Radiatively corrected lepton energy distributions in top quark decays $t \to bW^+ \to b(\ell^+ \nu_\ell)$ and $t \to bH^+ \to b (\tau^+ \nu_\tau)$ and single charged prong energy distributions from subsequent $\tau^+$ decays

TL;DR

This paper computes radiative QED and QCD corrections to lepton energy distributions in top quark decays within the Standard Model and beyond, with implications for testing weak interaction universality and detecting charged Higgs effects at colliders.

Contribution

It provides detailed calculations of radiative corrections to lepton energy spectra in top decays, including effects on subsequent tau decay distributions, aiding experimental searches for new physics.

Findings

QCD corrections are significant for precise measurements.

Radiative corrections affect tau decay product distributions.

Results assist in identifying charged Higgs signatures at colliders.

Abstract

We calculate the QED and QCD radiative corrections to the charged lepton energy distributions in the dominant semileptonic decays of the top quark $t \to b W^+ \to b(\ell^+ \nu_\ell)$ $(\ell=e, \mu, \tau)$ in the standard model(SM), and for the decay $t \to b H^+ \to b(\tau^+ \nu_\tau)$ in an extension of the SM having a charged Higgs boson $H^\pm$ with $m_{H^\pm} < m_t -m_b$. The QCD corrections are calculated in the leading and next-to-leading logarithmic approximations, but the QED corrections are considered in the leading logarithmic approximation only. These corrections are numerically important for precisely testing the universality of the charged current weak interactions in $t$-quark decays. As the $\tau^+$ leptons arising from the decays $W^+ \to \tau^+ \nu_\tau$ and $H^+\to \tau^+ \nu_\tau$ are predominantly left- and right-polarised, respectively, influencing the energy distributions of the decay products in the subsequent decays of the $\tau^+$, we work out the effect of the radiative corrections on such distributions in the dominant (one-charged prong) decay channels $ \tau^+ \to \pi^+ \bar{\nu}_\tau, \rho^+ \bar{\nu}_\tau, a_1^+ \bar{\nu}_\tau$ and $\ell^+ \nu_\ell \bar{\nu}_\tau$. The inclusive $\pi^+$ energy spectra in the decay chains $t \to b(W^+,H^+) \to b (\tau^+ \nu_\tau) \to b (\pi^+ \bar{\nu}_\tau \nu_\tau +X)$ are calculated, which can help in searching for the induced $H^\pm$ effects at the Tevatron and the LHC.