Particle Production and Vacuum Selection with Higher Dimensional Operator

1. Particle Productionand Vacuum Selectionwith Higher Dimensional Operator Sesihi Enomoto ( Nagoya Univ. ) Collaborators :NobuhiroMaekawa ( Nagoya Univ. ) Tomohiro Matsuda ( Saitama Institute of Tech. ) Satoshi Iida ( Nagoya Univ. ) Summer Institute 2012 @ Sum Moon Lake

2. Contents 1. Introduction 2. How about Higher Dimensional Interaction? 3. Conclusion Summer Institute 2012 @ Sum Moon Lake

3. 1. Introduction • Problems 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 The vacuum wherethe symmetry is enhanced tends to be selected. ? ? ? Summer Institute 2012 @ Sum Moon Lake

4. 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 Solution ( ) : Moduli , : Quantum field, : coupling “Enhanced Symmetry Point” (ESP) Wave func. Creation / Annihilation op. ESP Summer Institute 2012 @ Sum Moon Lake

5. particles are produced when approaches the ESP. • The produced # density : • Once is produced, then the effective potential for is established. Kinetic Energy Potential Energy ＝ ESP is trapped around the ESP. --> vacuum selection Summer Institute 2012 @ Sum Moon Lake

6. 2. How about Higher Dimensional Interaction? • Why do we consider in the higher dimensional interaction? • Lagrangian : ( : cutoff ) • The frequency of: 　　　⇒　 ★ The trapping effect may be enhanced steeply @. • How about the produced particle number? • How about the produced Area? Summer Institute 2012 @ Sum Moon Lake

7. The particle production area from the ESP is roughly, 　　⇒　　. ★ If ,then the production area is spread. • Estimate of produced particle number • WKB type solution ( , : Bogoliubov coefficients ) • Initial condition ： 　　⇒　 ( from the Bogoliubov transformation ) • EOM Wave func. Summer Institute 2012 @ Sum Moon Lake

8. 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. ESP Summer Institute 2012 @ Sum Moon Lake

9. Comparing to the numerical calculation • EOMs ( ) • We calculate the above EOMs, and obtain the number density ( ) from . • Number density formula from the wave function [B. Garbrecht, T. Prokopec, M. Schmidt, Eur. Phys. J. C 38, 135 (2004)] • We evaluate for variable and the impact parameter. Summer Institute 2012 @ Sum Moon Lake

10. ( ) • The relation of impact parameter and produced particle number • Obviously, particle production area is spread for larger . • It is seems that the analytic solution for is roughly good. ESP Summer Institute 2012 @ Sum Moon Lake

11. Parametric resonance and the trapping effect • In case of approaching the ESP many time, particles are explosively produced by the parametric resonance. • The trapping effect is enhanced in case of larger , and so, production effect is enhancedbecause of approaching to the ESP many times. Summer Institute 2012 @ Sum Moon Lake

12. 3. Summary • We study 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 is available for larger area. • The trapping effect is enhanced at cutoff scale, and also the particle production effect is enhanced due to approaching to the ESP many times. Summer Institute 2012 @ Sum Moon Lake

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