Dynamics of Qballs Phys.Rev.D62:047301,2000 L. Perivolaropoulos Institute.
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Transcript of Dynamics of Qballs Phys.Rev.D62:047301,2000 L. Perivolaropoulos Institute.
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
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.