Strong CP violation in hot QCD: from heavy ion collisions to cosmology

1
Strong CP violation in hot QCD from heavy ion
collisions to cosmology
Winter Workshop on Nuclear Dynamics, La Jolla,
2006

• D. Kharzeev
• BNL

Phys.Lett.B633 (2006) 260, work in progress
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QCD and the UA(1) problem
Invariant under chiral
Left Right

transformations in the limit of massless quarks
UL(Nf)xUR(Nf) chiral symmetry parity
doubling in the
hadron spectrum (not seen!)
.i
If broken spontaneously, Nf2 9 Goldstone
bosons. Only 8 exist the ninth, h is heavier
than the proton!
gt Something is wrong with the flavor-singlet
UA(1)
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Axial anomaly
Consider the flavor singlet current It is not
conserved even in the m -gt 0 limit due to quantum
effects
Divergence can be written down as a surface term,
and so is seemingly irrelevant
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Instantons and the UA(1) problem
But sometimes, surface terms are important
Instantons classical Euclidean solutions of QCD
which map color SU(2) onto the sphere S3 in
Minkowski space, describe quantum tunneling
between degenerate vacua with different
topological Chern-Simons numbers
As a result, chiral charge is no longer conserved
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QCD vacuum as a Bloch crystal
q - vacuum
quasi-momentum coordinate
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The lost symmetries of QCD
The prescription
with the Bloch weight
is equivalent to adding to the Lagrangian a new
piece
which is odd under P, T, CP symmetries !
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The strong CP problem
Unless q0, P, T and CP invariances are lost!
Experiment (e.d.m. of the neutron)
Why q is so small?
Axions? - PVLAS
-recent evidence?
Will assume q0 for the rest of the talk
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The strong CP problemand the structure of QCD
vacuum
Vafa-Witten theorem P and CP cannot be broken
spontaneously
in QCD
But 1. it does not constrain metastable states
2. it does not apply at finite
temperature, finite baryon density,
finite isospin density
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CP-odd domains in heavy ion collisionshow to
look for them?
DK, Pisarski, Tytgat 98
v.e.v. of the h field is equivalent to non-zero q
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Diffusion of Chern-Simons number in QCD real
time lattice simulations
P.Arnold and G.Moore, Phys.Rev.D73025006,2006
DK, A.Krasnitz and R.Venugopalan, Phys.Lett.B5452
98-306,2002
What are the experimental signatures?
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What are the observable signatures of strong CP
violation?
rotate all CP violating phase into the quark
piece of the Lagrangian
is a complex mass parameter
In a CP-odd domain, This leads to the asymmetry
between left and right quarks
What is left and what is right? Quarks are
massive, so the definition of chirality depends
on the frame
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Azimuthal anisotropycollective flow of strongly
interacting matter
Description in terms of relativistic hydrodynamics
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Quark-gluon plasma more fluid than water?
A.Nakamura and S.Sakai, hep-lat/0406009
Superfluid helium
KSS bound strongly coupled SUSY QCD classical
supergravity
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Azimuthal anisotropy angular momentum
What happens if a superfluid is rotated?
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Magnetic vortices in rotating super-fluids
E.J. Yarmchuk, M.J.V. Gordon, and R.E. Packard,
Observation of Stationary
Vortex Arrays in Rotating Superfluid Helium,
Phys. Rev. Lett. 43, 214 (1979).
J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W.
Ketterle, Observation of Vortex Lattices in
Bose-Einstein Condensates, Science 292, 476
(2001).
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Magnetic vortices
Energy density
Higgs field
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Magnetic vortices in QCD superfluid and CP
violation
Right anti-quarks
E
Left quarks
Pz
Fluctuation of chromo-electric field in the
presence of chromo-magnetic vortex produces left
quarks and right anti-quarks (level crossing at
the 0th Landau level)
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Magnetic vortices in QCD superfluid and CP
violation
Left quarks in the electric field, energy
increases Decreases by the same amount for
right anti-quarks. Density of states
longitudinal x transverse
Rate of chirality generation
Analogous to cosmic strings, except not 1D
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Magnetic vortices in QCD superfluid and CP
violation
The Fermi momentum has to be smaller than the
mass of the quark in the fluid otherwise,
energetically unfavorable - quark can escape into
the fluid (no CP violation for massless
quarks!) What is M in a strongly coupled fluid?
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Magnetic vortices in QCD superfluid and CP
violation
Analogs Magnetic monopole - induced baryon
decay
Cosmic strings
Chirality generation in superfluid 3He
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Charge asymmetry w.r.t. reaction plane as a
signature of strong CP violation
excess of positive charge

-
excess of negative charge
Electric dipole moment of QCD matter!
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Charge asymmetry w. r.t. reaction plane violates
T, P, and (by CPT theorem) CP
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Analogy to P violation in weak interactions
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Charge asymmetry w.r.t. reaction plane how to
detect it?
m

-
k
S.Voloshin, hep-ph/0406311
Expect
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Do we see strong CP violation?
I. Selyuzhenkov et al., STAR Coll.,
nucl-ex/0510069 October 25, 2005
Need to analyze the systematics and to understand
if the effect is real
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Other signatures?
I. Separation of baryon number with respect to
reaction plane? Protons and anti-protons II.
Other observables composed of pion momenta?
Chern-Simons number of chiral fields III. Lambda
helicity correlations? J. Sandweiss
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What are the implications for the Early Universe?
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What is the origin of cosmic magnetic fields?
Magnetic fields are abundant in the Universe at
large scales 3 mG field in Milky Way 1-40 mG
fields in clusters of galaxies
Magnetic field in M51 Polarization of emission
Beck 2000
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What is the origin of magnetic fields in the
Universe?
Primordial magnetic field (E.Fermi,
1949)? Dynamo in proto-galaxy? Stars?
Galaxy? Domain walls and vortices associated
with the q-vacua carry magnetic
field (magnetic helicity,) Primordial
magnetic field generation at the QCD phase
transition?
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Baryons in the Universe
Baryons in the Universe are rare 1 baryon per
2 billions photons in the Cosmic Microwave
Background Radiation 400 photons/cm3 1
proton/m3 (Almost) no visible antimatter - why
the asymmetry?
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What is the origin of the matter-antimatter
asymmetry in the Universe?

• B violation
• CP violation
• Non-equilibrium
• dynamics

A.D. Sakharov, JETP Lett. 5 (1967) 24
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Baryon asymmetry in the Universe and strong CP
violation
1. Generation of Chern-Simons number at the QCD
phase transition is analogous to baryon number
generation in the electroweak phase transition
e.g. V.Kuzmin, V.Rubakov and M.Shaposhnikov,
Phys.Lett.B155(1985)36
2. Strong CP violation separation of
matter and antimatter in the Universe at the QCD
phase transition ?
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Summary

• P and CP violation in hot QCD is not forbidden

2. All what is not forbidden is allowed and may
exist a specific dynamical mechanism -
magnetic vortices
3. Rejecting or confirming the signal of P and CP
violation at RHIC is an urgent problem of
fundamental importance