Helicity Amplitudes and Angular Decay Distributions

Abstract

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 ${\Lambda }_b\to \Lambda (\to p{\pi }^{-})+J/\psi (\to {\ell }^{+}{\ell }^{-})$.

Comments: 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)