Download The Chiral Magnetic Effect and Local Parity Violation D. Kharzeev

26th Winter Workshop on Nuclear Dynamics, Ocho Rios, Jamaica, January 2-9, 2010
The Chiral Magnetic Effect
and
Local Parity Violation
D. Kharzeev
BNL & Yale
1
Since the beginning of physics, symmetry
considerations have provided us with an
extremely powerful and useful tool in our
effort to understand nature. Gradually
they have become the backbone of our
theoretical formulation of physical laws.
T.D. Lee
2
P and CP invariances are violated
by weak interactions
What about
strong interactions?
C.N.Yang
T.D.Lee
1957
CP violation J.W.Cronin, V.L.Fitch
1980
Complex CKM mass matrix
Y. Nambu, M. Kobayashi, T. Maskawa
2008
Very strict experimental limits exist on
the amount of global violation of P and
CP invariances in strong interactions
(mostly from electric dipole moments)
But: P and CP conservation in QCD is
by no means a trivial issue...
Can a local P and CP violation occur in
QCD matter?
Charge asymmetry w.r.t. reaction plane
as a signature of strong P violation
excess of positive
charge
+
-
excess of negative
charge
Electric dipole moment of QCD matter!
DK, Phys.Lett.B633(2006)260 [hep-ph/0406125]
Talks by S. Voloshin and G. Wang [STAR]
6
Local P, CP violation at high T ?
Talks by
S. Voloshin,
G. Wang
[STAR Coll.]
Large, statistically
significant difference!
Stronger opposite-charge correlations in CuCu
(less absorption?)
STAR Coll.,
arXiv:0909.1717
8
The PHENIX result
talk by N. Ajitanand, Dec 17
Data 0-5% 0.4<pT<0.7
unreflected
reflected
Fast Sim (with decay)
a1=0.04
a1=0.033
a1=0.02
1.005
Data 20-30% 0.4<pT<0.7
unreflected
reflected
Fast Simulator (with decay)
a1=0.065
a1=0.055
a1=0.04
1.01
Cp
Cp
1.01
1
1.005
1
PHENIX Preliminary
0.995 -1
-0.5
PHENIX Preliminary
0
!S
0.5
1
0.995 -1
-0.5
0
0.5
!S
9
1
Charge separation = parity violation:
!
B
!
B
P - reflection
P-odd
P:
! → B;
!
p! → −!
p; B
! →L
!
L
Analogy to P violation in weak interactions
C.S. Wu, 1912-1997
BUT:
the sign of
the asymmetry
fluctuates
event by event
Annals of
Mathematics,
1974
Chern-Simons forms
What does it mean for a gauge theory?
Chern-Simons theory
What does it mean for a gauge theory?
Geometry
Physics
Riemannian connection
Curvature tensor
SCS
k
=
8π
!
M
d3 x "ijk
Gauge field
"
Field strength tensor
#
2
Ai Fjk + Ai [Aj , Ak ]
3
Abelian
non-Abelian
Chern-Simons theory
SCS
k
=
8π
!
d3 x "ijk
M
"
#
2
Ai Fjk + Ai [Aj , Ak ]
3
Remarkable novel properties:
gauge invariant, up to a boundary term
topological - does not depend on the metric, knows only
about the topology of space-time M
when added to Maxwell action, induces a mass for the gauge
boson - different from the Higgs mechanism!
breaks Parity invariance
Topology in QCD
Energy of
gluon field
NC
S
= 2
-1
0
instanton
sphaleron
Sphalerons:
random walk of
topological charge at finite T:
1
2
16
Topological number fluctuations in QCD vacuum
(“cooled” configurations)
D. Leinweber
17
Topological number fluctuations in QCD vacuum
ITEP Lattice Group
18
Diffusion of Chern-Simons number in QCD:
real time lattice simulations
DK, A.Krasnitz and R.Venugopalan,
Phys.Lett.B545:298-306,2002
P.Arnold and G.Moore,
Phys.Rev.D73:025006,2006
Is there a way to observe topological charge
fluctuations in experiment?
Relativistic ions create
a strong magnetic field:
H
Heavy ion collisions as a source of the strongest
magnetic fields available in the Laboratory
DK, McLerran, Warringa
46
Heavy ion collisions: the strongest magnetic
field ever achieved in the laboratory
47
θF F
µν = θ∂µ JCS = ∂µ [θJCS ] − ∂µ θJCS .
f
(16)
µ a full derivative and can be omitted; introfirst term
on sign
r.h.s. ofis A
again
fficient
and
µJ
g notationof Maxwell-Chern-Simons, or axion, electrodynamgrangian
The situation is different if the
field θ = θ("x, t) varies in space-tim
"
pair
of
Maxwell
equations
(which
is
a
consequence
of the fact that
Pµin=(12)
∂µ θ represents
= (M, P ) a full divergence
(17)
tant, Indeed,
then theinlast
term
this case we have
expressed
through the(12)
vector
potential)
isform:
not modified:
nare
re-write
the Lagrangian
in
the
following
µ
µ
µ
µ
F˜µν Fµν =θ∂Fµ˜µν
JCS
Fµν = θ∂µ JCS
= ∂µ [θJCS
] −(14)
∂µ θJCS
.
(1
1∂µ F̃µνµν = J ν . µ c
µ
(21)
L
=
−
.
(18)
F
F
−
A
J
+
P
J
MCS
µν
µ
µ
CS
The
first
term
on
r.h.s.
is
again
a
full
derivative
and
can
be
Axial omitted;
current intr
4
4
mons current
ducing
notation
"
of quarks
enient
to write
down
these
equations
also
in
terms
of
the
electric
E
θ is a pseudo-scalar
field,
P
is
a
pseudo-vector;
as
is
clear
from
(18),
µ
µ
µνρσ
Pµ = ∂µ θ = (M, P" ) (15)
(1
J
=
'
A
F
,
"
ν
ρσ
CS
netic
B
fields:
ys a role of the potential coupling to the Chern-Simons current (15).
we canthe
re-write
Lagrangian
in the
following variable
form: and
ver, unlike
vector the
potential
Aµ , Pµ(12)
is not
a dynamical
lian analog of (4). ∂Being
a
full
divergence,
this
term
does
!
"
" by the dynamics of chiral charge – in our case,
E
seudo-vector
that
is
fixed
"motion
" −and does
"not
"µνthe
"electrodynamics.
" ,µ c
1 B
×B
=
J
+
c
M
−
P
×
E
(22)
µ
uations of∇
affect
L
=
−
.
(1
F
F
−
A
J
+
P
J
µν
µ
µ CS
mined by the fluctuations
of topological
charge
in
QCD.
∂t MCS
4
4
"4 · E
" = ρ +the
"µ is a pseudo-vector;
(3 + Since
1) space-time
dimensions,
Pµ selects aasdirection
θ is a pseudo-scalar
field,
P
is(23)
clear from (18
∇
cP"pseudo-vector
· B,
ace-time
and athus
Lorentz
and rotational
invariance: the
it plays
rolebreaks
of the the
potential
coupling
to the Chern-Simons
current (15
"
∂invariance
Bpotential w.r.t.
oral component
M breaks
the
while
However, unlike
the
vector
is not aboosts,
dynamical
variable an
"
"
∇×E+
= 0, Aµ , PµLorentz
(24)
∂t by
patialiscomponent
P" picks
direction
in space.
On the
other
a pseudo-vector
thata iscertain
fixed
the dynamics
of chiral
charge
– in our cas
Photons "
in (2determined
+ 1) dimensions
for the spatial
" ·B
" is=no
by the there
fluctuations
of topological
chargecomponent
in QCD.
∇
0, need
(25)P
the Chern-Simons current (15) in this case reduces to the pseudo-scalar
" $are
(3
1)the
space-time
dimensions,
thethe
pseudo-vector
νρσ the
µ selects
J)
electric
charge
and
densities.
One can P
see
that a directio
ity
AIn
,+so
last term
incurrent
(18) takes
form
ν Fρσ
in Chern-Simons
space-time andterm
thus leads
breaksto the
Lorentz
and rotational
invariance: th
nce of
essential
modifications
of the
νρσ
From QCD back to electrodynamics:
Maxwell-Chern-Simons theory
te down these equations also in terms of the electric E
"
:
∂
B
"
"
∇×E+
∂t
= 0,
(24)
! Magnetic
monopole
"
" ·B
" = 0,"
∇
(25)
∂
E
"
"
"
"
"
×B−
= J + at
c M
B − P :×the
E Witten
,
(22)
"
finite
effect
where ∂t
(ρ, J) are the electric charge
θ and current densities. One can see that
the presence of Chern-Simons term leads to essential modifications of the
! illustrating the dyE
Maxwell
theory.
Let
us
look
at
a
few
known
examples
" ·E
" = ρ + cP" · B,
"
∇
(23)
!
B
namics contained in Eqs(22),(23),(24),(25).
θ != 0
"
∂
B
4.2.1. The
" ×Witten
" + effect = 0,
∇
E
(24)
Let us consider, following
Wilczek [10], a magnetic
monopole in the pres∂t
q = eθ
ence of finite θ angle. In the core of the monopole πθ = 0, andθ =
away
0 from
" θ· acquires
" = 0,a finite non-zero value – therefore within
∇
B
(25)
the monopole
a finite
" pointing radially outwards from
domain wall we have a non-zero P" = ∇θ
the monopole.
to (23),densities.
the domain wall
thus
acquires
a non-zero
lectric
charge According
and current
One
can
see that
" · B.
" An integral along P" (across the domain wall) yields
charge
density
c
∇θ
E.
Witten;
n-Simons
term
leads
to essential modifications
of
the
#
dl ∂θ/∂l = θ, and the integral over all directions of P" yields the total magusnetic
lookflux
atΦ.aByfew
known
examples
illustrating
the dyF. Wilczek
Gauss
theorem,
the flux is equal
to the magnetic
charge of
qs(22),(23),(24),(25).
the monopole g, and the total electric charge of the configuration is equal to
e
θ
e2
q = c θ g = 2 θ g = 2 θ (eg) = e ,
2π
2π
π
(26)
ect
lowing
Wilczek [10],Figure
a magnetic
in
the
pres1:expression
Magneticmonopole
monopole
at finite
θ angle
acquiresc,an electric cha
where we have used an explicit
(13) for the
coupling
constant
localized on the domain wall where the value of θ changes from zero
2
to
restore
this
factor
in
front
of
e
needed.
"
rite down these equations also in terms of the when
electric
E
s:
The Chiral! Magnetic"Effect I:
"
∂
E
"−
"separation
" ,
×B
= Charge
J" + c M B
− P" × E
!
B
∂t
" ·E
" = ρ + cP" · B,
"
∇
(22)
(23)
θ=0
∼ − eθ
π ·
eB
2π
"
∂
B
" ×E
"+
! ≡ ∇θ
!
∇
= 0,
(24)
P
∂t
" ·B
" = 0,
∇
(25) L between
!
ng
that
the
domain
walls
are
thin
compared
to
the
distance
E
main walls are thin compared to the distance L between
we
find that
the and
system
possesses
an electric
dipole
moment
eelectric
system
possesses
an electric
dipole
moment
θsee
!= that
0
charge
current
densities.
One can
# to
" essential
# "modifications
# "
rn-Simons !
term "
leads
of#the
eθ eB
!
eB
·
S
θ
∼
+
· 2π
eB
·
S
θ
2
2 L;
π
(B
·
S)
L
=
q
(29)
e
f
us look
de =atc aθ few
(B
· known
S)
L =examples
qf eillustrating the dyL;
(29)
π
2π
π
2π
f
Eqs(22),(23),(24),(25).
f
$ 2
ll for the brevity of notations put f qf = 1; it is easy $
will for
the brevity of notations put f qf2 = 1; it is easy
ffect
nfollows
front of we
e2 when
needed.
θ=0
2
re this factor
in front
e when needed.
DK ’04;
ollowing
Wilczek
[10], of
a magnetic
monopole in the presA. Zhitnitsky
’06;
e. In the DK,
core
of the monopole
θ = 0, and away from
DK arXiv:0911.3715
uires a finite non-zero value – therefore within a finite
" Charge
e a non-zeroFigure
P" = 2:∇θ
pointing
radially
from
separation
effect outwards
– domain walls
that separate the region of θ !=
! is static) we find that when θ changes from zero to some θ "= 0, this
B
in a separation of charge and the electric dipole moment (29).
The chiral magnetic effect II:
chiral induction
!
B
θ=0
J! ∼
2
e
!
J! = − 2 θ̇B
2π
DK, L. McLerran, H. Warringa ’07;
K. Fukushima, DK, H. Warringa ’08;
DK, H.Warringa arXiv:0907.5007
θ̇ != 0
eθ̇
π
·
#
eB
2π
What powers the CME current?
µR
µL
Left
µL − µR = 2 θ̇
Right
Figure 4: Dirac cones of the left and right fermions. In the presence of the changing chiral
“Numerical evidence for chiral magnetic effect
in lattice gauge theory”,
P. Buividovich, M. Chernodub, E. Luschevskaya, M. Polikarpov, ArXiv 0907.0494; PRD’09
Red - positive charge
Blue - negative charge
SU(2) quenched, Q = 3; Electric charge density (H) - Electric charge density (H=0)
“Chiral magnetic effect in 2+1 flavor QCD+QED”,
M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou, ArXiv 0911.1348;
Columbia-Bielefeld-RIKEN-BNL
Red - positive charge
Blue - negative charge
2+1 flavor Domain Wall Fermions, fixed topological sectors, 16^3 x 8 lattice
Electric current susceptibility
K.Fukushima, DK,
H. Warringa, arXiv:0912.2961
The fluctuations of electric
current in magnetic
background are anisotropic,
the difference of
susceptibilities is UV finite.
Lattice data are well
reproduced theoretically.
30
Induced charge in the
confined chirally broken
phase is suppressed
DK, S. Mukherjee,
to appear
31
described by a chiral
chemical
potential µ5 whic
s of the Chiral Magnetic Effectcan
onbeastrophysa good
approximation
in
couples to the zero component of the axial vector curren
mena have recently been discussed
in Ref.
[27]; Thetures
where
theinstrong
co
in the
Lagrangian.
induced
current
such situa
rophysical implication can be found
tion caninbe[28].
written as jsmall.
= σχ B, where σχ is the Chir
Magnetic
conductivity. For
constant
homogeneou
m of massless fermions with nonzero
chirality
We
will and
take
the m
magnetic fields its value is determined by the electro
ribed by a chiral chemical potential
µ which
The forgamma
matrices
magnetic5axial anomaly and
one
flavor
and one colo
µ
ν
µν
he zero component of the axial equal
vector
current
γ } = 2g . We w
to [22,
29, 30] (see{γ
also, [31])
µ
angian. The induced current in such situathe four-vector
p
= (p
2
e
written as j = σχ B, where σχ is the Chiral
= |p|.
µ5 ,
σχ (ω = 0, p vector
= 0) ≡ σp0 =
7 (2
2π 2
onductivity. For constant and homogeneous
0.4
1
where ω and p denote
frequency and momentum respe
!
elds its value is determined σχby
the
electroτ = 1/T
tively,
and
e
equals
the
unit
charge.
For a finite numbe
!!
II.
KUBO
FOR
τ
=
0.2/T
σ
xial anomaly and for one flavor
and
one
color
χ of
colors
N
and
flavors
f
one
has
to
multiply
this
resu
0.3
c
! 2
τ
=
0.1/T
MAGNETIC
by Nc f qf where qf denotes the charge
of a quark i
2, 29, 30] (see also [31])
Chiral magnetic conductivity
σχ (ω)
σ0
0.5
σχ (ω = 0, p = 0) ≡ σ0 =
0
units of e. The generation of currents due to the anoma
j(t) 0.2
2 in background
fields or rotating systems is also discusse
e
σ0 B0
For
small magnetic fie
in
related
contexts
in
Refs.
[31–35].
µ
,
(2)
5
0.1
2π 2 For constant magnetic
can
bewhich
found
the K
fields
are using
inhomogeneou
in the plane transverse tousthe
field to
onefirst
finds order
that theintott
that
momentum
current J respecalong B0 equals [22],
d p denote frequency and
the induced vector curre
e equals the unit0 charge.
For 20a finite30number
" eΦ
# Lvector
10
of
the
current
z5µ5
-5
0
15 wit
(3
and flavors f one has toω/T
multiply this result J = e 2π π , 10
equilibrium.
More explic
t/τ
2
32
where
q
denotes
the
charge
of
a
quark
in
f
D.K.,
Warringa
PRD‘09
FIG. 3:fReal (red, solid)
andH.
imaginary
(blue,
dashed)
partis
of theFIG.
4: Induced
current
in time-dependent
magneti
$
where
L
length
of
the
system
in
the
z-directio
z
:
Real
(red,
solid)
and
imaginary
(blue,
dashed)
part
of
FIG.
4:
Induced
current
in
time-dependent
magnetic
field,
the
leading
order
normalized
Chiral
Magnetic
conductivity
at
Eq.
(49),
as
a
function
of
time,
at
very
high
tempe
The generation of currents due to
the
anomaly
and
the
flux
is
equal
to
the integral
of
theof the
magnet
µ
ding orderhigh
normalized
Chiral
at
Eq. fields
(49), Φ
as The
a function
ofplotted
time,
at different
very high
temperature.
temperatures
(TMagnetic
> µ ) for conductivity
homogeneous
magnetic
results are
for
values
characd
%j
(x)&
=
nd fields
or
systems
isfields
also
discussed
(p =
= 0homogeneous
the normalized
conductivity
is equal
toresults
1. transverse
time
scale τforof
the magnetic
emperatures
(T0).
> At
µ rotating
)ωfor
magnetic
The
are
plotted
different
valuesfield.
of the characteristic
field
over
the
plane,
5
5
Holographic chiral magnetic conductivity:
the strong coupling regime
A. Rebhan et al, JHEP 0905, 084 (2009),
and to appear;
G.Lifshytz, M.Lippert, arXiv:0904.4772
Sakai-Sugimoto model;
D.Son and P.Surowka, arXiv:0906.5044
CME in relativistic hydrodynamics;
E. D’ Hoker and P. Krauss, arXiv:0911.4518
H.-U. Yee, arXiv:0908.4189
5D Einstein gravity with
Reissner-Nordstrom black hole
coupled to
33
Topological number diffusion at strong coupling
Chern-Simons number
diffusion rate
at strong coupling
Black hole
33
D.Son,
A.Starinets
hep-th/
020505
NB: This
calculation is
completely
analogous to the
calculation of
shear viscosity
that led to the
“perfect liquid”
Classical topological solutions
at strong coupling?
yes: D-instantons in (dual) weakly coupled supergravity
D-instanton as
an Einstein-Rosen
wormhole;
the flow of RR charge
down the throat of
the wormhole describes
change of chirality
D-instantons as a source of multiparticle production in N=4 SYM?
DK, E.Levin, arXiv:0910.3355
33
What next?
Experiment
Theory and
Phenomenology
Lattice
Dynamical real-time modeling, quantitative description of
the data and detailed predictions are urgently needed, and
are on the way
36
Organizing Committee
•
•
•
•
•
Kenkji Fukushima (Kyoto Univ)
Dmitri Kharzeev (BNL)
Harmen Warringa (Johann Wolfgang Goethe-Univ)
Abhay Deshpande (Stony Brook Univ. / RBRC)
Sergei Voloshin (Wayne State Univ.)
Save the date: April 26-30, 2010
http://www.bnl.gov/riken/hdm/
International Advisory Committee
•
•
•
•
•
•
•
•
•
•
•
•
•
•
J. Bjorken (SLAC)
H. En'yo (RIKEN)
M. Gyulassy (Columbia Univ.)
F. Karsch (BNL & Bielefeld)
T.D. Lee (Columbia Univ.)
A. Nakamura (Hiroshima Univ.)
M. Polikarpov (ITEP)
K. Rajagopal (MIT)
V. Rubakov (INR)
J. Sandweiss (Yale Univ.)
E. Shuryak (Stony Brook Univ.)
A. Tsvelik (BNL)
N. Xu (LBNL)
V. Zakharov (ITEP)
P- and CP-odd effects in:
nuclear, particle, condensed
matter physics and cosmology
Supported by RIKEN-BNL, BNL-CATHIE,
37
and Stony Brook University
Back-up slides
38
Further tests at RHIC
• Parity-odd observable?
S
K
Correlations
for
identified
hadrons?
•
0 ?
• Low-energy run: the effect is expected to
weaken below the deconfinement/chiral
symmetry transition
• P-odd decays? R. Millo & E.Shuryak, ‘09
• Double diffractive production in pp collisions: sphaleron decay
in magnetic field?
Disentangle
azimuthal,
p_t dependence
from the data:
A.Bzdak, V.Koch,
J.Liao,
arXiv:0912.5050
P-odd-correlated pairs are produced at small p_t!?
40
41
42