Precision Corrections in the Minimal Supersymmetric Standard Model

TL;DR

The paper provides a comprehensive one-loop analysis of the minimal MSSM with radiative electroweak symmetry breaking and unified boundary conditions, computing pole masses and running couplings in the $ m ar{DR}$ scheme from standard low-energy inputs such as $oldsymbol{ o}oldsymbol{ ext{ }}$ and $m_t$. It shows that SUSY corrections can shift the $W$ mass by up to $ oughly 250$ MeV and the effective weak mixing angle by roughly a few times $10^{-4}$, while finite threshold effects at the unification scale constrain viable GUTs via $oldsymbol{ o}oldsymbol{ o} o$ thresholds like $oldsymbol{oldsymbol{ o}} o oldsymbol{ o}oldsymbol{ o}$, e.g., $oldsymbol{oldsymbol{ o}} oldsymbol{ o}-2 oot 0{ extpercent}$ for $oldsymbol{ o}}$ inputs. The work also shows sizable, often nonlogarithmic one-loop corrections to the superpartner and Higgs masses, including large $ aneta$-enhanced bottom-quark effects that influence Yukawa unification. Importantly, the authors provide compact, accurate approximations (often at $ ext{O}(1 ext{--}{ m few} ext{ extpercent})$) across the unified parameter space, enabling practical use in interpreting potential collider signals and testing high-scale unification scenarios.

Abstract

In this paper we compute one-loop corrections to masses and couplings in the minimal supersymmetric standard model. We present explicit formulae for the complete corrections and a set of compact approximations which hold over the unified parameter space associated with radiative electroweak symmetry breaking. We illustrate the importance of the corrections and the accuracy of our approximations by scanning over the parameter space. We calculate the supersymmetric one-loop corrections to the W-boson mass, the effective weak mixing angle, and the quark and lepton masses, and discuss implications for gauge and Yukawa coupling unification. We also compute the one-loop corrections to the entire superpartner and Higgs-boson mass spectrum. We find significant corrections over much of the parameter space, and illustrate that our approximations are good to O(1%) for many of the superparticle masses.

Figures (19)

• Figure 1: Supersymmetric corrections to the effective weak mixing angle, $\sin^2\theta^{\rm lept}_{\rm eff}$. Figure (a) shows the corrections from top and bottom squark loops versus the heavy top squark mass $m_{\tilde{t}_1}$; (b) shows the neutralino/chargino contribution versus the light chargino mass; (c) shows the slepton correction from all three generations against $m_{\tilde{e}_L}$; and (d) shows the complete supersymmetric correction plotted against $m_{{\tilde{\chi}}_1^+}$.
• Figure 2: Finite corrections to $M_W$, in MeV. Figures (a-d) are as in Fig. \ref{['sw']}.
• Figure 3: (a) The unification-scale correction, $\varepsilon_g$, necessary to obtain $\alpha_s(M_Z) = 0.118$, plotted versus $M_{\tilde{q}}$. (b) The maximum and minimum $\varepsilon_g$ allowed in minimal SU(5) (top two regions) and missing doublet SU(5) (bottom two regions), against $M_{\tilde{q}}$. (c) Same as (a) with $\alpha_s(M_Z) = 0.112$. (d) Same as (a) with $\alpha_s(M_Z) = 0.124$.
• Figure 4: Corrections to the top quark mass, versus $M_{\tilde{q}}$. Figure (a) shows the full one-loop correction. Figure (b) illustrates the correction from the squark/gluino loop; the solid line shows the gluon contribution for comparison. Figure (c) shows the electroweak corrections. In Fig. (d) we plot the difference between the full one-loop result and the approximation given in the text.
• Figure 5: Corrections to the $\overline{\rm DR}~$ bottom quark mass $\hat{m}_b(M_Z)$, plotted versus $\tan\beta$. Figure (a) shows the full one-loop correction; (b) illustrates the full correction from the bottom squark/gluino loops; (c) shows the correction from the top squark/chargino loops. Figure (d) plots the difference between the full one-loop result and the approximation given in the text.