Chiral Magnetic Effect on the Lattice
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Transcript of Chiral Magnetic Effect on the Lattice
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
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
cf.) permanent magnet ~ 102 eV2 magnetar ~ 10 MeV2
magnetic field ~ 104 MeV2
non-central collision of heavy ions
beam
beam
magnetic field
electric current electric current
If L = R, the net current is zero.If L R, the net current is nonzero.
the index theorem:
Globally,
Locally,
topological fluctuation in lattice QCD [from D.Leinweber’s web
page]
topological fluctuation
beam
magnetic field
beam
“event-by-event” charge separation
electric current
[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
[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
magnetic field
electric current
positive helicity
negative helicity
[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
“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
Wilson-Dirac operator
NO sign problem !!
continuum QCD:
discretization
uncountable infinitefunctional integral
countable infinite (finite)multiple integral
Lattice simulation is powerful in nonperturbative QCD !!
lattice QCD:
Lattice QCD Simulation
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
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
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
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)]
• 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
Chiral charge density
Induced current
Induced current
[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
Systematic Analysisquenched QCD simulation
lattice spacing dependencevolume dependencequark mass dependence
of
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 ,
Lattice spacing
The induced current depends on the lattice spacing.
Spatial volume Quark mass
Independent of volume, quark mass, and temperature
chiral limit
P and its susceptibility is independent of the spatial volume.
crossover
confinement
deconfinement
Phase Diagram
crossover
1.0
?
isospin chemical potential[J.B.Kogut, D.K.Sinclair (2004)]
For a first-order transition,
confinement
deconfinement
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 ?