Constant mode in meson correlators at finite temperature
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 1
Constant mode in meson correlatorConstant mode in meson correlatorss at finite temperature at finite temperature
Takashi Umeda
This talk is based on the hep-lat/0701005.
Tsukuba Theory Seminar, Univ. of Tsukuba, Apr. 20, 2007
to appear in Phys. Rev. D
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 2
ContentsContents
Introduction- Overview- Search for Quark Gluon Plasma- (Sequential) J/ψ suppression
Quenched QCD calculations- Lattice setup- T dependence of charmonium correlators- Constant mode in meson correlators
Discussion & summary
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 3
Quark Gluon Plasma Quark Gluon Plasma (QGP)(QGP)
from Munster Univ. web-site
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 4
ExperimentsExperiments
SPS : CERN ( – 2005) Super Proton Synchrotron RHIC: BNL (2000 – now) Relativistic Heavy Ion Collider LHC : CERN (2009 - ) Large Hadron Collider
from the Phoenix group web-site
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 5
Signatures of Signatures of QGPQGP
Talk by Ozawa @ Heavy Ion Cafe
J/ψ suppression
T.Hashimoto et al.,PRL57 (1986) 2123.T.Matsui & H.Satz,PLB178 (1986) 416.
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 6
First paper on the J/First paper on the J/ψψsuppressionsuppression
photo : Prof. Osamu Miyamura
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 7
J/J/ψψ suppression in Exp. suppression in Exp.
Phys.Lett.B477(2000)28NA50 Collaboration
QM2006 PHENIX Collaboration
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 8
Spectral Function in lattice Spectral Function in lattice QCDQCD
Quenched QCD- T. Umeda et al.,
EPJC39S1, 9, (2005).- S. Datta et al.,
PRD69, 094507, (2004).- T. Hatsuda & M. Asakawa,
PRL92, 012001, (2004).- A. Jakovac et al.,
PRD75, 014506 (2007).Full QCD- G. Aarts et al.,
hep-lat/0610065.
In the studies of SPFs on the lattice, all studies indicate survival of J/ψ state above Tc (1.5Tc?)
C(t) : meson correlatorNt = 1/(aT) T: temperature
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 9
Sequential J/Sequential J/ψψsuppressionsuppressionParticle Data Group (2006)
Ps V S Av
E705 Collaboration, PRL70, 383, (1993).
10%30%
60%
Dissociation temperatures of J/ψ and ψ’& χc
are important for QGP phenomenology.
for the total yield of J/ψ
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 10
χχ cc states on the lattice states on the lattice
S. Datta et al., PRD69, 094507 (2004).A.Jakovac et al., PRD75, 014506 (2007).
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 11
ContentsContents
Introduction- Overview- Search for Quark Gluon Plasma- (Sequential) J/ψ suppression
Quenched QCD calculations- Lattice setup- T dependence of charmonium correlators- Constant mode in meson correlators
Discussion & summary
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 12
Quenched QCD at Quenched QCD at T>0T>0
Lattice setup
anisotropic lattices : 203 x Nt
1/as = 2.03(1) GeV, as/at = 4 Clover quark action with tadpole imp. on anisotropic lattice H. Matsufuru et al., PRD64, 114503 (2001). rs=1 to reduce cutoff effects in higher energy states F. Karsch et al., PRD68, 014504 (2003). quark mass is tuned with MJ/ψ(= 3097MeV)
equilib. is 20K sweepseach config. is separated by 500 sweeps
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 13
Effective mass (local Effective mass (local mass)mass)
Definition of effective mass
In the (anti) periodic b.c.
when
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 14
At zero At zero temperaturetemperature
(our lattice results)MPS = 3033(19) MeVMV = 3107(19) MeV
(exp. results from PDG06)Mηc = 2980 MeVMJ/ψ = 3097 MeVMχc0 = 3415 MeVMχc1 = 3511 MeV
In our lattice Nt ⋍ 28 at Tc
t = 1 – 14 is available near Tc
Spatially extended (smeared) op. is discussed later
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 15
Quenched QCD at Quenched QCD at T>0T>0
small change in S-wave states survival of J/ψ & ηc at T>Tc
drastic change in P-wave states dissociation of χc just above Tc (?)
S. Datta et al., PRD69, 094507 (2004). etc...
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 16
Constant mode Constant mode
Pentaquark (KN state): two pion state: Dirichlet b.c.c.f. T.T.Takahashi et al., PRD71, 114509 (2005).
exp(-mqt) x exp(-mqt)= exp(-2mqt)
exp(-mqt) x exp(-mq(Lt-t))= exp(-mqLt)
mq is quark mass or single quark energy
Lt = temporal extent
in imaginary time formalismLt = 1/Temp.
gauge field : periodic b.c. quark field : anti-periodic b.c.
in confined phase: mq is infinite
the effect appears only in deconfined phase
Now we consider the meson correlator with p=0 & mq1=mq2
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 17
Free quark Free quark calculationscalculations
for Ps, V, S and Av channels
163 x 32 isotropic lattice Wilson quark action
with mqa = 0.2
Obvious constant contribution in P-wave states
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 18
Free quark Free quark calculationscalculations
Continuum form of the correlators calculated by S. Sasaki
: single quark energy with relative mom. p where
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 19
Spectral Spectral representationrepresentation
Spectral function of the correlator
with
F. Karsch et al., PRD68, 014504 (2003).G. Aarts et al., NPB726, 93 (2005).
chiral symmetry in massless limit
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 20
Physical Physical interpretationinterpretation
constant contribution remainsin the continuum form & infinite volume
The constant term is related to some transport coefficients.
From Kubo-formula, for example, a derivative of the SPF in the V channel is related to the electrical conductivity σ.
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 21
Without constant Without constant modemode
How much does SPF change at the region
from “An Introduction to Quantum Field Theory” Michael E. Peskin, Perseus books (1995)
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 22
Midpoint subtractionMidpoint subtraction
An analysis to avoid the constant mode
Midpoint subtracted correlator
Free quarks Free quarks
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 23
ZZ33 symmetrization symmetrizationHere we consider the Z3 transformation
Z3 symmetric
Z3 asymmetric
The asymmetry of diag-(b) is coming from a factor of Re[exp(-i2πn/3)]
Z3 asym. terms are removed because
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 24
Averaged Averaged correlatorscorrelators
However, this is not an exact method to avoid the constant contribution.
The 3 times wrapping diagram is also Z3 symmetric. the contribution is not canceled.but, O(exp(-mqNt)) » O(exp(-3mqNt))
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 25
Midpoint subtraction Midpoint subtraction analysisanalysis
usual effective masses at T>0
the drastic change in P-wave states disappears in meffsub(t)
the change is due to the constant mode
subtracted effective mass
0.1
at=
80
0M
eV
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 26
Polyakov loop sector dependencPolyakov loop sector dependencee
Results for Av channel
after Z3 transformation const. Re(exp(-i2πn/3))*const.
even below Tc, small const. effect enhances the stat. fluctuation.
drastic change in P-states disappears.
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 27
Results with extended Results with extended op.op.
The extended op. yields large overlap with lowest states
Spatially extended operators:
with a smearing func. φ(x) in Coulomb gauge
point source func. smeared source func.
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 28
Results with extended Results with extended op.op.
extended op. enhances overlap with const. mode
small constant effect is visible in V channel
no large change above Tc
in meffsub(t) and meff
ave(t)
usual effective mass subtracted effective mass
averaged effective mass
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 29
DiscussionDiscussion
The drastic change of P-wave states is due to the const. contribution. There are small changes in SPFs ( except for ω=0 ).
Why several MEM studies show the dissociation of χc states ?
point operators extended operatorssubtracted averaged subtracted averaged
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 30
Difficulties on non-lowest Difficulties on non-lowest statesstates
M(J/ψ(1S)) = 3097MeVM(ψ(2S)) = 3686MeV
MEM test using T=0 data
# datafor T/Tc=0
# datafor T/Tc=0.6
# datafor T/Tc=1.2
It is difficult to reproduce the non-lowest states peak at T>0Furthermore P-wave states have larger noise than S-wave states
T. Hatsuda & M. Asakawa, PRL92, 012001 (2004).
English is strange ….
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 31
DiscussionDiscussion
A.Jakovac et al., hep-lat/0611017.
Most systematic & reliable calc. using MEM for charmonium SPFs
They have concluded that the results of SPFs for P-states
are not so reliable. e.g. large default model dep.
the drastic change just above Tc is reliable results.
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 32
ConclusioConclusionn
There is the constant mode in charmonium correlators above Tc
The drastic change in χc states is due to the constant mode
the survival of χc states above Tc, at least T=1.4Tc.
The result may affect the scenario of J/ψ suppression.
In the MEM analysis, one has to check consistency of the results at using, e.g., midpoint subtracted correlators.
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 33
DiscussionDiscussion
H. Iida et al., PRD74, 074502 (2006).
Several groups have presented
almost no change in Ps channel
small but visible change in V channel
These results can be explainedby the constant contribution. - no constant in Ps channel - small constant in V channel (proportional to pi
2) in free quark case
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 34
DiscussionDiscussion
H. Iida et al., PRD74, 074502 (2006).
S-wave states : PBC p=( 0, 0, 0 ) < xAPBC p=( π/L, 0, 0 )P-wave states : PBC p=( 2π/L, 0, 0 ) > xAPBC p=( π/L, 0, 0 ) P-const. : PBC p=( 0, 0, 0 ) < xAPBC p=( π/L, 0, 0 )
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 35
DiscussionDiscussion
Polyakov loop sector dependence
S. Chandrasekharan et al., PRL82, 2463, (1999).
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Tsukuba Theory Seminar T.Umeda (Tsukuba) 36
Volume Volume dependencedependence
Size of the constant contribution depends on the volume Ns3
The dependence is negligible at Ns/Nt ≳ 2
Results on 963 x 32 ( Ns/Nt=3 similar to T>0 quench QCD calculation )