The polarization of the $W$ boson in $t\to Wb$ decay is unambiguously predicted by the standard model of electroweak interactions and is a powerful test of our understanding of the $tbW$ vertex. We measure this polarization from the invariant mass of the $b$ quark from $t\to Wb$ and the lepton from $W\to l\nu$ whose momenta measure the $W$ decay angle and direction of motion, respectively. In this paper we present a measurement of the decay rate ($f_{V+A}$) of the $W$ produced from the decay of the top quark in the hypothesis of $\mathrm{V}+\mathrm{A}$ structure of the $tWb$ vertex. We find no evidence for the nonstandard $\mathrm{V}+\mathrm{A}$ vertex and set a limit on $f_{V+A}$ $<$ 0.80 at $95\%$ confidence level. By combining this result with a complementary observable in the same data, we assign a limit on $f_{V+A}$ $<$ 0.61 at $95\%$ CL. This corresponds to a constraint on the right-handed helicity component of the W polarization of $f_{+}<0.18$ at $95\%$ CL. This limit is the first significant direct constraint on $f_{V+A}$ in top decay.

• Received 2 December 2004
• Corrected 25 February 2005

DOI:https://doi.org/10.1103/PhysRevD.71.031101