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 contributions from new physics via a $Z'$ boson.

Contribution

It establishes the equivalence between two different spinor formalisms and relates their coupling parameters in the context of top quark pair production.

Findings

Both formalisms yield identical amplitude squares.

Relations between $Z'$ couplings in the two formalisms are derived.

The equivalence simplifies comparisons between different theoretical approaches.

Abstract

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 equivalance 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 in the four component spinor formalism.