Use of $\Lambda_b$ polarimetry in top quark spin-correlation functions

C.A. Nelson

doi:doi:10.1007/s100520100609

EPJ

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 19, 323-337
DOI: 10.1007/s100520100609

Use of $\Lambda_b$ polarimetry in top quark spin-correlation functions

C.A. Nelson

Department of Physics, State University of New York at Binghamton, Binghamton, NY 13902-6016, USA

(Received: 26 January 2001 / Published online: 15 March 2001 -© Springer-Verlag 2001)

Abstract
Due to the absence of hadronization effects and the large m_t mass, top quark decay will be uniquely sensitive to fundamental electroweak physics at the Tevatron, at the LHC, and at a future linear collider. A "complete measurement" of the four helicity amplitudes in $t \rightarrow W^+ b$ decay is possible by the combined use of $\Lambda_b$ and W polarimetry in stage-two spin-correlation functions (S2SC). In this paper, the most general Lorentz-invariant decay density matrix is obtained for the decay sequence $t \rightarrow W^+ b$ where $b\rightarrow l^{-}\bar{\nu}c$ and $W^{+}\rightarrow l^{+}\nu _{l}$ [ or $W^{+}\rightarrow j\overline{_{d}}j_{u}$ ] , and likewise for $\bar{t} \rightarrow W^- \bar{b}$ . These density matrices are expressed in terms of b-polarimetry helicity parameters which enable a unique determination of the relative phases among the $A(\lambda_{W^+},\lambda_b)$ amplitudes. Thereby, S2SC distributions and single-sided b-W-interference distributions are expressed in terms of these parameters. The four b-polarimetry helicity parameters involving the A(-1,-1/2) amplitude are considered in detail. $\Lambda_b$ polarimetry signatures will not be suppressed in top quark analyses when final $\bar{\nu}$ angles-and-energy variables are used for $b\rightarrow l^{-}\bar{\nu}c$ .