two topics on dense quark matter
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Two topics on dense quark matter
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0. What are they?
1. QCD phase diagram and collective modes Ginzburg-Landau study for dense matter with axial anomaly, strange quark mass, and meson (Kaon) condensation. [work w/ T. Hatsuda, N. Yamamoto, G. Baym: A. Schmitt and S. Stetina]
2. Astrophysical application Collective modes in CFL quark matter and its application to superfluid-vortex dynamics [in progress w/ M. Ruggieri and M. Mannarelli]
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Content of 1st topic
1. QCD phase transition and its phase diagram
1. Chiral-super interplay ー anomaly-driven CP ー
2. Collective modes ー generalized pion ー (Rho-Wirzba-Zahed, 1999)
4. Meson condensation ー CFLK condensate ー0
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Content of 2nd topic
1. The r-mode instability of neutron star
1. Mutual friction ー vortex dynamics in superfluidity ー
2. Collective modes in CFL quark matter
3. Caroli-de Gennes-Matricon (CdGM) mode
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3 recent topics of NS observations
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Steiner-Lattimer-Brown (1005.0811)Ozel-Baym-Guver (1002.3153). . ..
From TOV to EOSFrom TOV to EOS
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A NS measured using Shapiro-delay
Demorest et al., Nature 467:1081–1083(2010)
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”Evidence” of superfluidity in NS ?
D. Page et al, Phys.Rev.Lett.106, 081101 (2011)
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NS cooling via ν-emission through the interactions with the Nambu-Goldstone bosons
ν
Neutron Star Color
Superconductivity (Color Flavor Locking)
D. K. Hong, H. K. Lee, M. A. Nowak and M. Rho hep-ph/0010156, Reddy-Sadzikowski-Tachibana(‘02), Jaikumar-Prakash-Schafer(‘02)
..
CFL
ν ν
νν
Neutrino mean free path (λ)Neutrino emissivity (ε)
(Diffusion equation)
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1. Ginzburg-Landau study in dense QCD: chiral-super interplay, axial anomaly, and meson condensation(s)
Hadrons(AZUKI)
Hadronic matter(TSUBU-AN)
Quark matter(KOSHI-AN)
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QCD phase transition and its phase diagram
[ Collins-Perry (1975) ]QCD @ high temperature(T ) / density(ρ)
QCD vacuum undergoes a phase change at some values of T and ρ!
μ
T
Quark-gluon plasma (QGP)
HadronColor superconductor (CSC)
“Conjectured phase diagram” (roughly speaking)
Each phase characterized by
chiral condensate
diquark condensate
”order parameters”
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SB CSC
QGP
1. Competition between different orders
2. Strong coupling
Common features in QCD, HTS, and ultracold atoms
• Sigrist and Ueda, (‘91)• Babaev, Int. J. Mod. Phys. A16 (‘01) • Kitazawa, Nemoto, Kunihiro, PTP (‘02)• Abuki, Itakura & Hatsuda, PRD (’02) • Chen, Stajic, Tan & Levin, Phys. Rep. (’05)
Similarity between QCD and High Tc Superconductor
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• Large μ/T regime → sign problem
• T=0, but μ≠0 → Quantum Phase Transition
• Entanglement among orders (eg. High-Tc SC)
Ginzburg-Landau (GL) study in dense QCD
(Bailin-Love, Iida-Baym)
What we REALLY know is surprisingly less!
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QCD symmetry:
GL potential
Chiral field: Diquark field:
Order parameters
Underlying sym. (QCD)
Chiral-super interplay in dense QCDHatsuda, Yamamoto, Baym, M.T., PRL(’06)
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Axial anomaly
leading int. term come from anomaly
KMT
2 possible ways of contraction of 6-q KMT vertex in dense QCD !!
(Pisarski-Wilczek)
(Iida-Baym)
(New)
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(II) 2-flavor massless quark matter
Ansatz
2-flavor color superconductivity (2SC)
(I) 3-flavor massless quark matter
Ansatz Color-Flavor Locking (CFL)Alford-Rajagopal-Wilczek (1998)
Some simple ansatz for condensate fieldsSome simple ansatz for condensate fields
(※)Srednicki-Susskind proposed a similar idea in the context of χSB (1981)
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For 3 flavor massless quarks
Chiral condensate
Diquark condensate (CFL)
GL parameters
・ d ,σ≠0 is favored
•ext. source for σ
Equivalent to Ising-ferro !
Possible phases
NOR
NG
CSC
COE → Critical point !
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SB CSC
QGP
“Anomaly-induced critical point in dense QCD” Hatsuda, Tachibana, Yamamoto & Baym,
PRL(’06)
AY
HTYB
Possible phase diagram in QCD
AY=Asakawa•Yazaki
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Collective modes ----pions at intermediate density----
A concrete realization of quark-hadron continuity?
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T
Color Color superconductivitysuperconductivity
HadronsHadrons
Quark-Gluon PlasmaQuark-Gluon Plasma
?What is the form & mass spectrum of What is the form & mass spectrum of the pion at intermediate densitythe pion at intermediate density?
Pion at intermediate densityPion at intermediate density
Gell-Mann-Oakes-Gell-Mann-Oakes-Renner (GOR) relationRenner (GOR) relation
Inverse meson mass Inverse meson mass orderingordering
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・・ Mass term:Mass term: (up to )
““PionPion”” on the hadron on the hadron sideside
““PionPion”” on the CSC on the CSC sideside
・・ Mixing Mixing term:term:
Ginzburg-Landau effective LagrangianGinzburg-Landau effective Lagrangian
Effective Effective Lagrangian:Lagrangian:・・ Kinetic Kinetic term:term:
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Mass spectrum of the generalized pionMass spectrum of the generalized pion
Generalized Gell-Mann-Oakes-Renner (GOR) Generalized Gell-Mann-Oakes-Renner (GOR) relationrelation
• Hadron-quark continuity is also realized for excited Hadron-quark continuity is also realized for excited states.states.
• Axial anomaly plays a crucial role on pion mass Axial anomaly plays a crucial role on pion mass spectrum.spectrum.
= Axial anomalyAxial anomaly(( breakingbreaking U(1)U(1)AA ))
Mass eigenstate :Mass eigenstate :
Iis a mixed state of & with mixing Iis a mixed state of & with mixing angle .angle .
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Mass splittingMass splitting
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★ Physics of external stress★ー Meson (Kaon) condensation in CFL ー
A.Schmitt, S.Stephan, M.T., PRD (2011)
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Question
If finite strange quark mass is introduced from asymptotically high density side, what happens?
1. Direct effect from Ms
2. Indirect effect from Ms
→ Meson condensation in CFL
『 Physics of stress 』
(Bedaque-Schafer, 2002)
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CFL meson condensation in GL
K^0 field Kaon chemical potentialMuto-Tatsumi, PLB(92)
Chiral condensate
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Casalbuoni-Gatto PLB464(‘99)111, Hong-Rho-Zahed PLB468(‘99)261 Son-Stephanov PRD61(‘00)074012, Bedaque-Schafer NPA697(‘02)802
eff=
(Π : NG bosons)
χ: instanton contribution (T. Schafer, PRD65(‘02)094033)
.
.
perturbative results
poorly known at low densities
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Comment on gauge invariance
Elitzur’s theorem = “Local gauge invariance cannot be broken”
The use of diquark operators is just conventional. Alternatively,
one can utilize the operators of the form for chiral
and baryon symmetry breaking, respectively.
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GL free energy with Ms and meson condensation
After taking for simplicity, we obtain
GL coefficient via direct Ms
★ If one takes we recover the original GL potential.★ Below put and fix and so as to recover the previous result in Hatsuda et al. Then . ★ For each set of , one can draw the a-α phase diagram.
Muto
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GL phase diagrams
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Collective modes in CFL quark matter and its application to vortex dynamics in superfluidity
Key ingredients
• The r(otational)-mode instability of NS
• Mutual friction in superfluid vortex system
• Collective modes in CFL quark matter - A chance to pin-down NS matter content -
Work in progress w/ M. Ruggieri & M. Mannarelli
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The r(otational) mode instability of NS
Non-radial oscillations of the star with the Coriolis force acting as the restoring force
If dissipative phenomena are not strong enough, the oscillations will grow exponentially, and the star will keep slowing down until some dissipation mechanism can damp the r-modes.
Therefore, the study of the r-modes isuseful in constraining the stellar structure.
Various mechanisms been proposed
(eg. N. Andersson)
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Mutual friction in superfluid vortex system [Hall-Vinen (1956)]
An interaction btw normal & superfluid componentsprovided by vortices. It manifests in experiment as a dissipation present in rotating superfluid state.
• Magnus force btw superfluid comp. and vortex
• Force produced by the normal excitations
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• Force balance condition for a vortex
• The vortex velocity is given by
where,
(Hall-Vinen parameters)
depend on microscopicphysics and related toscattering cross sections
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• Mutual friction is the force on the superfluid
If a perturbation of the superfluid velocityis introduced, there is no guarantee that twoforces are balanced ( ).
Application to color-flavor locked quark matterIn CFL phase, baryon number symmetry is broken.
So CFL quark matter is a superfluid. If such a state exists
in NS, then it is worth to consider the mutual friction.
Energy dissip:
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Caroli-de Gennes-Matricon (CdGM) mode
In the system of fermionic superfluidity with vortex, thereare fermionic excitations trapped in a vortex core, called the Caroli-de Gennes-Matricon (CdGM) modes. Roughly speaking, the excitation energy is given by binding energy associated with radial direction of the vortex.
(mini-gap)
In ordinary superconductor, since the value ofis going to be around , the spectrum is almostcontinuous. So they dominate the low energy dynamics.While, in color superconductor, according to some modelcalculations, . Instead of those modes,one can consider fluctuations around superfluid gap.
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We are on the way of the calculations. . .
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Summary
QCD phase diagram and collective dynamics
1.Chiral-super interplay2.Generalized pion (cf. generalized vector meson in QSR)3. CFLK condensate
Vortex dynamics in rotating superfluidity 1.Mutual friction
2.Application to CFL quark matter
0
Thank you!