Non-linear MSSM

TL;DR

The paper addresses the MSSM's difficulty in surpassing the LEP Higgs bound and the associated electroweak fine-tuning by introducing a non-linear MSSM with a light goldstino. It develops a model-independent framework using constrained superfields and expands in $1/f$ to derive the full effective Lagrangian and Higgs potential, showing that the tree-level Higgs mass $m_h$ can reach the LEP bound for $1.5\,\mathrm{TeV} \lesssim \sqrt f \lesssim 7\,\mathrm{TeV}$ due to an enhanced Higgs quartic coupling. The work also analyzes novel invisible decays, e.g., $h^0\to \chi_1^0\psi_X$ and $Z\to \chi_j^0\psi_X$, which place a lower bound on $\sqrt f$ (around $700$ GeV) and constrain parameter space. Collectively, these results show that low-scale SUSY breaking with a constrained goldstino can alleviate fine-tuning and yield distinctive collider signals, while reproducing MSSM expectations in the large-$f$ limit.

Abstract

Using the formalism of constrained superfields, we derive the most general effective action of a light goldstino coupled to the minimal supersymmetric standard model (MSSM) and study its phenomenological consequences. The goldstino-induced couplings become important when the (hidden sector) scale of spontaneous supersymmetry breaking, $\sqrt f$, is relatively low, of the order of few TeV. In particular, we compute the Higgs potential and show that the (tree level) mass of the lightest Higgs scalar can be increased to the LEP bound for $\sqrt f\sim 2$ TeV to 7 TeV. Moreover, the effective quartic Higgs coupling is increased due to additional tree-level contributions proportional to the ratio of visible to hidden sector supersymmetry breaking scales. This increase can alleviate the amount of fine tuning of the electroweak scale that exists in the MSSM. Among the new goldstino couplings, beyond those in MSSM, the most important ones generate an invisible decay of the Higgs boson into a goldstino and neutralino (if m_h>m_{χ_1^0}), with a partial decay rate that can be comparable to the SM channel h^0-> γγ. A similar decay of Z boson is possible if m_Z>m_{χ_1^0} and brings a lower bound on $\sqrt f$ that must be of about 700 GeV. Additional decay modes of the Higgs or Z bosons into a pair of light goldstinos, while possible, are suppressed by an extra 1/f factor and have no significant impact on the model.

Figures (2)

• Figure 1: The tree-level Higgs masses (in GeV) and expansion coefficients as functions of $\sqrt f$ (in GeV). In (a), (b) $\mu\!=\!900$ GeV, $\tan\beta\!=\!50$, $m_A$ increases upwards from $90$ to $150$ GeV in steps of $10$ GeV. The increase of $m_h$ is significant even at larger $\sqrt f$, if one increases $\mu$, as seen in (c), (d). In figs. (c), (d), $m_A\!=\!150$ GeV and $m_h$ increases as $\mu$ varies from 400 to 3000 GeV in steps of 100 GeV. In (c) $\tan\beta\!=\!50$ while in (d) $\tan\beta\!=\!5$, showing a milder dependence on $\tan\beta$ than in MSSM. For $\tan\beta\!\geq\! 10$ there is little difference from (c). In (e), (f) the expansion coefficients are shown, for $m_A=[90,650]$ GeV with steps of $10$ GeV, $\mu\!=\!900$ GeV, $\tan\beta\!=\!50$; they are always less than unity, even at larger values of $\sqrt f$ or $\mu$ shown in (c), (d), as required for a convergent expansion.
• Figure 2: The partial decay rate of $h^0\rightarrow \psi_X\chi_1^0$ for (a): $\tan\beta=50$, $m_{\lambda_1}=70$ GeV, $m_{\lambda_2}=150$ GeV, $\mu$ increases from 50 GeV (top curve) by a step 50 GeV, $m_A=150$ GeV. Compare against Figure \ref{['higgs1']} (c) corresponding to a similar range for the parameters. At larger $\mu$, $m_h$ increases, but the partial decay rate decreases. Similar picture is obtained at low $\tan\beta\sim 5$. (b): As for (a) but with $\tan\beta=5$. Compare against Figure \ref{['higgs1']} (d). Note that the total SM decay rate, for $m_h\sim 114$ GeV, is of order $10^{-3}$, thus the branching ratio in the above cases becomes comparable to that of SM Higgs going into $\gamma\gamma$ (see Figure 2 in Djouadi:1997yw).