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STUDY OF FIELD THEORIES HAVING ULTRA-VIOLET FIXED POINTS

具有紫外不动点的场论研究

基本信息

批准号：
63540228
负责人：
BANDO Masako
金额：
$ 0.9万
依托单位：
FACULTY OF GENERAL ARTS, AICHI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540228/
关键词：
Ultraviolet Fixed Point Spontaneous Symmetry Breakdown Dynamical Breaking of Chiral Symmetry Modern Renormalization Technique Asymptotically Free Technicolor Theory Flavor Changing Neutral Current Compositeness Condition 動力学的対称性の破れ現代的くり

项目摘要

Techinicolor(TC) is a very attractive idea so far as the gauge sector is concerned. Unfortunately ETC leads to a phenomenological disaster, the excessive flavor-changing neutral currents (FCNC). The theories having nontrivial ultraviolet fixed point, if they really exist, are found to solve the FCNC problem because of the large anomalous dimension which automatically raised the dynamical fermion masses, preserving the enough suppression of FCNC. This is the reason why the latter model was seriously examined. The purpose of this project is to study and analyze the structure of the theories having a nontrivial ultraviolet fixed point. Our main results are:(1) Using the ladder Schwinger-Dyson equation. comparison is made of the theories with fixed coupling constant with the usual running coupling constant. It is found that the latter is not enough to suppress FCNC.(2) Using the modern renormalization technique we made clear the problems of gauge dependence of the solutions of ladder S-D equation; the Landau gauge ia found to be an ultra-violet fixed point. Also the structure of the ultr-violet points of asymptotically-free (AF) and asymptotically nonfree(ANF) gauge theories; we propose the framework for treating both AF and ANF theories in a unified way.(3) The top quark mass is found to be very heavy from the recent experiments. This indicates that the interaction relevant to top quark is very strong. In such cases Higgs particles may be composite and there are some critical energy scale above which a new physics begin. The compositeness condition, combined with the renormalization group equations, plays an important role in formulating such dynamical system. However if one use the usual mass independent renormalization group equations, we are led to the inconsistency with the compositeness condition. We pointed out that this is because of the effects of the heavy Higgs mass and the mass-dependent renormalization group equation must be used.

就仪表行业而言，Technicolor（TC）是一个非常有吸引力的想法。不幸的是，ETC导致了现象学上的灾难，过度的变味中性电流（FCNC）。具有非平凡紫外不动点的理论，如果它们真的存在的话，被发现可以解决FCNC问题，因为大的反常维数自动地提高了动力学费米子质量，保持了FCNC的足够抑制。这就是为什么后一种模式受到认真审查的原因。该项目的目的是研究和分析具有非平凡紫外不动点的理论的结构。我们的主要结果是：（1）利用阶梯Schwinger-Dyson方程。对固定耦合常数的理论与通常的运行耦合常数的理论进行了比较。发现后者不足以抑制FCNC。(2)利用现代重整化技术，我们解决了梯形S-D方程解的规范依赖性问题，发现朗道规范是一个紫外不动点。也渐近自由（AF）和渐近非自由（ANF）规范理论的紫外点的结构，我们提出了治疗AF和ANF理论在一个统一的框架。(3)最近的实验发现顶夸克质量很重。这表明与顶夸克有关的相互作用是很强的。在这种情况下，希格斯粒子可能是复合粒子，并且存在某个临界能量尺度，在此之上，新的物理学开始。复合性条件与重整化群方程相结合，在建立这样的动力系统中起着重要的作用。然而，如果使用通常的质量无关重整化群方程，我们将导致与复合性条件的不一致。我们指出这是由于重Higgs质量的影响，必须使用与质量相关的重整化群方程。