Dynamics of Qballshttp://leandros.chem.demokritos.gr/qballs

Phys.Rev.D62:047301,2000

L. Perivolaropouloshttp://leandros.chem.democritos.gr

Institute for Nuclear Physics Research

Demokritos Research Center

Work in collaboration with

M. Axenides, E. FloratosDemokritos Research Center

and

S. KomineasUniv. of Bayreuth (Germany)

Structure of Talk

1. Introduction What is a Q Ball

Q Ball FormationThe Role of Dynamics

2. Q Balls on the lineExistence - Stability - Virial TheoremInteractions - Scattering

3. Q Balls on the PlaneFusion or Fision?

4. Scattering in 3D5. Conclusion

Motivation: Understand the evolution ofQ Balls in a cosmological setup

What is a Qball?Dynamically Stable Time Dependent Solutionwith a rotating internal phase. Its stability is due to the conservation of Noether charge.

Simplest Example:

Field Equation (1+1 dim):

Qball ansatz:

Conserved Noether Charge

Solution Exists for:

Q Ball FormationInstabilities of Coherent Affleck-Dine Scalar

due to flat directions of SUSY breaking induced potentials

Example of Affleck-Dine Potential

( K < 0 )

Affleck-Dine Field:

Fluctuations:2

22

0 3 Q Ball Formationk

m K Instabilitiesa

Kasuya - Kawasakihep-ph/0002285

The Role of Dynamics

MSSM: Qballs form as condensates of squarks and sleptons with conserved charge the Baryon and Lepton number.

Thus:

•Qballs can form by the Aflecck-Dine mechanism(Instabilities of Homogeneously Rotating AD Scalar)

•Large Stable Qballs can form Cold Dark Matter

•Unstable Qballs can lead to Baryon AsymmetryIsocurvature baryon fluctuations

Q: How do interactions and scattering affect thecosmological evolution of Qballs?

Q Balls on the Line I:Existence - Stability

Energy:

For Stability:20 (qball solution), 0Q QE E

Find B, ω for 0 eigevalue Ground State

x

x

Virial Theorem

The Qball energy may be written as:

Rescale Spatial Coordinate x:

Minimize with respect to rescaling parameter α:

Virial Theorem

Condition for stabilityalways satisfied.

Q Balls on the Line II:Interactions - Scattering

Ansatz for two interacting Qballs at distance 2 x0

1 0 2 0where ( ), ( )x x x x

DominantTerm

2 24, 0.9,

9B

Analytic

Numerical

Spatial Oscilation Frequency is Double the Internal Rotation Symmetry

BreatherOscillations

Scattering

Define:

Boosted Configuration:

Initial Conditions:

Evolved System 0 1 2

40.2, 0.51, B=

9v

Long-lived central Q Ball

Q Balls on the PlaneFusion or Fision I

1 2 00.75, v 0.2 Fusion (merging)

1 2 00.75, v 0.4 Fision (right angle)

Q Balls on the PlaneFusion or Fision I

1 2 00.75, v 0.8 Pass Through

Qualitative Preliminary Result (not published)

cv

Q

Particle Behavior (pass through)

Particle Behavior (merge)

Soliton Behavior (fision)

Q Balls on the PlaneFusion or Fision

1 2 1 2i f0.75, v 0.4 0.6, v 0.25i i f f

Q/Q0: Fractional Charge in Forward Scattering

Scattering in 3D I

Head on Collision (unpublished preliminary results)

Scattering in 3D II

Non-zero impact parameter

Conclusion

Studied Dynamics of Q Balls in 1D, 2D, 3D.

1D: Stability Sector, Virial Theorem,Breather Oscillations of Q Ball pairs

int( ) 2 space

2D Scattering:

1

1 2

2

( )

c

c c

c

v v fusion

v v v fision right angle

v v Pass Through

3D Scattering (Preliminary):Q Ring Formation

Implications:Q Ball Cosmological EvolutionFision implies tha Q Ball number may increasewhile size decreases leading to instabilities.