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Particle Production and Vacuum Selection with Higher Dimensional Interaction

Particle Production and Vacuum Selection with Higher Dimensional Interaction. Sesihi Enomoto ( Nagoya Univ. ) Collaborators : Nobuhiro Maekawa ( Nagoya Univ. ) Tomohiro Matsuda ( Saitama Institute of Tech. ) Satoshi Iida ( Nagoya Univ. ). Contents.

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Particle Production and Vacuum Selection with Higher Dimensional Interaction

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  1. Particle Production and Vacuum Selectionwith Higher Dimensional Interaction Sesihi Enomoto ( Nagoya Univ. ) Collaborators : NobuhiroMaekawa ( Nagoya Univ. ) Tomohiro Matsuda ( Saitama Institute of Tech. ) Satoshi Iida ( Nagoya Univ. ) Contents 1. Introduction 2. How about Higher Dimensional Interaction? 3. Summary COSMO 2012 @ Beijin

  2. 1. Introduction • Problem of the Vacuum Selection • There exists many vacua in the GUT or the string theory…  Which vacuum is selected? How? • “Beauty is attractive.” ・・・ L.Kofman, A.Linde, X.Liu, A.Maloney, L.McAllister, E.Silverstein (2004) The vacuum wherethe symmetry is enhanced tends to be selected. ? ? ? COSMO 2012 @ Beijin

  3. Moduli Trapping & Particle Creation [L.Kofman, A.Linde, X.Liu, A.Maloney, L.McAllister, E.Silverstein, JHEP 0405, 030 (2004)] • Lagrangian : Note : becomesmassless @ ! • EOMs ， 　　　　⇒　　　 ( : frequency of ) • The Asymptotic Solutions ( , valid in ) : complex moduli (classical) , : real scalar particle (quantum), : coupling “Enhanced Symmetry Point” (ESP) Wave func. Creation / Annihilation op. ESP COSMO 2012 @ Beijin

  4. particles are produced when approaches the ESP (). • Because becomes massless @ ESP, the kinetic energy of converts to particles. • The produced number density : • Once is produced, then the effective potential is established for . Potential Energy Initial Kinetic Energy ＝ production! ESP is trapped around the ESP. --> vacuum selection production! COSMO 2012 @ Beijin

  5. 2. How about Higher Dimensional Interaction? • The higher dim. int. becomes important in some case. • Lagrangian : ( : cutoff ) • For example : The established effective potential The frequency of : ⇒ ★ The trapping effect is enhanced steeply @. • How about the produced particle number? • How about the size of particle production area? COSMO 2012 @ Beijin

  6. The particle production area from the ESP can be evaluated roughly, 　　⇒　　. ★ If ,then the production area is larger than the case of . • Estimation of produced particle number • WKB type solution (wave func. of) ( , : Bogoliubov coefficients ) • EOMs • Initial conditions ： 　　⇒　 Bogoliubov transformation COSMO 2012 @ Beijin

  7. Solution by the leading order, ・　　⇒　 　・　Using the steepest descent method , we obtain as [D. Chung, Phys. Rev. D 67, 083514(2004)] ★ This result does not contain the impact parameter. So, it is expected that particle production area is broad in this region. (cosnt.) ESP COSMO 2012 @ Beijin

  8. Comparing with the numerical calculation • EOMs ( ) • We calculate the above EOMs numerically, and obtain the number density ( ) from . • The number density can be calculated from the wave functionby [B. Garbrecht, T. Prokopec, M. Schmidt, Eur. Phys. J. C 38, 135 (2004)] • We evaluate the number density by changing and the impact parameter . COSMO 2012 @ Beijin

  9. The relation of impact parameter and produced particle number • The analytic solution for is roughly good. • The produced particle number at small is reduced when is larger. • However, the production area is larger. ESP ( , ) By the first introduced article. COSMO 2012 @ Beijin

  10. , • Parametric resonance and trapping effect 5 • In case of approaching the ESP many time, particles are exponentially produced by the parametric resonance. • The trapping effect is enhanced in case of larger • Therefore, particle production effect is enhancedbecause of approaching to the ESP many times. 5 5 COSMO 2012 @ Beijin Same time scale each other

  11. 3. Summary • We studied about the particle production and the trapping effect with higher dimensional interaction. • The trapping effect is enhanced at cutoff scale. • The particle production area is larger for larger . • And also, the particle production effect is enhanced due to approaching to the ESP many times. COSMO 2012 @ Beijin

  12. Back up COSMO 2012 @ Beijin

  13. COSMO 2012 @ Beijin

  14. 3. Summary • We studied about the particle production and the trapping effect with higher dimensional interaction. • The produced particle number due to approaching to the ESP 1 time is reduced for larger. • However, the particle production area is larger for larger . • The trapping effect is enhanced at cutoff scale, and also the particle production effect is enhanced due to approaching to the ESP many times. COSMO 2012 @ Beijin

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