Baryon Number Violation in TeV range and Asymptotic Behavior of Perturbative series
Project/Area Number  05640341 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
素粒子・核・宇宙線

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
AOYAMA Hideki Faculty of Integrated Human Studies, Kyoto University, As.Professor, 総合人間学部, 助教授 (40202501)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1994 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Standard Model / Baryon Number Violation / Lepton Number Violation / Tunnel effect / Nonperturbative effects / Saddlepoint method / Pathintegral / Valley Method / 標準模型 / バリオン数非保存 / レプトン数非保存 / トンネル効果 / 非摂動的効果 / 鞍点法 / 経路積分 / バレー・メソッド / 標準弱電磁理論 / バリオン数 / レプトン数 / アノマリー / 非摂動論的効果 / 漸近性 
Research Abstract 
In this research, we have studied tunneling phenomena in field theories, motivated by baryon number violation processes in the standard model. One important issue is that of the interrelation between the perturbative calculation and nonperturbative one. In models with tunneling phenomena, it is known that the perturbation theory is not summable, not even by Borel's method. Thus some cutoff for the higher order terms are necessary. We have analyzed this issue and found that when a cutoff is introduced for the above purpose, it also cuts off the perturbativelike configurations in the nonperturbative calculation, i.e., instantonantiinstanton pair with short separation. Another interesting development is that of the Valley method. It was originally proposed to handle instantonantiinstanton pair by myself and Kikuchi. In this research, we applied it to continuous theory for the first time and solved it for a scalar theory in 4dim. When there is a false vacuum, a vacuum of true vacuum
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can be created by quantum tunneling. This is studied by Coleman and is known to lead to a decay rate of the false vacuum. The valley method enables one to extend Coleman's analysis for 'induced decay' of the false vacuum. We have solved the valley equation for this case and identified bubbles that are created for induced decay. We further studied the complextime methods. It is based on the saddlepoint method for Fourier transform of the time variable in the Feynman kernel. Existence of the saddlepoints in the complextimeplane leads one to deform the integration contour to complex time. In the past, it was assumed that the integration contour deformed as such go though all the physical saddle points. We have carefully analyzed this problem and managed to prove the validity of this method and identified the weights of each saddle points which were so far in the clouds. Through these research I believe that I have been able to advance our undeerstanding of various aspects of quantum tunneling phenomena. Less

Report
(4results)
Research Output
(10results)