Effective lagrangian for the tbH^+ interaction in the MSSM and charged Higgs phenomenology

TL;DR

This work develops an effective 2HDM-like lagrangian for the MSSM in the large $\tan\beta$ regime to resum dominant SUSY-threshold and QCD corrections that modify the bottom Yukawa coupling via $\Delta m_b$. It then computes radiative corrections to the decays $t\rightarrow bH^+$ and $H^+\rightarrow t\bar{b}$, combining universal $\Delta m_b$-driven SUSY effects with RG-improved QCD logarithms through an operator-product-expansion (OPE) framework. The authors present RG-improved decay widths and branching ratios, show that SUSY corrections can be sizable (tens of percent) and strongly depend on $\mu$ and $\tan\beta$, and demonstrate how these refinements shift collider exclusion bounds on the charged Higgs in the $M_{H^+}$–$\tan\beta$ plane. The results provide a robust, efficient tool for charged-Higgs phenomenology across SUSY spectra and offer a concrete method for reinterpreting Tevatron (and future collider) limits. Overall, the paper delivers a coherent, all-orders treatment of $\tan\beta$-enhanced SUSY effects and their interplay with QCD corrections in charged-Higgs processes.

Abstract

In the framework of a 2HDM effective lagrangian for the MSSM, we analyse important phenomenological aspects associated with quantum soft SUSY-breaking effects that modify the relation between the bottom mass and the bottom Yukawa coupling. We derive a resummation of the dominant supersymmetric corrections for large values of \tb to all orders in perturbation theory. With the help of the operator product expansion we also perform the resummation of the leading and next-to-leading logarithms of the standard QCD corrections. We use these resummation procedures to compute the radiative corrections to the \tbH, \Htb decay rates. In the large \tb regime, we derive simple formulae embodying all the dominant contributions to these decay rates and we compute the corresponding branching ratios. We show, as an example, the effect of these new results on determining the region of the \mH--\tb plane excluded by the Tevatron searches for a supersymmetric charged Higgs boson in top quark decays, as a function of the MSSM parameter space.

Figures (9)

• Figure 1: One-loop SUSY-QCD diagram contributing to the effective coupling $\Delta h_b$. The solid lines inside the loop denote the gluino propagator, the dashed lines correspond to sbottom propagators. The cross represents the $M_{\tilde{g}}^{}$ insertion coming from the gluino propagator.
• Figure 2: Two-loop SUSY-QCD diagram containing a large logarithm $\log \left( M_{SUSY}^{}/m_b^{}\right)$.
• Figure 3: One-loop diagram derived from the effective lagrangian in (\ref{['eq:uli:lag']}) corresponding to the diagram in fig. \ref{['fig:uli1']}. It contains the large logarithm of fig. \ref{['fig:uli1']} as $\log m_b^{}/Q$. This logarithm is summed to all orders by solving the renormalization group for $h_b$ in eq. (\ref{['eq:uli:lag']}).
• Figure 4: One-loop SUSY-QCD diagram contributing to $\Delta m_b^{}$.
• Figure 5: Feynman diagrams contributing to the bottom pole mass up to first order in PT. From left to right, the renormalized bottom mass, the bottom mass counterterm and the finite one-loop Feynman graph contributions are shown. The dashed line in the last diagram denotes a sbottom and the solid line a gluino. The cross represents the insertion of the bottom mass counterterm.