第一章: 簡介論文內容
第二章: 討論標準模型精密測量; 分析精密測量數據可得知 zbb 耦合有異於標準模型, 因此我們創造一個模型

可以解釋這個現象. 簡而言之, 我們預測1995 年在 FermiLab發現的 頂夸克事例, 其實是一個 電荷4/3的

右旋SU(2)-doublet 新粒子, 而真正的頂夸克可能重於230 GeV. 我們並展示這個新模型可以通過所有的

精密測量檢驗且提供與實驗相符更好的結果.

第三章: 討論輕子反常磁耦極的原理, 理論上的預測及實驗上的測量結果. 我們並且計算了所有可能超越標準模型

純量場及偽 純量場 2-loop Barr-Zee graph 對渺子 g-2 的貢獻. 我們發現對一般現有理論模型而言, 這個貢獻相 當於整個標準模型電弱的貢獻, 不能被忽略.

第四章: 討論Minimum Supersymmetric Standard Model 偽純量場 2-loop Barr-Zee 對電子電偶極及中子電偶極的貢獻.

第五章: 討論由R-對稱破壞及 2-loop Barr-Zee graph 對中子電偶極的貢獻, 並由和實業的比較得出R-對稱破壞耦合

常數大小的限制.

---

1989 marks an important year for high energy community.
In August of that year, LEP at CERN started taking unprecedentedly precise data at Z-pole

which can probe the electroweak quantum correction.

The accuracy of $Z$- mass measurement achieved to $0.1\%$ at that year.

About the same time, SLC and the Mark II detector were switched on at SLAC, and FNAL

began the precision studies of the W mass.

%

The experiments which measure SM observables, the accuracy often reach $0.1\%$ and sometimes

much better, usually be called precision measurements.

Through measuring the EW loop quantum correction to some observables, people knew top mass

should range in $150-190$GeV before the discovery of top . The estimate was not far from

the observed value. That's an impressive success of SM.

The precision measurements are not only used to test SM but also have been used to probe

the effects of physics beyond SM.

%

In Chapter 2, firstly, I want to give some examples to show how the renormalization(RG)

program of SM works and how the quantum correction modifies the observables. But the subject

is vest and well-known, I would only provide some `flavor' of it.

Secondly, I would like to emphasize that there are many ways to do RG and the observables

are different from scheme to scheme. One has to be careful when comparing the theoretical

predictions and experiment data.

Thirdly, I would like to include the projects we have done[4,5] which was motivated by

the deviation($\sim 3\sigma$) of $Zb\bar{b}$ coupling between the SM prediction and precision

measurements.

%

Following the line, in Chapter 3, I present the project[8] we were doing while

composing this note. We calculated the 2-loop Barr-Zee type diagrams\footnote{\prl 65 21 1990 . }

involving exotic Higgs sector contributing to muon $(g-2)$.

The electron $g-2$ is the most accurate experiment, to $10^{-12}$, human being has ever done.

But the quantum loop effects, except the photonic loops, are severely suppressed by the

tiny mass of electron. So it serves mainly as a rigid proof of QED but left very little

information of EW quantum correction let alone the new physics.

In the case of muon, since the mass of muon is about 200 times bigger then electron's,

the EW quantum correction, although small, must be included. With the on going improvement

of experiment E821 at BNL\footnote{ see for example, B. Lee Roberts, hep-ex/0002005 (2000).}

, which was planned to achieve the accuracy of $10^{-10}$, we are

very likely to test the 2-loop EW quantum correction. If lucky, we can also see the effects

of new physics. On the other hand, by comparing with muon $g-2$ experiment one can put

stringent limit on physics beyond SM.

%%

%% Discuss why the Barr-Zee diagram is important.

Before the project on muon $(g-2)$, we had applied the same technique to study the 2-loop EDM of

electron and neutron due to the charged Higgs[6]( Chapter 4) and constraint on R-parity

violation parameter by neutron EDM[7](Chapter 5).

%

In general, the two loop calculation is very tedious and involving too many diagrams.

And two loop diagrams involving Higgs are most suppressed by at least two powers of light fermion

mass. The only 2-loop diagram involving Higgs sector which escape the light fermion mass

suppression is Barr-Zee type diagram. For having a glance at how it looks like, turn to

Chapter 3.

Also we have a trick to do it. In short, the leading one-loop effective vertex of

vector-vector-scalar or vector-vector-pseudoscalar coupling can be expressed as an

gauge invariant form. Say, let the Lorentz index of the two vector be $\mu$ and $\nu$,

the momentums they carry are $k$ and $q$, then the effective vertex must be in the form of

$S[k^\nu q^\mu-k\cdot q g^{\mu\nu}]+i\epsilon^{\mu\nu\alpha\beta}k_\alpha q_\beta P$, where

the $S$ and $P$ are functions of $k$ and $q$.

%%

Basically, the calculations of $(g-2)$ and EDM are the same but just being applied to different

topics. I will only present the detail of the calculations in the Appendix of Chapter 3 which deals

with muon $(g-2)$.

The other two projects on EDM will be presented like a journal paper, in facts, I just copy and

paste from our paper version with little modification. The needed information and some

calculation details are arranged in the Appendix. The other technical points are scattered in

the explanation boxes in the text.

1 ``pQCD study of the $B_{s.l.}$ and $<n_{c}>$ controversy in inclusive B decay'', C-H Chang, D Chang, W-F Chang, H-n Li, H-L Yu, {\bf Phys.Rev.D58}:094019, 1998; hep-ph/9803360.
2 ``Perturbative QCD analysis of $BR(B\to Xl\bar{\nu})$, $<n_{c}>$ and $% \tau (\Lambda _{b})/\tau (B_{d})$ '', W-F Chang, H-n Li, H-L Yu(1998),{\bf Phys.Lett.B457}:341-346, 1999; hep-ph/9809553.
3 ``Poles in complex coupling plane of Pure Wilson Action'', W-F Chang and B.Rosenstein, 1998; ``Strong-Weak Coupling Expansion for Improved Wilson Action'' D. Chang, W-F Chang, B.Rosenstein, 1998, unpublished.
4 ``Alternative Interpretation of Tevatron Top Events'', D Chang, W-F Chang, E. Ma, {\bf Phys.Rev.D59}:091503, 1999; hep-ph/9810531.
5 ``Fitting precision electroweak data with exotic heavy quarks", D Chang, W-F Chang, E.Ma, {\bf Phys.Rev.D61}:037301, 2000; hep-ph/9909537.
6 ``Additional two loop contributions to electric dipole moments in supersymmetric theories.", D Chang, W-F Chang, W-Y Keung, {\bf Phys.Lett.B478}:239-246, 2000; hep-ph/9910465.
7 `` The Neutron Electric Dipole Moment and CP Violating Couplings in the Supersymmetric Standard Model Without
R-Parity.", D Chang, W-F Chang, M Frank, W-Y Keung; Submitted to {\bf Phys.Rev.D}; hep-ph/0004170.
8 ``Large Two Loop Contributions to $g-2$ from a Light Pseudoscalar boson.", D. Chang, W-F Chang, C-H Chou and W-Y Keung.( in preparation )

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