chiral magnetic effect on the lattice seminar @ komaba, june 13, 2012 arata yamamoto (riken) ay,...
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Chiral Magnetic Effect on the LatticeChiral 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
reac
tion
plane
emis
sion
[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
[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
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
[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 Analysis
quenched QCD simulation
lattice spacing
dependence
volume dependence
quark 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 ,
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