Quantum effects on $t\to H^{+} b$ in the MSSM: a window to ``virtual'' supersymmetry?

Abstract

We analyze the one-loop effects (strong and electroweak) on the unconventional top quark decay mode $t\rightarrow H^{+} b$ within the MSSM. The results are presented in the on-shell renormalization scheme with a physically well motivated definition of $\tan\beta$. The study of this process at the quantum level is useful to unravel the potential supersymmetric nature of the charged Higgs emerging from that decay. As compared with the standard mode $t\rightarrow W^{+} b$, the corrections to $t\rightarrow H^{+} b$ are large, slowly decoupling and persist at a sizeable level even for all sparticle masses well above the LEP 200 discovery range. As a matter of fact, the potential size of the SUSY effects, which amount to corrections of several ten percent, could counterbalance the standard QCD corrections and even make them to appear with the ``wrong'' sign. Therefore, if the charged Higgs decay of the top quark is kinematically allowed -a possibility which is not excluded by the recent measurements of the branching ratio $BR(t\rightarrow W^{+} b)$ at the Tevatron - it could be an invaluable laboratory to search for ``virtual'' supersymmetry. While a first significant test of these effects could possibly be performed at the upgraded Tevatron, a more precise verification would most likely be carried out in future experiments at the LHC.Comment: 60 pages, LaTeX, 25 figs included as a separate file, full postscript version avaliable at ftp://ftp.ifae.es/preprint/ft/uabft397.ps . In this improved version we give an extended discussion of our renormalization framework and of the numerical analysis. Two additional figures are included. Some missprints have been correcte