[Paper Review] Charge and Color Breaking Constraints in the Minimal Supersymmetric Standard Model

Nikita Blinov, David E. Morrissey|arXiv (Cornell University)|Sep 28, 2013

Particle physics theoretical and experimental studies5 references3 citations

TL;DR

This paper investigates metastability constraints in the Minimal Supersymmetric Standard Model (MSSM) due to charge and color breaking (CCB) minima, focusing on the stop sector. Using numerical bounce calculations via CosmoTransitions, it shows that vacuum metastability imposes stronger constraints on MSSM parameters—particularly stop mixing and soft masses—than previously thought, excluding regions of parameter space compatible with the measured Higgs boson mass of 126 GeV.

ABSTRACT

The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) admits the existence of vacua with non-vanishing expectation values of electrically and color charged fields. If such minima are deep enough, the physical electroweak vacuum is rendered unstable by quantum tunneling. By comparing the lifetime of the electroweak vacuum with the age of the universe, the MSSM parameter space can be constrained. Furthermore, the appearance of charge and color breaking minima associated with the stop sector is strongly correlated with the Higgs mass, which has been recently measured at the Large Hadron Collider. We carry out a metastability analysis in the stop sector of the MSSM, improving upon previous results. We exclude parts of the parameter space allowed by the Higgs mass measurement.

Motivation & Objective

• To assess the stability of the electroweak vacuum in the MSSM against quantum tunneling to charge and color breaking (CCB) minima.
• To re-evaluate metastability constraints in light of the measured Higgs boson mass (~126 GeV) at the LHC.
• To improve upon previous numerical bounds on trilinear stop couplings by incorporating realistic Higgs mass constraints.
• To determine whether metastability provides a stronger constraint than the Higgs mass measurement alone in the stop sector.
• To validate numerical methods for bounce computation using independent codes and consistency checks.

Proposed method

• Uses the one-loop MSSM Higgs mass formula with two-loop corrections via FeynHiggs to compute $ m_h $.
• Applies the Callan-Coleman method to compute the Euclidean bounce action $ B $, with decay rate $ \Gamma/V = C \exp(-B/\hbar) $.
• Employs the CosmoTransitions code to numerically compute the bounce action for multi-field scalar potentials in the stop sector.
• Imposes the metastability condition $ B/\hbar \geq 400 $, corresponding to a vacuum lifetime $ \geq 13.8 \, \text{Gyr} $.
• Fixes $ \tan\beta = 10 $, $ m_A = 1 \, \text{TeV} $, $ \mu = 250 \, \text{GeV} $, and sets other sfermion masses to 2 TeV with $ A_f = 0 $.
• Performs independent checks using a second numerical code to validate bounce results and ensure methodological reliability.

Experimental results

Research questions

• RQ1 How do charge and color breaking minima in the stop sector affect the metastability of the electroweak vacuum in the MSSM?
• RQ2 To what extent does the measured Higgs boson mass of ~126 GeV constrain the parameter space when combined with vacuum metastability?
• RQ3 Are the previously used empirical bounds on trilinear couplings (e.g., $ A_t^2 + 3\mu^2 < 7.5(m_{Q_3}^2 + m_{u_3}^2) $) still valid under updated Higgs mass constraints?
• RQ4 How do large stop mixing and soft masses influence the existence and depth of CCB minima?
• RQ5 Can numerical computation of the bounce action provide more stringent constraints than analytical approximations?

Key findings

• Metastability constraints from CCB minima are stronger than previously estimated, excluding regions of the stop parameter space that are otherwise compatible with the measured Higgs mass.
• The study finds that the empirical bound from Ref. [10] ($ A_t^2 + 3\mu^2 < 7.5(m_{Q_3}^2 + m_{u_3}^2) $) is insufficient, as it underestimates the true metastability constraints.
• For $ \tan\beta = 10 $, $ m_A = 1 \, \text{TeV} $, and $ \mu = 250 \, \text{GeV} $, models with large stop mixing and small soft masses are excluded due to $ B/\hbar < 400 $, indicating instability.
• Models with $ m_h \in (123, 127) \, \text{GeV} $ and $ m_{Q_3}^2 = m_{u_3}^2 \gtrsim 1.5 \, \text{TeV}^2 $ are found to be absolutely stable and viable, while those with smaller masses and large $ X_t $ are excluded.
• The inclusion of two-loop Higgs mass corrections via FeynHiggs reveals that metastability provides a complementary and non-trivial constraint on MSSM parameters.
• Numerical consistency checks using an independent code confirm the reliability of the bounce calculations, supporting the robustness of the metastability bounds.