Some Special Topics on Particle Phenomenology

• Main Authors: We-Fu Chang, 張維甫
• Other Authors: Darwin Chang
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/90014755926842437001

博士 === 國立清華大學 === 物理學系 === 88 === 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.