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We calculate the QED and QCD radiative corrections to the charged leptonenergy 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 standardmodel(SM), and for the decay $t \to b H^+ \to b(\tau^+ \nu_\tau)$ in anextension 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-leadinglogarithmic approximations, but the QED corrections are considered in theleading logarithmic approximation only. These corrections are numericallyimportant for precisely testing the universality of the charged current weakinteractions in $t$-quark decays. As the $\tau^+$ leptons arising from thedecays $W^+ \to \tau^+ \nu_\tau$ and $H^+\to \tau^+ \nu_\tau$ are predominantlyleft- and right-polarised, respectively, influencing the energy distributionsof the decay products in the subsequent decays of the $\tau^+$, we work out theeffect 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 insearching for the induced $H^\pm$ effects at the Tevatron and the LHC.

european physical journal. c, particles and fields

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