The Soft Supersymmetry-Breaking Lagrangian: Theory and Applications

TL;DR

This work surveys the soft SUSY-breaking Lagrangian within the MSSM framework, detailing how a general 105-parameter soft sector governs radiative electroweak symmetry breaking, flavor and CP violation, collider phenomenology, dark matter, baryogenesis, and inflationary considerations. It articulates a hierarchy of SUSY-breaking mediation mechanisms—gravity, gauge, and bulk mediation—along with their characteristic spectra and SM-compatibility, while emphasizing the role of renormalization group evolution and the MSSM’s parameter space under minimal flavor violation. It further discusses cosmological implications (neutralino/gravitino/axion dark matter, leptogenesis, electroweak baryogenesis, and inflation) and how future collider data could translate measured masses and couplings into the underlying soft parameters, potentially illuminating the high-scale theory (string/M-theory, GUTs) that seeds SUSY breaking. The review highlights MSSM extensions (seesaw, NMSSM, and R-parity violation) and outlines the practical challenges of parameter reconstruction from data, underscoring the need for combined collider, astrophysical, and precision measurements to reveal the structure of fundamental physics beyond the Standard Model.

Abstract

After an introduction recalling the theoretical motivation for low energy (100 GeV to TeV scale) supersymmetry, this review describes the theory and experimental implications of the soft supersymmetry-breaking Lagrangian of the general minimal supersymmetric standard model (MSSM). Extensions to include neutrino masses and nonminimal theories are also discussed. Topics covered include models of supersymmetry breaking, phenomenological constraints from electroweak symmetry breaking, flavor/CP violation, collider searches, and cosmological constraints including dark matter and implications for baryogenesis and inflation.

Figures (11)

• Figure 1: mSUGRA/CMSSM parameter space exclusion plots taken from Ellis:2003cw, in which $A_{0}=0$ and other parameters are as shown. The darkest "V" shaped thin strip corresponds to the region with $0.094\leq \Omega h^{2}\leq 0.129$, while a bigger strip with a similar shape corresponds to the region with $0.1\leq \Omega h^{2}\leq 0.3$. (There are other dark strips as well when examined carefully.) The triangular region in the lower right hand corner is excluded by $m_{\widetilde{\tau }_{1}}<m_{\widetilde{\chi }^{0}}$, since DM cannot be charged and hence is a neutralino $\widetilde{\chi }^{0}$). Other shadings and lines correspond to accelerator constraints. In the lower figure ( $\mu <0$), most of the DM favored region below $m_{1/2}<400$ GeV is ruled out by the $b\rightarrow s\gamma$ constraint. In the upper figure, the medium shaded band encompassing the bulge region shows that the region favored by dark matter constraints is in concordance with the region favored by $g_{\mu }-2$ measurements. The Higgs and chargino mass bounds are also as indicated: the parameter space left of these bounds is ruled out. Unless excluded by accelerator constraints, the region below the darkest "V" region is not excluded, but is not cosmologically interesting due to the small relic abundance.
• Figure 2: Typical exclusion plot taken from Benoit:2001zu. The region above the curves are excluded. The closed curve represents the $3\sigma$ positive detection region of DAMA experiment.
• Figure 3: Taken from Bertin:2002ky, the left figure shows the direct detection scalar elastic scattering cross section for various neutralino masses, and the right figure shows the indirect detection experiments' muon flux for various neutralino masses. The scatter points represent "typical" class of models. Specifically, the model parameters are $A_{0}=0,\tan \beta =45,\mu >0,m_{0}\in [40,3000],m_{1/2}\in [40,1000].$ The dotted curve, dot dashed curved, and the dashed curve on the right figure represents the upper bound on the muon flux coming from Macro, Baksan, and Super-Kamiokande experiments, respectively. This plot should be taken as an optimistic picture, because the threshold for detection was set at 5 GeV, where the signal-to-noise ratio is very low in practice.
• Figure 4: Reheating temperature upper bound constraints from BBN as a function of the gravitino mass taken from Holtmann:1998gd. The various "high" and "low" values refer to the usage of observationally deduced light nuclei abundances in deducing the upper bound. Hence, the discrepancy can be seen as an indication of the systematic error in the upper bound constraint from observational input uncertainties.
• Figure 5: The leading diagrams contributing to the CP-violating currents that eventually sources the quark chiral asymmetry. The diagram a) corresponds to the right-handed squark current $J_R^\mu$ and the diagram b) corresponds to the higgsino current $J_{{\tilde{H}}}^\mu$. The effective mass terms correspond to $m_{LR}^2 =Y_t (A_t H_u - \mu^* H_d)$ and $\mu_a = g_a (H_d P_L + \frac{\mu}{|\mu|}H_u P_R)$ where $P_{L,R}$ are chiral projectors and $g_a=g_2$ for $a=1,2,3$ and $g_a=g_1$ for $a=4$.