[Paper Review] A Motivated Non-Standard Supersymmetric Spectrum

Paolo Lodone|arXiv (Cornell University)|Dec 9, 2011

Particle physics theoretical and experimental studies6 references4 citations

TL;DR

This thesis proposes a motivated non-standard supersymmetric spectrum with heavy first- and second-generation sfermions (above 20 TeV) and a relatively heavy Higgs boson (200–300 GeV), motivated by naturalness and the absence of flavor-violating signals. It shows that such a spectrum can satisfy naturalness bounds, suppress flavor-changing neutral currents via effective Minimal Flavour Violation, and remain consistent with electric dipole moment constraints—offering a viable, phenomenologically distinct alternative to the MSSM with testable LHC and dark matter signatures.

ABSTRACT

After an introduction to the Hierarchy Problem and to Supersymmetry we discuss the phenomenology of a motivated non-standard pattern of sparticle masses in the context of extensions of the Minimal Supersymmetric Standard Model.

Motivation & Objective

• To explore a non-standard supersymmetric spectrum where the first and second generation sfermions are heavy (>20 TeV), motivated by the absence of flavor-violating signals in experiments.
• To investigate the viability of a relatively heavy Higgs boson (200–300 GeV) in a supersymmetric model while maintaining naturalness and consistency with electroweak precision data.
• To analyze how hierarchical sfermion masses lead to effective Minimal Flavour Violation (eMFV), suppressing dangerous flavor-changing neutral currents and electric dipole moments.
• To propose and study a more ambitious flavor symmetry pattern based on $U(2)^3$, which correlates $\Delta F=2$ amplitudes and resolves tensions in $K^0$–$\bar{K}^0$ and $B_d$–$\bar{B}_d$ mixing.
• To provide a dynamical realization of the $U(2)^3$ flavor symmetry framework and assess its phenomenological consequences, including CP asymmetries in $B_s \to \psi\phi$.

Proposed method

• Uses a bottom-up approach to compare extensions of the MSSM with extra tree-level contributions to the lightest Higgs mass, focusing on $U(1)$ and $SU(2)$ gauge extensions.
• Applies naturalness bounds and running of gauge couplings to constrain the scale of new physics, requiring soft terms to be generated at relatively low scales.
• Imposes constraints from color conservation and electroweak precision tests to rule out unphysical parameter regions.
• Derives effective MFV conditions from hierarchical sfermion masses, including QCD corrections and previously neglected effects in the calculation of flavor-violating amplitudes.
• Introduces a $U(2)^3 = U(2)_Q \times U(2)_u \times U(2)_d$ flavor symmetry acting on quarks and squarks, broken in a way that reproduces the observed quark masses and mixings.
• Performs a numerical analysis of EDMs and $\Delta B=1$ amplitudes, showing that phases in soft-breaking terms can be large without violating experimental bounds due to heavy first-generation sfermions.

Experimental results

Research questions

• RQ1 Can a supersymmetric model with a heavy Higgs boson (200–300 GeV) and first- and second-generation sfermions above 20 TeV remain natural and consistent with electroweak precision data?
• RQ2 How do hierarchical sfermion masses lead to effective Minimal Flavour Violation, and what are the resulting bounds on the masses of heavy squarks when QCD corrections are included?
• RQ3 Can a $U(2)^3$ flavor symmetry pattern explain the observed tensions in $\Delta F=2$ amplitudes in $K^0$–$\bar{K}^0$ and $B_d$–$\bar{B}_d$ mixing while predicting $B_s$–$\bar{B}_s$ mixing?
• RQ4 What are the implications of such a spectrum for dark matter relic abundance and direct detection, especially with a heavy Higgs?
• RQ5 How do phases in the soft-breaking terms affect electric dipole moments and CP asymmetries in $B$ physics, and can they be large without violating constraints?

Key findings

• A non-standard supersymmetric spectrum with sfermions above 20 TeV and a Higgs boson up to 300 GeV can satisfy naturalness bounds and remain consistent with electroweak precision data.
• The model predicts a positive CP asymmetry in $B_s \to \psi\phi$ above the Standard Model value, with $0.05 \lesssim S_{\psi\phi} \lesssim 0.2$, providing a distinctive LHC signature.
• Effective MFV arises from hierarchical sfermion masses, allowing large phases in soft-breaking terms without violating EDM constraints due to the heavy first-generation sfermions.
• The $U(2)^3$ flavor symmetry framework correlates $\Delta F=2$ amplitudes in $K^0$, $B_d$, and $B_s$ systems, resolving the tension between $S_{\psi K_S}$ and $\epsilon_K$ in the CKM fit.
• The preferred mass range for the gluino and left-handed sbottom is below 1.5 TeV, making them potentially discoverable at the LHC.
• The model remains viable even after the LHC exclusion of a SM-like Higgs boson below 476 GeV at 95% C.L., provided the Higgs couplings or branching ratios deviate significantly from SM expectations.