Looking Beyond the Standard Model through Precision Electroweak Physics

The most important hint of physics beyond the Standard Model (SM) from the 1995 precision electroweak data is that the most precisely measured quantities, the total, leptonic and hadronic decay widths of the $Z$ and the effective weak mixing angle, $\sin^2\theta_W$, measured at LEP and SLC, and the quark-lepton universality of the weak charged currents measured at low energies, all agree with the predictions of the SM at a few $\times 10^{-3}$ level. By taking into account the above constraints I examine implications of three possible disagreements between experiments and the SM predictions. It is difficult to interpret the 11\% (2.5-$\sigma$) deficit of the $Z$-partial-width ratio $R_c=\Gamma_c/\Gamma_h$, since it either implies an unacceptably large $\alpha_s$ or a subtle cancellation among hadronic $Z$ decay widths in order to keep all the other successful predictions of the SM. The 2\% (3-$\sigma$) excess of the ratio $R_b=\Gamma_b/\Gamma_h$ may indicate the presence of a new rather strong interaction, such as the top-quark Yukawa coupling in the supersymmetric (SUSY) SM or a new interaction responsible for the large top-quark mass in the Technicolor scenario of dynamical electroweak symmetry breaking. Another interpretation may be additional tree-level gauge interactions that couple only to the third generation of fermions. A common consequence of these attempts is a rather small $\alpha_s$, \alpha_s(\mz )_{\msbar}=0.104\pm 0.08. The 0.17\% (1-$\sigma$) deficit ...Comment: Talk presented at Yukawa International Seminar (YKIS)~'95, 23 pages, uuencoded compressed tar file of LaTeX file and 13 EPS files (uses ptptex.sty,wrapfig.sty,psfig.sty,axodraw.sty) PostScript version of complete paper available at ftp://ftp.kek.jp/kek/preprints/TH/TH-463/kekth463.ps.g

Generating QCD amplitudes in the color-flow basis with MadGraph

We propose to make use of the off-shell recursive relations with the color-flow decomposition in the calculation of QCD amplitudes on MadGraph. We introduce colored quarks and their interactions with nine gluons in the color-flow basis plus an Abelian gluon on MadGraph, such that it generates helicity amplitudes in the color-flow basis with off-shell recursive formulae for multi-gluon sub-amplitudes. We demonstrate calculations of up to 5-jet processes such as $gg\rightarrow 5g$, $u\bar{u}\rightarrow 5g$ and $uu\rightarrow uuggg$. Although our demonstration is limited, it paves the way to evaluate amplitudes with more quark lines and gluons with Madgraph.Comment: 29 pages, 13 figure