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Dynamics of Qballs http://leandros.chem.demokritos.gr/qballs Phys.Rev.D62:047301,2000 L. Perivolaropoulos http://leandros.chem.democritos.gr Institute for Nuclear Physics Research Demokritos Research Center Work in collaboration with M. Axenides, E. Floratos Demokritos Research Center and S. Komineas Univ. of Bayreuth (Germany)
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Structure of Talk 1. Introduction What is a Q Ball Q Ball Formation The Role of Dynamics 2. Q Balls on the line Existence - Stability - Virial Theorem Interactions - Scattering 3. Q Balls on the Plane Fusion or Fision? 4. Scattering in 3D 5. Conclusion Motivation: Understand the evolution of Q Balls in a cosmological setup
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What is a Qball? Dynamically Stable Time Dependent Solution with 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:
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Q Ball Formation Instabilities 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: Kasuya - Kawasaki hep-ph/0002285
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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 Asymmetry Isocurvature baryon fluctuations Q: How do interactions and scattering affect the cosmological evolution of Qballs?
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Q Balls on the Line I: Existence - Stability Energy: For Stability: Find B, ω for 0 eigevalue Ground State x x
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Virial Theorem The Qball energy may be written as: Rescale Spatial Coordinate x: Minimize with respect to rescaling parameter α: Virial Theorem Condition for stability always satisfied.
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Q Balls on the Line II: Interactions - Scattering Ansatz for two interacting Qballs at distance 2 x 0 Dominant Term Analytic Numerical Spatial Oscilation Frequency is Double the Internal Rotation Symmetry Breather Oscillations
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Scattering Define: Boosted Configuration: Initial Conditions: Evolved System Long-lived central Q Ball
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Q Balls on the Plane Fusion or Fision I
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Qualitative Preliminary Result (not published) Particle Behavior (pass through) Particle Behavior (merge) Soliton Behavior (fision)
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Q Balls on the Plane Fusion or Fision Q/Q 0 : Fractional Charge in Forward Scattering
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Scattering in 3D I Head on Collision (unpublished preliminary results)
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Scattering in 3D II Non-zero impact parameter
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Conclusion Studied Dynamics of Q Balls in 1D, 2D, 3D. 1D: Stability Sector, Virial Theorem, Breather Oscillations of Q Ball pairs 2D Scattering: 3D Scattering (Preliminary): Q Ring Formation Implications: Q Ball Cosmological Evolution Fision implies tha Q Ball number may increase while size decreases leading to instabilities.
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