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

D. Kharzeev

BNL

Winter Workshop on Nuclear Dynamics, La Jolla, 2006

Phys.Lett.B633 (2006) 260,+ work in progress

QCD and the UA(1) problem

.i

Invariant under chiral transformations in the limit of massless quarks

UL(Nf)xUR(Nf) chiral symmetry parity doubling in the hadron spectrum (not seen!)

If broken spontaneously, Nf2 = 9 Goldstone bosons.

Only 8 exist; the ninth, ’ is heavier than the proton!

Left Right

=> Something is wrong with the flavor-singlet UA(1)…

Axial anomaly

Consider the flavor singlet currentIt is not conserved even in the m -> 0 limit due to quantum effects:

Divergence can be written down asa surface term, and so is seemingly irrelevant:

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

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As a result, chiral chargeis no longer conserved

QCD vacuum as a Bloch crystal

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“quasi-momentum” “coordinate”

“ - vacuum”

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 !

The strong CP problem

Unless =0, P, T and CP invariances are lost!

Experiment:(e.d.m. of the neutron)

Why is so small? Axions? - PVLAS -recent evidence?

Will assume =0 for the rest of the talk

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

CP-odd domains in heavy ion collisions:how to look for them?

v.e.v. of the field is equivalent to non-zero

DK,Pisarski,Tytgat‘98

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

What are the experimental signatures?

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…

Azimuthal anisotropy:collective flow of strongly interacting matter

Hydro limit

STAR

PHOBOS

Hydro limit

STAR

PHOBOS

Description in terms of relativistic hydrodynamics

A.Nakamura and S.Sakai, hep-lat/0406009

Quark-gluon plasma: more fluid than water?

KSS bound:strongly coupled SUSY QCD = classical supergravity

Superfluidhelium

Azimuthal anisotropy = angular momentum

What happens if a superfluid is rotated?

Magnetic vortices in rotating super-fluids

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of Vortex Lattices in Bose-Einstein Condensates, Science 292, 476 (2001).

E.J. Yarmchuk, M.J.V. Gordon, and R.E. Packard,

Observation of Stationary VortexArrays in Rotating Superfluid Helium, Phys. Rev. Lett. 43, 214 (1979).

Magnetic vortices

“Higgs” field Energy density

Magnetic vortices in QCD superfluid and CP violation

E

Pz

Left quarksRight anti-quarks

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)

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

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 - quarkcan escape into the fluid

(no CP violation for massless quarks!)

What is M in a strongly coupled fluid?

Magnetic vortices in QCD superfluid and CP violation

Analogs:

Magnetic monopole - induced baryon decay Cosmic strings Chirality generation in superfluid 3He

…………

Charge asymmetry w.r.t. reaction plane as a signature of strong CP violation

+

-

excess of positivecharge

excess of negativecharge

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:

Analogy to P violation in weak interactions

Charge asymmetry w.r.t. reaction plane: how to detect it?

+

-

m

kS.Voloshin, hep-ph/0406311

Expect

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

…

What are the implications for the Early Universe?

What is the origin of cosmic magnetic fields?

Magnetic field in M51:Polarization of emission

Beck 2000

Magnetic fields are abundantin the Universe at large scales:

3 G field in Milky Way;

1-40 G fields in clusters of galaxies

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 vacua carry magnetic field;(“magnetic helicity”,…)Primordial magnetic field generation at the QCD phase transition?

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?

What is the origin of the matter-antimatter asymmetry

in the Universe?

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1. B violation2. CP violation3. Non-equilibrium dynamics

A.D. Sakharov,JETP Lett. 5 (1967) 24

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

2. Strong CP violation separation of matter and antimatter in the Universe at the QCD phase transition ?

e.g. V.Kuzmin, V.Rubakov and M.Shaposhnikov, Phys.Lett.B155(1985)36

Summary

1. 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