
Ágnes Mócsy, Bad Honnef 08 8
Screening seen in lattice QCD
no T effects
€
r < r1(T)
strong screening
€
r > rmed (T)
Free energy of static Q-Qbar pair: F1
RBC-Bielefeld Coll. (2007)
The range of interaction between Q and Qbar is strongly reduced.Need to quantify what this means for quarkonia.
Ágnes Mócsy, Bad Honnef 08 9
J/ suppression measured
… but interpretation not understood
• Hot medium effects - screening? Must know dissociation temperature, in-medium
properties • Cold nuclear matter effects ? • Recombination?
PHENIX, QM 2008
Ágnes Mócsy, Bad Honnef 08 10
Studies of quarkonium in-medium
Potential Models
Lattice QCD
Matsui, Satz, PLB 178 (1986) 416Digal, Petreczky, Satz, PRD 64 (2001) 094015Wong PRC 72 (2005) 034906; PRC 76 (2007) 014902Wong, Crater, PRD 75 (2007) 034505Mannarelli, Rapp, PRC 72 (2005) 064905Cabrera, Rapp, Eur Phys J A 31 (2007) 858; PRD 76 (2007) 114506Alberico et al,PRD 72 (2005) 114011; PRD 75 (2007) 074009 PRD 77 (2008) 017502Mócsy, Petreczky, Eur Phys J C 43 (2005) 77; PRD 73 (2006) 074007
PRD 77(2008) 014501; PRL 99 (2007) 211602
Umeda et al Eur. Phys. J C 39S1 (2005) 9Asakawa, Hatsuda, PRL 92 (2004) 012001Datta et al PRD 69 (2004) 094507Jakovac et al PRD 75 (2007) 014506 Aarts et al Nucl Phys A785 (2007) 198Iida et al PRD 74 (2006) 074502Umeda PRD 75 (2007) 094502
Ágnes Mócsy, Bad Honnef 08 11
Studies of quarkonium in-medium
Potential Models
Lattice QCD
Spectral functions
Still inconclusive(discretization effects,
statistical errors)
Assume: medium effects can be understood in terms of
a temperature-dependent screened
potential
Contains all info about a given channel.Melting of a state corresponds to disappearance of a peak.
Ágnes Mócsy, Bad Honnef 08 12
Quarkonium from lattice
• Euclidean-time correlator measured on the lattice
• Spectral functions extracted from correlators inverting the integrals using Maximum Entropy Method
€
G τ ,r p ,T( ) = d3∫ xe i
r p
r x jH τ ,
r x ( ) jH
+ 0,r 0 ( )
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
Kernel cosh[(-1/2T)]/sinh[/2T]
q qγ5
q qμγ
q qμγ γ5
j =
scalar
pseudoscalar
vector
axialvector
c b
c0 b0
J/
c1 b1
q q
Ágnes Mócsy, Bad Honnef 08 13
Spectral function from lattice
• Shows no large T-dependence • Peak has been commonly interpreted as ground
state • Uncertainties are significant!
limited # data pointslimited extent in tau systematic effectsprior-dependence
c
Details cannot be resolved.
“..it is difficult to make any conclusive statement based on the shape of the spectral functions … ”
Jakovác et al PRD (2007)
Jakovac et al, PRD (2007)
Ágnes Mócsy, Bad Honnef 08 14
Ratio of correlators
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
€
Grec τ ,T( ) = σ ω,T = 0( )K τ ,ω,T( )dω∫
Compare high T correlators to correlators “reconstructed” from
spectral function at low T
Pseudoscalar Scalar
Datta et al PRD (2004) T-dependence of correlator ratiodetermines dissociation temperatures: c survives to ~2Tc & c melts at 1.1Tc
Initial interpretation
Seemingly in agreement with spectral function interpretation.
2004: “J/ melting” replaced by “J/ survival”
Ágnes Mócsy, Bad Honnef 08 15
Recently: Zero-mode contribution
Bound and unbound Q-Qbar pairs
(>2mQ)
Bound and unbound Q-Qbar pairs
(>2mQ)
Quasi-free heavy quarks interacting with the
medium
Quasi-free heavy quarks interacting with the
medium€
σ ,T( ) = Tχ s T( )ωδ ω( ) + σ high ω,T( )
€
σ ,T( ) = Tχ s T( )ωδ ω( ) + σ high ω,T( )
Low frequency contribution to spectral function at finite T,scattering states of single heavy quarks (commonly overlooked)
Gives constant contribution to correlator =>> Look at derivativesUmeda, PRD 75 (2007) 094502
€
G τ ,T( ) = σ ω,T( )K τ ,ω,T( )dω∫
Ágnes Mócsy, Bad Honnef 08 16
Ratio of correlator derivatives
• Flatness is not related to survival: no change in the derivative
scalar up to 3Tc ! c survives until 3Tc???
• Almost the entire T-dependence comes from zero-modes. Understood in terms of quasi-free quarks with some effective mass - indication of free heavy quarks in the deconfined phase
All correlators are flat.
Datta, Petreczky, QM 2008, arXiv:0805.1174[hep-lat]
Ágnes Mócsy, Bad Honnef 08 17
From the lattice
Dramatic changes in spectral function are not reflected in the correlator
Ágnes Mócsy, Bad Honnef 08 18
Lessons from Lattice QCD
Small change in the ratio of correlators does not imply (un)modification of states. Small change in the ratio of correlators does not imply (un)modification of states.
Dominant source of T-dependence of correlators comes from zero-modes (low energy part of spectral function). Understood in terms of free heavy quark gas.
Dominant source of T-dependence of correlators comes from zero-modes (low energy part of spectral function). Understood in terms of free heavy quark gas.
High energy part which carries info about bound states shows almost no T-dependence until 3Tc in all channels. High energy part which carries info about bound states shows almost no T-dependence until 3Tc in all channels.
Although spectral functions obtained with MEM do not show much T-dependence, the details (like bound state peaks) are not resolved in the current lattice data.
Although spectral functions obtained with MEM do not show much T-dependence, the details (like bound state peaks) are not resolved in the current lattice data.
Ágnes Mócsy, Bad Honnef 08 19
Would really the J/ survive in QGP up to 1.5-2Tc even though strong screening is seen in the medium?
Would really the J/ survive in QGP up to 1.5-2Tc even though strong screening is seen in the medium?
Ágnes Mócsy, Bad Honnef 08 20
Potential model at T=0
• Interaction between heavy quark (Q=c,b) and its antiquark Qbar described by a potential: Cornell potential
• Non-relativistic treatment
• Solve Schrödinger equation - obtain properties, binding energies
• Describes well spectroscopy; Verified on the lattice; Derived from QCD.
heavy quark massmQ>>QCD
and velocityv<<1
V(r)Confined
r
V(r)
€
−1
m∇ r
2 + V r( ) ⎡ ⎣ ⎢
⎤ ⎦ ⎥ψ r( ) = Eψ r( )
Ágnes Mócsy, Bad Honnef 08 21
Potential model at finite T
• Matsui-Satz argument: Medium effects on the interaction between Q and Qbar described by a T-dependent screened potential
• Solve Schrödinger equationfor non-relativistic Green’s function - obtain spectral function
• Utilize lattice data
V(r,T) Confined
Deconfined T>Tc
r
V(r)
€
−1
m∇ 2 + V (
r r ) + E
⎡ ⎣ ⎢
⎤ ⎦ ⎥G
NR (r r ,
r r ',E) = δ 3(
r r −
r r ')
€
σ E( ) =2Nc
πImGNR r
r ,r r ', E( ) r
r =r r '= 0
Ágnes Mócsy, Bad Honnef 08 22
Lattice & Potential models
Potential Models
Lattice QCD
Quarkonium correlators
ReliableReliable
Spectral functions
Free energy of static quarks
Potential from pNRQCD
Quarkonium correlators
Spectral functions
Not yet reliableNot yet reliable
Ágnes Mócsy, Bad Honnef 08 23
First lattice-based potentialFree energy of static Q-Qbar pair: F1
Digal, Petreczky, Satz, PRD (2001)
RBC-Bielefeld Coll. (2007)
Free energy F1≠ Potential VContains entropy F1=E1-ST
Ágnes Mócsy, Bad Honnef 08 24
Lattice-based potentials Most confining potential
Our physical potential
– Deeper potentials: stronger binding, higher Tdiss
– Open charm (bottom) threshold = 2mQ+Vinf(T)– Explore uncertainty assuming the general features of F1
• r < r1(1/T): vacuum potential • r > r2(1/T): exponential screening
Wong potential1.2Tc
1.2Tc
T=0 potential
Internal energyTS
- lower limit
- upper limit
Mócsy, Petreczky 2008
Free energy
r1r2
Can we constrain them using correlator lattice data?
Ágnes Mócsy, Bad Honnef 08 25
Pseudoscalar correlators
1.2Tc
No, we cannot determine quarkonium properties from such comparisons;If no agreement found, model is ruled out; We can set upper limits.
Set of potentials all agree with lattice data; yield indistinguishable
results.
with set of potentials within the allowed ranges
~ 1-2%
Ágnes Mócsy, Bad Honnef 08 26
Pseudoscalar spectral function
c
most confining potentialusing most confining potential
Mocsy, Petreczky 08
Large threshold (rescattering) enhancement even at high T- indication of Q-Qbar correlation
- compensates for melting of states keeping correlators flat
~ 1-2%
Ágnes Mócsy, Bad Honnef 08 27
Pseudoscalar spectral function
c
most confining potentialusing most confining potential
Mocsy, Petreczky 08
State is dissociated when no peak structure is seen.At which T the peak structure disappears? Ebin=0 ?!
Ebin = 2mq+V∞(T)-M
Warning! Widths are not physical - broadening not included
Ágnes Mócsy, Bad Honnef 08 28
Binding energies
€
Ebin < Tweak binding
€
Ebin > Tstrong binding
Binding energies decrease as T increases. True for all potential models.
What’s the meaning of a J/ with 0.2 MeV binding?
With Ebin< T a state is weakly bound and thermal fluctuations can destroy it
Mocsy, Petreczky, PRL 08
Do not need to reach Ebin=0 to dissociate a state.Do not need to reach Ebin=0 to dissociate a state.
Ágnes Mócsy, Bad Honnef 08 29
Upper limit melting temperatures
Estimate dissociation rate due to thermal activation (thermal width)
Dissociation condition:
Ebin = 2mQ+V∞(T)-MQQbar < T
€
Γ T( ) ≥ 2Ebin T( )
Kharzeev, McLerran, Satz, PLB (1995)
Broadening in agreement with:pQCD calculation QCD sum ruleImaginary part in resummed pQCD
pNRQCD at finite T
Laine,PhilipsenLee, Morita
Park et al
Brambilla et al
J/ melts before it bounds.
T/TC 1/r [fm-1]
(1S)
J/(1S) ’(2S)
c(1P) ’(2S)b’(2P) ’’(3S)TC
2
1.2
b(1P)
Ágnes Mócsy, Bad Honnef 08 30
Lessons from potential models
Set of potentials (between the lower and upper limit constrained by lattice free energy data) yield agreement with lattice data on correlators (S- and P-wave) Precise quarkonium properties cannot be determined this way, only upper limit.
Set of potentials (between the lower and upper limit constrained by lattice free energy data) yield agreement with lattice data on correlators (S- and P-wave) Precise quarkonium properties cannot be determined this way, only upper limit.
Large threshold enhancement above free propagation even at high T
- compensates for melting of states (flat correlators) - correlation between Q and Qbar persists
Large threshold enhancement above free propagation even at high T
- compensates for melting of states (flat correlators) - correlation between Q and Qbar persists
Upper limit potential predicts that all bound states melt by 1.3Tc, except the upsilon, which survives until 2Tc. Lattice results are consistent with quarkonium melting.
Upper limit potential predicts that all bound states melt by 1.3Tc, except the upsilon, which survives until 2Tc. Lattice results are consistent with quarkonium melting.
Decrease in binding energies with increasing temperature. Decrease in binding energies with increasing temperature.
Ágnes Mócsy, Bad Honnef 08 31
Implications for RHICollisions
survival J/ survival
Karsch et al
Consequences:• J/ RAA: J/ should melt at SPS and RHIC
• suppressed at RHIC (centrality dependent?); definitely at LHC• expect correlations of heavy-quark pairs
DD correlations? non-statistical recombination?
Ágnes Mócsy, Bad Honnef 08 32
Final note
• All of the above discussion is for isotropic medium
• Anisotropic plasma: Q-Qbar might be more strongly bound in an anisotropic medium, especially if it is aligned along the anisotropy of the medium (beam direction)
Dumitru, Guo, Strickland, PLB 62 (2008) 37
Ágnes Mócsy, Bad Honnef 08 33
Final note IIThe future is in:
Effective field theories from QCD at finite T
QCD
NRQCD
pNRQCDpotential model
Ebin~mv2
1/r ~ mv
m
Hierarchy of energy scales
r: distance between Q and QbarEbin: binding energy
Brambilla, Ghiglieri, Petreczky, Vairo, arXiv:0804.0993[hep-ph]
TmD ~gT
NRQCDHTL
pNRQCDHTL
Real and Imaginary part of potential derived
Also: Laine et al 2007, Blaizot et al 2007
Ágnes Mócsy, Bad Honnef 08 34
The QGP thermometer
Potential Models Lattice QCD
ExtractedSpectral Functions
Free energyof q-antiq
Quarkonium correlators
Quarkoniumcorrelators
Spectral Functions
T/TC 1/r [fm-1]
(1S)
J/(1S) ’(2S)
c(1P) ’(2S)
b’(2P) ’’(3S)TC
2
1.2
b(1P)
Ágnes Mócsy, Bad Honnef 08 35
****The END****