Gluino Decays in Split Supersymmetry

TL;DR

This work provides a comprehensive, RG-improved calculation of gluino decays in Split Supersymmetry by constructing a $G$-odd, dimension-6 effective Lagrangian below the sfermion scale $ ilde{m}$ and deriving the full leading-log renormalization-group evolution of its Wilson coefficients. By resumming large $rac{ ilde{m}}{m_{ ilde{g}}}$-enhanced corrections, the authors show substantial modifications to gluino branching fractions, notably enhancing three-body decays relative to radiative two-body decays. They present explicit analytic formulae and numerical results for decay widths and lifetimes, with a clear scaling behavior in terms of $m_{ ilde{g}}$ and $ ilde{m}$, and discuss the potential dominance of decays into gravitinos (goldstinos) in models with direct mediation of SUSY breaking. The findings have important implications for LHC phenomenology and cosmology, illuminating how radiative corrections shape observable gluino signatures and lifetimes across a wide parameter space.

Abstract

We compute the gluino lifetime and branching ratios in Split Supersymmetry. Using an effective-theory approach, we resum the large logarithmic corrections controlled by the strong gauge coupling and the top Yukawa coupling. We find that the resummation of the radiative corrections has a sizeable numerical impact on the gluino decay width and branching ratios. Finally, we discuss the gluino decays into gravitino, relevant in models with direct mediation of supersymmetry breaking.

Figures (6)

• Figure 1: Renormalization group flow of $C^{\,\widetilde{ H}}_2$ and $C^{\,\widetilde{ H}}_5$, expressed in terms of the coefficients $\Delta_{ij}$ of eq. (\ref{['Deltas']}), for $\alpha_s(\widetilde{m} )=0.05$ and $\alpha_t(\widetilde{m} )=0.03$. The solid, dashed, dotted, and dot--dashed lines correspond to $\Delta_{22}$, $\Delta_{25}$, $\Delta_{52}$ and $\Delta_{55}$, respectively.
• Figure 2: Gluino lifetime $\tau_{\tilde{g}}$ as a function of the sfermion mass scale $\widetilde{m}$, for different values of the physical gluino mass $m_{\tilde{g}}$. The other free parameters are chosen as $\tan\beta = 2$ and $\mu>0$. The dashed horizontal line corresponds to the age of the universe, $\tau_{ U}=14$ Gyr.
• Figure 3: Branching ratios for the gluino decay channels $\chi^0 g$ (dashed lines), $\chi^0 q \bar{q}$ (dotted) and $\chi^{\pm} q \bar{q}^{\,\prime}$ (dot--dashed), summed over all possible neutralino or chargino states, as a function of $\widetilde{m}$, for three values of $m_{\tilde{g}}$: 500 GeV (upper plots), 1 TeV (middle) and 2 TeV (lower). The curves in the left (right) plots do (do not) include the resummation of the leading logarithmic corrections. Other parameters are $\tan\beta=20$ and $\mu>0$.
• Figure 4: Effect of the radiative corrections on the partial widths for the decays $\tilde{g}\rightarrow\chi^0 g$ (dashed lines), $\tilde{g}\rightarrow\chi^0 q \bar{q}$ (dotted) and $\tilde{g}\rightarrow\chi^{\pm} q \bar{q}^{\,\prime}$ (dot--dashed) as a function of $\widetilde{m}$. The parameters are chosen as $m_{\tilde{g}} = 1$ TeV, $\tan\beta = 20$ and $\mu>0$.
• Figure 5: The normalization $N$ of eq. (\ref{['scaling']}) as a function of the sfermion mass scale $\widetilde{m}$, with (solid lines) and without (dashed lines) resummation of the leading logarithmic corrections. The upper, middle and lower sets of curves correspond to $m_{\tilde{g}} =$ 0.5, 1 and 2 TeV, respectively. The other free parameters are chosen as $\tan\beta = 20$ and $\mu>0$.