Equivalence of two component spinor mechanism and four component spinor mechanism in top quark pair production

TL;DR

This paper demonstrates the equivalence of two-component and four-component spinor formalisms in calculating top quark pair production amplitudes, including new physics contributions from a Z' boson.

Contribution

It establishes the equivalence between two spinor formalisms and relates their couplings in top quark pair production processes.

Findings

Confirmed the equivalence of the two formalisms in amplitude calculations.

Derived relations between couplings in different spinor formalisms.

Validated the formalism with contributions from new physics (Z' boson).

Abstract

In this article, we calculate the $S$-matrix elements for the process $e^{+} e^{-}\rightarrow t \bar{t}$ mediated by SM photon, $Z$ boson and an additional $Z^{'}$ boson indicating the contribution from new physics. We calculate the amplitude square using two component spinor formalism and four component spinor formalism and show the equivalence of the results using the two formalisms. We also establish the relations between the couplings of $Z^{'}$ boson to fermions in the two component spinor formalism and four component spinor formalism.