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Particle Production and Vacuum Selection with Higher Dimensional Operator

This work investigates the complex relationship between particle production and vacuum selection within the framework of higher dimensional interactions, presented at the Summer Institute 2012 at Sun Moon Lake. We discuss the dynamics of vacuum selection, particularly how enhanced symmetry points (ESP) influence particle creation and trapping effects. Our findings suggest that particle number density and production areas can be significantly impacted by approaching the ESP multiple times, leading to explosive production phenomena through parametric resonance. We present analytic solutions and compare them to numerical calculations, elucidating the conditions necessary for efficient particle generation.

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Particle Production and Vacuum Selection with Higher Dimensional Operator

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  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

  13. 85 6 Summer Institute 2012 @ Sum Moon Lake

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