Longitudinal, transverse-plus and transverse-minusWbosons in unpolarized top quark decays atO(αs)

Abstract

We consider the O(αs) radiative corrections to the decay of an unpolarized top quark into a bottom quark and a W -gauge boson where the helicities of the W are specified as longitudinal, transverse-plus and transverse-minus. The O(αs) radiative corrections lower the normalized longitudinal rate ΓL/Γ by 1.06% and increase the normalized transverse-minus rate Γ−/Γ by 2.17%. We find that the normalized transverse-plus rate Γ+/Γ, which vanishes at the Born term level for m b → 0, receives radiative correction contributions at the sub-percent level. We discuss m b = 0 effects for the Born term and the αs-contributions but find these to be small. Our results are discussed in the light of recent measurements of the helicity content of the W in top quark decays by the CDF Collaboration.

Electroweak and finite width corrections to top quark decays into transverse and longitudinalWbosons

“…Relative to the m b = 0 Born term rate they amount to −8.54% (QCD one-loop) [3,4,5,6,7,8], +1.54% (electroweak one-loop) [3,9,10] and −2.05% (−2.16%) (QCD two-loop; approximate) [11] ( [12]). The m b = 0 and finite width corrections reduce the Born width by 0.27% [13,14,15] (for m b = 4.8 GeV [16]) and 1.55% [17], respectively. Given the fact that the radiative and finite width corrections to the total rate are sizeable it is important to know also the respective corrections to the partial longitudinal and transverse rates.…”

“…Given the fact that the radiative and finite width corrections to the total rate are sizeable it is important to know also the respective corrections to the partial longitudinal and transverse rates. The QCD oneloop corrections to the partial helicity rates were given in [13,14,15]. In this letter we provide the missing oneloop electroweak (EW) corrections and the finite width (FW) corrections to the partial helicity rates.…”

“…[14]). Numerical values for the normalized helicity rates have been added in paranthesis using m t = 175 GeV and m W = 80.419 GeV.…”

“…The transverse-plus, transverse-minus and longitudinal components of the hadron tensor can be obtained with the help of the projectors (IP [14,15], resp., where…”

Measurement of the helicity fractions ofWbosons from top quark decays using fully reconstructedtt¯events with CDF II

“…The fraction of longitudinally polarized W bosons is defined by [3], gives F 0 = 0.697 ± 0.007, where the given uncertainty is only due to the uncertainty in the top quark mass. Next-toleading-order corrections to the total decay width and the partial decay width into longitudinal W bosons amount to about -10% [10,11,12,13,14,15,16,17,18,19]. However, the fraction of longitudinal W bosons is only negligibly changed.…”