Selected Topics in Top Quark Physics

I discuss three different selected topics in top quark physics. The first topic concerns the next-to-next-to-leading order calculation of the hadroproduction of top quark pairs and the role of multiple polylogarithms in this calculation. I report on an ongoing next-to-next-to-leading order calculation of heavy quark pair production in hadron collisions where the loop--by--loop part of the calculation is about to be completed. Calculating the loop-by-loop part allows one to take a glimpse at the mathematical structure of the full NNLO calculation. The loop-by-loop contributions bring in a new class of functions introduced only eight years ago by the Russian mathematician Goncharov called multiple polylogarithms. The second topic concerns a next-to-leading order calculation of unpolarized top quark decays which are analyzed in cascade fashion $t \to b + W^+$ followed by $W^+ \to l^+ + \nu_l$. Finally, I present some next-to-leading order results on polarized top quark decays which are analyzed in the top quark rest system.Comment: 11 pages, 4 figures, Invited talk given at the 12th Regional Conference of Mathematical Physics, Islamabad, Pakistan, March 2006, to be published in the proceeding

Helicity Amplitudes and Angular Decay Distributions

I discuss how to obtain angular decay distributions for sequential cascade decays using helicity methods. The angular decay distributions follow from a reasonably simple master formula involving bilinear forms of helicity amplitudes and Wigner's $d$ functions. I discuss in some detail the issue of gauge invariance for off-shell gauge bosons. As a technical exercise I calculate the linear relation between the helicity amplitudes and the invariant amplitudes of semileptonic and rare baryon decays. I discuss two explicit examples of angular decay distributions for (i) the decay $t\to b+W^+(\to \ell^+\nu_\ell)$ (which leads to the notion of the helicity fractions of the $W^+$), and (ii) the sequential decay $\Lambda_b\to\Lambda(\to p\pi^-)+J/\psi(\to \ell^+\ell^-)$.Comment: 16 pages, 2 figures, Lecture given at the Helmholtz International Summer School "Physics of Heavy Quarks and Hadrons", Dubna, Russia, July 15--28, 2013 (to be published in the Proceedings

A Supersymmetric Model with the Gauge Symmetry SU(3)_1 X SU(2)_1 X U(1)_1 X SU(3)_2 X SU(2)_2 X U(1)_2

A supersymmetric model with two copies of the Standard Model gauge groups is constructed in the gauge mediated supersymmetry breaking scenario. The supersymmetry breaking messengers are in a simple form. The Standard Model is obtained after first step gauge symmetry breaking. In the case of one copy of the gauge interactions being strong, a scenario of electroweak symmetry breaking is discussed, and the gauginos are generally predicted to be heavier than the sfermions.Comment: 14 pages, revtex, 1 figure, messenger contents modified, discussion on GUTs improve

Theory of Heavy Baryon Decay

We discuss various topics in the theory of heavy baryon decays. Among these are recent applications of the Relativistic Three Quark Model to semileptonic, nonleptonic, one-pion and one-photon transitions among heavy baryons, new higher order perturbative results on the correlator of two heavy baryon currents and on the semi-inclusive decay $\Lambda_b \to X_c + D_s^{(*)-}$.Comment: 10 pages, invited talk given by J.G. K\"orner at the 3rd International Conference on B Physics and CP Violation (BCONF99), Taipei, Taiwan, 3-7 Dec 1999, to appear in the Proceedings, edited by H.Y. Cheng and W.S. Hou (World Scientific, 2000

O(\alpha_s) Corrections to Longitudinal Spin-Spin Correlations in e+e- -> q qbar

We calculate the $O(\alpha_s)$ corrections to longitudinal spin-spin correlations in $e^+e^-\to q\bar q$. For top quark pair production the $O(\alpha_s)$ corrections to the longitudinal spin-spin asymmetry amount to less than 1% in the $q^2$-range from above $t\bar t$-treshold up to $\sqrt{q^2}= 1000 GeV$. In the $e^+e^-\to b\bar b$ case the $O(\alpha_s)$ corrections reduce the asymmetry value from its $m=0$ value of -1 to approximately -0.96 for $q^2$-values around the Z-peak. This reduction can be traced to finite anomalous contributions from residual mass effects which survive the $m\to 0$ limit. We discuss the role of the anomalous contributions and the pattern of how they contribute to spin-flip and no-flip terms.Comment: 10 pages, 2 postscript figure

Fully analytical O(\alpha_s) results for on-shell and off-shell polarized W-boson decays into massive quark pairs

We provide analytical $O(\alpha_s)$ results for the three polarized decay structure functions $H_{++},\,H_{00}$ and $H_{--}$ that describe the decay of a polarized $W$ boson into massive quark--antiquark pairs. As an application we consider the decay $t\to b+W^+$ involving the helicity fractions $\rho_{mm}$ of the $W^+$ boson followed by the polarized decay \hbox{W^+(\uparrow)}\to q_1\bar{q}_2 described by the polarized decay structure functions $H_{mm}$. We thereby determine the $O(\alpha_s)$ polar angle decay distribution of the cascade decay process $t\to b+W^+(\to q_1\bar{q}_2)$. As a second example we analyze quark mass and off-shell effects in the cascade decays $H\to W^{-}+W^{\ast +}(\to q_1\bar{q}_2)$ and $H\to Z+Z^{\ast}(\to q\bar{q})$. For the decays $H\to W^{-}+W^{\ast +}(\to c\bar b)$ and $H\to Z+Z^{\ast}(\to b\bar{b})$ we find substantial deviations from the mass-zero approximation in particular in the vicinity of the threshold region.Comment: 56 pages, 15 figures and 2 table