Complete angular analysis of polarized top decay at O(alpha_s)
M. Fischer, S. Groote, J. G. Körner, M. C. Mauser
TL;DR
The authors perform a complete O(alpha_s) analysis of polarized top quark decays, deriving analytical expressions for eight angular structure functions that describe cascade decays t -> W b -> (l nu) or hadrons, while keeping the bottom-quark mass general. They develop covariant projection techniques to obtain invariant and helicity structure functions, and compute Born, one-loop, and real-emission tree contributions, with mb retained in full and mb -> 0 limits yielding compact results. Radiative corrections are sizable (-6% to -12%), largely universal near infrared regions, and significantly affect angular distributions and polarization observables, enabling precision Standard Model tests and potential top mass determinations from angular measurements. The work provides both mb = 0 closed-form results and full mb ≠ 0 expressions, with discussions of experimental implications, finite width effects, and avenues for higher-order corrections and electroweak effects.
Abstract
We calculate the O(alpha_s) radiative corrections to the three spin independent and five spin dependent structure functions that describe the angular decay distribution in the decay of a polarized top quark into a W-boson (followed by the decay W^{+} -> l^{+} + nu_l or by W^{+} -> anti-q + q and a bottom quark. The angular decay distribution is described in cascade fashion, i.e. the decay t(uparrow) -> W^{+} + X_b is analyzed in the top rest system while the subsequent decay W^{+} -> l^{+} + nu_l (or W^{+} -> anti-q + q) is analyzed in the W rest frame. We present our results for the eight O(alpha_s) integrated structure functions in analytical form keeping the mass of the bottom quark finite. In the limit m_b -> 0 the structure function expressions reduce to rather compact forms.