[Paper Review] Updated values of running quark and lepton masses at GUT scale in SM, 2HDM and MSSM

Kalpana Bora|arXiv (Cornell University)|Jun 26, 2012

Particle physics theoretical and experimental studies20 citations

TL;DR

This paper updates the running masses of quarks and charged leptons at the Grand Unified Theory (GUT) scale (2×10¹⁶ GeV) in the Standard Model (SM), Two-Higgs-Doublet Model (2HDM), and Minimal Supersymmetric Standard Model (MSSM) using the latest experimental data and 2-loop renormalization group equations (RGEs). The key contribution is a significant revision of previously used values, with updated masses differing substantially from earlier results, enabling more accurate neutrino mass calculations and fermion mass model building in GUTs.

ABSTRACT

Updated values of running quark and lepton masses at GUT (Grand unified theories) scales are important for fermion mass model building, and to calculate neutrino masses, in GUTs . We present their values at GUT scales, in SM, MSSM and 2HDM theories, using the latest values of running quark and lepton masses.

Motivation & Objective

• To provide updated values of running quark and lepton masses at the GUT scale (2×10¹⁶ GeV) in the SM, 2HDM, and MSSM, using the latest experimental data.
• To address the gap in existing literature by replacing outdated input values from earlier studies with current PDG data and improved renormalization schemes.
• To enable more accurate calculations of neutrino masses and fermion mass textures in grand unified theories (GUTs) and models beyond the Standard Model.
• To ensure consistency with modern renormalization group evolution (RGE) techniques by separately evolving Yukawa couplings, gauge couplings, and vacuum expectation values (VEVs).
• To verify the reliability of the new results by reproducing known benchmarks and comparing with prior works, highlighting discrepancies due to scheme and input differences.

Proposed method

• Utilized 2-loop renormalization group equations (RGEs) for Yukawa couplings, gauge couplings, and Higgs vacuum expectation values (VEVs) in the SM and MSSM to evolve masses from low-energy scales to the GUT scale.
• Applied 1-loop RGEs for the 2HDM due to the model's complexity and lower precision requirements at this level.
• Converted masses from the $ar{\mathrm{MS}}$ scheme to the $\overline{\mathrm{DR}}$ scheme using established formulas to ensure consistency across calculations.
• Used the latest Particle Data Group (PDG) values for quark and lepton masses, including updated top quark mass, as input at the electroweak scale.
• Performed scale evolution from the electroweak scale to the GUT scale (2×10¹⁶ GeV), accounting for threshold effects and running in each theory.
• Validated results by reproducing benchmark values from Das and Parida (2012), confirming the correctness of the computational framework.

Experimental results

Research questions

• RQ1 How do updated quark and lepton running masses at the GUT scale differ from previously used values in SM, 2HDM, and MSSM?
• RQ2 What impact do the latest experimental inputs and improved RGE treatments have on the predicted GUT-scale fermion masses?
• RQ3 How do the new mass values affect the construction of neutrino mass models and fermion mass textures in GUTs?
• RQ4 Why do the results differ from those reported by Xing et al. and Das & Parida, and what does this imply about scheme dependence in fermion mass running?
• RQ5 To what extent do variations in $\tan\beta$ in 2HDM and MSSM affect the running masses at the GUT scale?

Key findings

• The updated running top quark mass at the GUT scale in the SM is 80.4472⁺².⁹¹²⁸₋₂.⁶¹⁵⁸ GeV, differing significantly from older estimates.
• In MSSM with $\tan\beta = 55$, the top quark mass at GUT scale is 80.4472⁺².⁹¹²⁸₋².⁶¹⁵⁸ GeV, showing strong dependence on $\tan\beta$ and renormalization scheme.
• For the 2HDM at $\tan\beta = 55$, the top quark mass at GUT scale is 77.3752⁺¹.⁴⁷⁴¹₋¹.⁴¹⁸⁷ GeV, indicating a notable reduction compared to earlier values.
• The strange quark mass in the SM at GUT scale is 17.6702⁺⁴.⁹²³³₋⁴.⁶⁹⁵⁰ MeV, with a large uncertainty reflecting sensitivity to input parameters and RGE evolution.
• Charged lepton masses at GUT scale show minimal change across models, with the electron mass at 0.3585⁺⁰.⁰⁰⁰¹₋⁰.⁰⁰⁰² MeV in the SM, consistent with previous results.
• The results differ substantially from those of Das and Parida (2012) and Xing et al., primarily due to updated inputs, scheme conversion, and separate treatment of Yukawa and VEV evolution.