Determining $V_{tb}$ at Electron-Positron Colliders

TL;DR

This paper proposes a model-independent method to measure the CKM matrix element $V_{tb}$ at electron-positron colliders by analyzing top-quark pair production, without relying on assumptions about the number of fermion generations or the $Wtb$ coupling strength.

Contribution

It introduces a novel approach to determine $V_{tb}$ using electroweak couplings and top-quark observables, independent of standard assumptions.

Findings

Pattern of deviations in electroweak couplings can be used to extract $V_{tb}$.

Accurate measurements of top-quark mass and width improve $V_{tb}$ determination.

Method is applicable at unpolarized electron-positron colliders.

Abstract

Verifying $V_{tb} \simeq 1$ is critical to test the three generation assumption of the Standard Model. So far our best knowledge of $V_{tb}$ is inferred either from the $3\times 3$ unitarity of CKM matrix or from single top-quark productions upon the assumption of universal weak couplings. The unitarity could be relaxed in new physics models with extra heavy quarks and the universality of weak couplings could also be broken if the $Wtb$ coupling is modified in new physics models. In this work we propose to measure $V_{tb}$ in the process of $e^+ e^- \to t\bar{t}$ without prior knowledge of the number of fermion generations or the strength of the $Wtb$ coupling. Using an effective Lagrangian approach, we perform a model-independent analysis of the interactions among electroweak gauge bosons and the third generation quarks, i.e. the $Wtb$, $Zt\bar{t}$ and $Zb\bar{b}$ couplings. The electroweak symmetry of the Standard Model specifies a pattern of deviations of the $Z$-$t_L$-$t_L$ and $W$-$t_L$-$b_L$ couplings after one imposes the known experimental constraint on the $Z$-$b_L$-$b_L$ coupling. We demonstrate that, making use of the predicted pattern and the accurate measurements of top-quark mass and width from the energy threshold scan experiments, one can determine $V_{tb}$ from the cross section and the forward-backward asymmetry of top-quark pair production at an {\it unpolarized} electron-positron collider.