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A Solution to the Supersymmetric Fine-Tuning Problem within the MSSM

Ryuichiro Kitano, Yasunori Nomura

TL;DR

The paper tackles the supersymmetric fine-tuning problem in the MSSM by proposing a framework that lowers the effective SUSY-breaking messenger scale without introducing new weak-scale MSSM fields. This is achieved through a deliberate balance of moduli and anomaly-mediated contributions, yielding a TeV-scale effective messenger and a spectrum with near-universal weak-scale gaugino and scalar masses, large A_t, and a small B-term, which together reduce the fine-tuning required for electroweak symmetry breaking. The authors provide concrete predictions: M_0 ≈ 450–900 GeV, M_mess ≈ 50 GeV–3 TeV, M_Higgs ≲ 120 GeV, tanβ ≳ 5, and a Higgsino LSP with m_{h̃^0} ≲ 190 GeV, plus potentially light top squarks around 200–270 GeV and relatively light Higgs bosons. They also discuss cosmological implications, with m_{3/2} ≈ 30–60 TeV and moduli-driven reheating enabling Higgsino dark matter, making the scenario testable at colliders and in dark matter searches while preserving MSSM structure at the weak scale.

Abstract

Weak scale supersymmetry has a generic problem of fine-tuning in reproducing the correct scale for electroweak symmetry breaking. The problem is particularly severe in the minimal supersymmetric extension of the standard model (MSSM). We present a solution to this problem that does not require an extension of the MSSM at the weak scale. Superparticle masses are generated by a comparable mixture of moduli and anomaly mediated contributions, and the messenger scale of supersymmetry breaking is effectively lowered to the TeV region. Crucial elements for the solution are a large A term for the top squarks and a small B term for the Higgs doublets. Requiring no fine-tuning worse than 20%, we obtain rather sharp predictions on the spectrum. The gaugino masses are almost universal at the weak scale with the mass between 450 and 900 GeV. The squark and slepton masses are also nearly universal at the weak scale with the mass a factor of \sqrt{2} smaller than that of the gauginos. The only exception is the top squarks whose masses split from the other squark masses by about m_t/\sqrt{2}. The lightest Higgs boson mass is smaller than 120 GeV, while the ratio of the vacuum expectation values for the two Higgs doublets, tanβ, is larger than about 5. The lightest superparticle is the neutral Higgsino of the mass below 190 GeV, which can be dark matter of the universe. The mass of the lighter top squark can be smaller than 300 GeV, which may be relevant for Run II at the Tevatron.

A Solution to the Supersymmetric Fine-Tuning Problem within the MSSM

TL;DR

The paper tackles the supersymmetric fine-tuning problem in the MSSM by proposing a framework that lowers the effective SUSY-breaking messenger scale without introducing new weak-scale MSSM fields. This is achieved through a deliberate balance of moduli and anomaly-mediated contributions, yielding a TeV-scale effective messenger and a spectrum with near-universal weak-scale gaugino and scalar masses, large A_t, and a small B-term, which together reduce the fine-tuning required for electroweak symmetry breaking. The authors provide concrete predictions: M_0 ≈ 450–900 GeV, M_mess ≈ 50 GeV–3 TeV, M_Higgs ≲ 120 GeV, tanβ ≳ 5, and a Higgsino LSP with m_{h̃^0} ≲ 190 GeV, plus potentially light top squarks around 200–270 GeV and relatively light Higgs bosons. They also discuss cosmological implications, with m_{3/2} ≈ 30–60 TeV and moduli-driven reheating enabling Higgsino dark matter, making the scenario testable at colliders and in dark matter searches while preserving MSSM structure at the weak scale.

Abstract

Weak scale supersymmetry has a generic problem of fine-tuning in reproducing the correct scale for electroweak symmetry breaking. The problem is particularly severe in the minimal supersymmetric extension of the standard model (MSSM). We present a solution to this problem that does not require an extension of the MSSM at the weak scale. Superparticle masses are generated by a comparable mixture of moduli and anomaly mediated contributions, and the messenger scale of supersymmetry breaking is effectively lowered to the TeV region. Crucial elements for the solution are a large A term for the top squarks and a small B term for the Higgs doublets. Requiring no fine-tuning worse than 20%, we obtain rather sharp predictions on the spectrum. The gaugino masses are almost universal at the weak scale with the mass between 450 and 900 GeV. The squark and slepton masses are also nearly universal at the weak scale with the mass a factor of \sqrt{2} smaller than that of the gauginos. The only exception is the top squarks whose masses split from the other squark masses by about m_t/\sqrt{2}. The lightest Higgs boson mass is smaller than 120 GeV, while the ratio of the vacuum expectation values for the two Higgs doublets, tanβ, is larger than about 5. The lightest superparticle is the neutral Higgsino of the mass below 190 GeV, which can be dark matter of the universe. The mass of the lighter top squark can be smaller than 300 GeV, which may be relevant for Run II at the Tevatron.

Paper Structure

This paper contains 3 sections, 31 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. Framework
  3. Electroweak Symmetry Breaking without Fine-Tuning

Figures (1)

  • Figure 1: The Higgs boson mass, $M_{\rm Higgs}$, and the fine-tuning parameter, $\Delta^{-1}$, as a function of $M_0$. The lower bound on $M_0$ is obtained from the left figure using the experimental bound of $M_{\rm Higgs} \mathrel{\hbox{$>$$\sim$}} 114.4~{\rm GeV}$, while the upper bound can be read off from the right figure with the requirement of $\Delta^{-1} \geq 20\%$.