1 / 22

Effect of interaction terms on particle production due to time-varying mass

Effect of interaction terms on particle production due to time-varying mass. [work in progress] Seishi Enomoto (Univ. of Warsaw) Collaborators : Olga Fuksińska (Univ . of Warsaw) Zygmunt Lalak (Univ. of Warsaw). Outline. Introduction

glynis
Download Presentation

Effect of interaction terms on particle production due to time-varying mass

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Effect of interaction terms on particle production due to time-varying mass [work in progress] Seishi Enomoto (Univ. of Warsaw) Collaborators : Olga Fuksińska (Univ. of Warsaw) ZygmuntLalak (Univ. of Warsaw) Outline Introduction Bogoliubov transformation law with interaction terms Application to our model Summary Summer Institute 2014 @ Fuji Calm

  2. VACUUM 1. Introduction )) )) x • Particle production from vacuum • It is known that a varying background causes production of particles • Oscillating Electric field  pair production of electrons [E. Brezin and C. Itzykson, Phys. Rev.D 2,1191 (1970)] • Changing metric  gravitational particle production [L. Parker, Phys. Rev.183, 1057 (1969)] [L. H. Ford, Phys. Rev.D 35, 2955 (1987)] • Oscillating inflaton  (p)reheating [L. Kofman, A. D. Linde, A. A. Starobinsky, Phys. Rev. Lett.73, 3195 (1994)] [L. Kofman, A. D. Linde, A. A. Starobinsky, Phys. Rev. D 56, 3258 (1997)] • etc… Summer Institute 2014 @ Fuji Calm

  3. : coupling • Example of scalar particle production • Let us consider : • If goes near the origin…  mass of ()becomes small around  kinetic energy of converts to  particles are produced !! • produced occupation number : : complex scalar field (classical) : real scalar particle (quantum) [L. Kofman, A. D. Linde, X. Liu, A. Maloney, L. McAllister and E. Silverstein, JHEP0405, 030 (2004)] Summer Institute 2014 @ Fuji Calm

  4. Our interests • How about supersymmetric model? • How do (quantum) interaction terms affect particle production? • Usually production rates are calculated in the purely classical background  We would like to estimate the contribution of the quantum interaction term classical quantum classical classical quantum quantum Summer Institute 2014 @ Fuji Calm

  5. Model in this talk • Super potential :  Interaction terms in components : • Stationary point : • , but can have any value • Masses •  , : massless : coupling Production may be possible Impossible…? Our main study! Summer Institute 2014 @ Fuji Calm

  6. How do we calculate with interaction term? • Towards the calculation of produced numbers • Solving Equations of Motion for field operators : : : : : • Bringing out creation/annihilation operators from field operators • Estimation of produced numbers Our approach : Using Yang-Feldman equation How do we bring out? ?Relation? ?Relation? ?Relation? ?Relation? Summer Institute 2014 @ Fuji Calm

  7. 2. Bogoliubov transformation law with interaction terms • An example with a real scalar field • Operator field equation : • Commutation relation :  Formal solution (Yang-Feldman equation) : some const. : asymptotic field x x x x x Summer Institute 2014 @ Fuji Calm

  8. Relation between in- & out-field operator • Set “as” = “in” “as” = “out” 1 Summer Institute 2014 @ Fuji Calm

  9. Representation of with field operator • is free particle, so we can expand with plane waves as • inner product relation : which comes from conditions , plane wave (time dependent) wave func. creation/annihilation op. 2 Summer Institute 2014 @ Fuji Calm

  10. Bogoliubov transformation law • Relation between and 2 1 (ordinary) Bogoliubov tf law Interaction effects Summer Institute 2014 @ Fuji Calm

  11. Produced (occupation) number :  Particles can be produced even if ! Summer Institute 2014 @ Fuji Calm

  12. 3. Application to our model • Equation of Motion (again) : • EOM for asymptotic fields (as = in, out): : : : : : : : : : macroscopic , , : microscopic Summer Institute 2014 @ Fuji Calm

  13. Solutions for Asymptotic fields • Assuming for simplicity, then ,  ( valid for ) (analytic continuation)  Summer Institute 2014 @ Fuji Calm

  14. eigen spinor for helicity op. : • Solutions for Asymptotic fields  ( valid for ) (analytic continuation)  Summer Institute 2014 @ Fuji Calm

  15. Produced Particle number  leading term is obtained  need to calculate next to leading order Focus on! Summer Institute 2014 @ Fuji Calm

  16. X • Leading term of  We estimated in special case with steepest decent method steepest decent method Summer Institute 2014 @ Fuji Calm

  17. Analytical Result @ (c.f.) • Produced number of is suppressed by factor comparing with or • This results is consistent with perturbativity Summer Institute 2014 @ Fuji Calm

  18. Leading term of (only final formula) X X Summer Institute 2014 @ Fuji Calm

  19. Numerical Results Preliminary consistent with analytical expected value Summer Institute 2014 @ Fuji Calm

  20. 4. Summary • We constructed the Bogoliubov transformation taking into account interaction effects • We calculated produced particle’s (occupation) number • , • Massless particle can be produced, however the production is suppressed by the coupling • However, the produced number in case of strong couplings may be comparable to massive particles Summer Institute 2014 @ Fuji Calm

  21. Summer Institute 2014 @ Fuji Calm

  22. Numerical Results 2 Preliminary Summer Institute 2014 @ Fuji Calm

More Related