Pions emerging from an Arbitrarily Disoriented Chiral Condensate.

Chandrasekher MukkuDeptt. of Mathematics & Deptt. of Computer

Science & ApplicationsPanjab UniversityChandigarh, India.

Collaborative and ongoing work with

Bindu Bambah:

Phys Rev D70 (2004) 034001-(1-18).

From QFT to the DCC.

Annals of Physics 314 (2004) 54-74.

Isospin squeezed states, dcc & pion production: a dynamical group

theoretic approach

And with

Bindu Bambah and Shiv Chaitanya.

HEAVY ION COLLISIONS PRESENT TO US FOR THE FIRST TIME THE OPPORTUNITY

To see the Universe in a heavy ion collisionAnd the Big Bang in a QGP,

Hold Pions in parts of our LabsAnd explain them in twenty minutes.

With Apologies to William Blake

QCD at high temperature

Quark – gluon plasmaChiral symmetry restored“Deconfinement” ( no linear heavy quark potential at large distances )Lattice simulations : both effects happen at the same temperature

Important parameters

Chiral symmetry initially restored and later broken in expanding and cooling PlasmaPlasma expanding and cooling and field roll down into broken vacuum

two competing time scalesOrientation of roll down creates domainsDomain size?Squeezing provides signalsLater discuss anisotropic expansions of plasma.

QCD admits spontaneous breaking of its approximate SU(2)XSU(2) chiral symmetry.

Spontaneous breaking of this approximate symmetry gives very small pion masses; in the limit of exact chiral symmetry these particles would be massless Nambu bosons.

Sigma Model models the QCD phase transition well.

It respects the SU(2)XSU(2) chiral symmetry of QCD with two light flavours of quark and contains a scalar field (sigma) that has the same chiral properties as the quark condensate. The sigma field represents the order parameter for the chiral phase transition.

The phase transition of the linear sigma model (without quarks) therefore provides a good starting point.

 

Modelling phase transitions in QCD

Chiral symmetry restoration at high temperature

High THigh TSYM SYM <<φφ>=0>=0

Low TLow T

SSBSSB

<<φφ>=>=φφ0 0

≠≠ 0 0at high T :at high T :

less orderless order

more symmetrymore symmetry

examples:examples:

magnets, crystalsmagnets, crystals

DCC FORMATION

Chiral order parameter in a far from equilibrium situation in the case of a sudden quench, long wavelength modes enhanced. Gives "baked Alaska" situation and in this rapidly expanding plasma the configuration of the evolving pion field will lag behind the rapid expansion

A region of DCC can be thought of as a cluster of Pions of near identical momentum around zero( coherently produced) with anomalously large amount of fluctuation of the neutral fraction

In order to produce such a state in a quark gluon plasma, the hot plasma must evolve far from equilibrium and in particular it must reach an unstable configuration such that the long-wavelength pion are amplified exponentially when the system relaxes to the stable vacuum state. Thus questions of whether a DCC forms and it evolves cannot be addressed in the framework of equilibrium thermodynamics. Techniques for applying QCD directly to such situations do not exist at present. To explain these non-equilibrium phenomena, we need to restructure the theory of phase transitions to incorporate the micro structures (or states) instead of macro structures

Traditional experimental

signals for DCC

f

fd

f

NN

Nf

c

2

1cos

4)(

cos

21

2

0

0

NEW SIGNALS EASIER TO MEASURE???

1. Pion correlations2. Total pion multiplicity distributions.3. Momentum dependent two pion correlations4. Oscillations in pion multiplicity distributions5. Oscillations in two particle correlations.

THEORETICAL QUESTIONS ABOUT DCC

Complete theoretical analysis which forms a basis of these signals

Situation can be more general leading to richer signals

Hamiltonian

Consider three scenarios of disorientation.

Woods-Saxon potential with parameter allowing for transition from adiabatic to quench.

The neutral and charged pion distribution for small squeezing (adiabatic limit)I without DCC:

The neutral and charged pion distribution for large squeezing (quenched limit) with DCC

Pion pair correlation functions at zero relative momentum

Dashed graph is for neutral pions and the continuous graph is for charged

pions.

Correlations

From the Hamiltonian,

There is an entanglement of the forward and backward pions. This entanglement provides us with correlations between the pionswith forward and backward momenta for both the charged and neutralsector, The forward momentum positively charged pions with thebackward momentum negatively charged pions and the backwardmomentum positively charged pions and the forward momentumnegatively charged pions. As the effect of DCC formation is that the difference is enhanced dramatically for the zero momentum limit. k->0

Answers to questions posed at beginning

Testing with WA98

Event Display

84 gammas12 charged particles

Xpos(cm)

Yp

os(c

m)

February 8-12 ICPAQGP 2005

Ref: M.M. Aggarwal et. al. Poster in lobby.