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

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

On the rigidity of back-to-back top quark pairs in e^+e^- annihilation

We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in $e^+e^-$ annihilation. Our results are presented in terms of the $E_q$-dependence of the $t\bar tg$ cross section and the dependence on the cosine of the opening angle $\theta_{12}$ between top and antitop for a center of mass energy of $\sqrt{q^2}=500 GeV$. We then go on to determine mean values for the top quark's energy as well as its longitudinal and transverse projections, and for the deviation of $\sin\theta_{12}$ and $\cos\theta_{12}$ from the anticollinearity limits $\sin\theta_{12}=0$ and $\cos\theta_{12}=-1$. For a center of mass energy of $500 GeV$ we obtain $=248.22 GeV$, $=247.24 GeV$ and $=4.70 GeV$. Thus, at this energy gluon radiation causes a total average energy loss of 0.71% of the top quark's energy. The average energy loss in the longitudinal direction is 1.06% and the average energy gain in the transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19% and 6.06%, respectively, at 1000\GeV. For the mean of the acollinearity angle $\bar\theta_{12}=180^0-\theta_{12}$ we obtain $=1.25^0$ at $500 GeV$, the value of which goes up to $4.62^0$ at $1000 GeV$. From an analysis of the transverse momentum of the top we find that the mean transverse momentum of the top stays close to the mean total momentum of the gluon in the energy range from threshold to $1000 GeV$ showing that the gluon momentum has a large mean transverse component in this energy range.Comment: 17 pages, 7 postscript figures, to appear in Nucl. Phys.