Download - Chiral Magnetic Effect on the Lattice
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Chiral Magnetic Effect on the Lattice
Seminar @ Komaba, June 13, 2012
Arata Yamamoto(RIKEN)
AY, Phys. Rev. Lett. 107, 031601 (2011)AY, Phys. Rev. D 84, 114504 (2011)AY, Lect. Notes of Phys., in press
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Chiral Magnetic Effect[D.E.Kharzeev, L.D.McLerran, H.J.Warringa (2007)]
Early Universe
[from NASA’s web page]
[from BNL’s web page]
heavy-ion collision (RHIC&LHC)
[from KEK’s web page]
chiral magnetic effect:
charge separation induced by a strong magnetic field
via the axial anomaly, i.e., nontrivial topology
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cf.) permanent magnet ~ 102 eV2 magnetar ~ 10 MeV2
magnetic field ~ 104 MeV2
non-central collision of heavy ions
beam
beam
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magnetic field
electric current electric current
If L = R, the net current is zero.If L R, the net current is nonzero.
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the index theorem:
Globally,
Locally,
topological fluctuation in lattice QCD [from D.Leinweber’s web
page]
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topological fluctuation
beam
magnetic field
beam
“event-by-event” charge separation
electric current
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[STAR Collaboration (2009)(2010)]
Experiments
Some asymmetry was observed, but what is it?
charged-particle correlation in RHIC & LHC
magnetic field
reactio
n
plane
emiss
ion
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[K.Fukushima, D.E.Kharzeev, H.J.Warringa (2008)]
Chiral chemical potential produces a chirally imbalanced matter.
right-handedFermi sea
left-handedFermi sea
Chiral Chemical Potential
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magnetic field
electric current
positive helicity
negative helicity
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[K.Fukushima, D.E.Kharzeev, H.J.Warringa (2008)]
the Dirac equation coupled with a background magnetic field
Induced current
magnetic field
electric current induced electric current
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“sign problem”
In lattice QCD at finite density,
For small chemical potential,
reweighting, Taylor expansion, canonical ensemble,imaginary chemical potential, density of states, …
two-color QCD, isospin chemical potential,chiral chemical potential
For large chemical potential,
Sign problem
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Wilson-Dirac operator
NO sign problem !!
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continuum QCD:
discretization
uncountable infinitefunctional integral
countable infinite (finite)multiple integral
Lattice simulation is powerful in nonperturbative QCD !!
lattice QCD:
Lattice QCD Simulation
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magnetic field
vector current
L R
magnetic field
Q 0
+
-
Chiral magnetic effect in lattice QCD
topological charge: chiral chemical potential:
by A.Y. by Connecticut and ITEP
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2+1 flavor QCD+QED with the domain-wall fermion [M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou (2009)]
Lattice QCD with a fixed-topology
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SU(2) quenched QCD with the overlap fermion [P.V.Buividovich, M.N.Chernodub, E.V.Luschevskaya, M.I.Polikarpov
(2009)]
Lattice QCD with a background topology
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Why can we obtain nonzero current?
Lattice QCD at :
Lattice QCD at :
Q=2 gauge configuration[M.Garcia Perez, A.Gonzalez Arroyo,
A.Montero, P.van Baal (1999)]
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• the Wilson gauge action + the Wilson fermion
action
• flavor:
• lattice size:
• lattice spacing: fm
• pion/rho-meson mass:
• deconfinement phase
Lattice QCD with a chiral chemical potential
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Chiral charge density
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Induced current
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Induced current
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[K.Fukushima, D.E.Kharzeev, H.J.Warringa (2008)]
by fitting the lattice data
from the Dirac equation
Induced current
lattice artifacts
e.g. dielectric correction [K.Fukushima, M.Ruggieri (2010)]
e.g. renormalization
physical effects
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Systematic Analysisquenched QCD simulation
lattice spacing dependencevolume dependencequark mass dependence
of
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Renormalization
renormalization factor:
cf.) nonperturbative renormalization
[L.Maiani, G.Martinelli (1986)]
The local vector current is renormalization-group variant on the lattice.
discretization artifact:
In the continuum limit ,
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Lattice spacing
The induced current depends on the lattice spacing.
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Spatial volume Quark mass
Independent of volume, quark mass, and temperature
chiral limit
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P and its susceptibility is independent of the spatial volume.
crossover
confinement
deconfinement
Phase Diagram
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crossover
1.0
?
isospin chemical potential[J.B.Kogut, D.K.Sinclair (2004)]
For a first-order transition,
confinement
deconfinement
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Summary
• We have performed a lattice QCD simulation with the chiral chemical potential.
• By applying an external magnetic field, we have obtained the induced current by the chiral magnetic effect.
• The continuum extrapolation is quantitatively important.
• chiral symmetry ?