[Paper Review] Higgs-Boson Masses and Mixings in the MSSM with CP Violation and Heavy SUSY Particles

Nicholas A. Murphy, Heidi Rzehak|arXiv (Cornell University)|Sep 2, 2019

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper calculates the Higgs boson mass spectrum and mixing in the CP-violating MSSM with heavy SUSY particles using an effective field theory approach, matching the MSSM to a low-energy Two-Higgs-Doublet Model (2HDM) at the one-loop level and evolving parameters via two-loop RGEs. It finds that CP-violating phases can shift the lightest Higgs boson mass by several GeV, with significant CP mixing in the neutral Higgs sector.

ABSTRACT

We calculate the Higgs-boson mass spectrum and the corresponding mixing of the Higgs states in the Minimal Supersymmetric Standard Model (MSSM). We assume a mass-hierarchy with heavy SUSY particles and light Higgs bosons. To investigate this scenario, we employ an effective-field-theory approach with a low-energy Two-Higgs-Doublet Model (2HDM) where both Higgs doublets couple to up- as well as down-type fermions. We perform a one-loop matching of the MSSM to the 2HDM and evolve the parameters to the low energy scale by exploiting two-loop renormalization group equations, taking the complex parameters into account. For the calculation of the pole mass, we compare three different options: one suitable for large charged Higgs masses, one for low charged Higgs masses, and one approximation that interpolates between these scenarios. The phase dependence of the mass of the lightest neutral Higgs boson can be sizeable, i.e. on the order of a couple of GeV depending on the scenario. In addition, we discuss the CP composition of the neutral Higgs bosons.

Motivation & Objective

• To compute precise Higgs boson masses and mixing in the CP-violating MSSM under a heavy SUSY particle scenario.
• To address theoretical uncertainties in Higgs mass predictions due to large logarithms from heavy SUSY scales.
• To incorporate complex parameters and CP-violating phases into the Higgs mass calculation with high accuracy.
• To compare different pole mass computation schemes for varying charged Higgs masses and interpolate where needed.
• To assess the CP composition of the neutral Higgs bosons in the presence of complex phases.

Proposed method

• Employ an effective field theory approach by matching the MSSM to a low-energy Two-Higgs-Doublet Model (2HDM) at the one-loop level.
• Evolve the matching parameters from the high scale to the low energy scale using two-loop renormalization group equations (RGEs), including complex parameters.
• Use three distinct methods to compute the Higgs pole masses: one for large charged Higgs masses, one for small masses, and an interpolating approximation.
• Include one-loop self-energy and tadpole corrections with proper phase handling, accounting for complex Yukawa couplings and vacuum expectation value shifts.
• Apply on-shell renormalization conditions for the W and Z boson masses and the electric charge, using one-loop self-energies.
• Convert the on-shell vacuum expectation value to the $ar{\mathrm{MS}}$ scheme using full one-loop corrections, including $\Delta r$-type contributions.

Experimental results

Research questions

• RQ1 How do CP-violating phases affect the mass of the lightest neutral Higgs boson in the MSSM with heavy SUSY particles?
• RQ2 What is the impact of complex parameters on the mixing pattern and CP composition of the neutral Higgs states?
• RQ3 How do different pole mass computation schemes compare in scenarios with varying charged Higgs masses?
• RQ4 To what extent do large logarithms from heavy SUSY scales affect Higgs mass predictions, and how can they be resummed?
• RQ5 What is the quantitative size of the CP-violating corrections to the Higgs mass spectrum in the effective 2HDM framework?

Key findings

• The phase dependence of the lightest Higgs boson mass can be as large as a few GeV, depending on the CP-violating scenario.
• The CP composition of the neutral Higgs bosons is significantly affected by complex parameters, leading to non-trivial mixing between CP-even and CP-odd states.
• The three different pole mass computation methods—optimized for large or small charged Higgs masses and an interpolating scheme—yield consistent results across the parameter space.
• The inclusion of two-loop RGEs with complex parameters leads to a more accurate and reliable prediction of the Higgs mass spectrum.
• Numerical effects from the phase in the top-Yukawa coupling are negligible, as the phase remains small and does not significantly alter the mass matrix.
• The one-loop conversion from on-shell to $ar{\mathrm{MS}}$ scheme for the vacuum expectation value is consistently applied, ensuring accurate matching conditions.