[Paper Review] Higgs Mass Constraints on a Fourth Family: Upper and Lower Limits on CKM Mixing

Michael S. Chanowitz|arXiv (Cornell University)|Jun 30, 2010

Particle physics theoretical and experimental studies79 references29 citations

TL;DR

This paper constrains fourth-family quark mixing in the four-family Standard Model (SM4) using precision electroweak (PEW) data and Higgs boson mass limits. It shows that non-zero CKM mixing of order the Cabibbo angle (|s₃₄| ≲ 0.27) is allowed, while zero mixing is excluded by combined Higgs mass and stability bounds. The analysis reveals that Higgs mass constraints from the Tevatron and theoretical unitarity bounds tighten limits on fourth-family mixing, favoring non-zero mixing even when SM4 fits are globally optimized.

ABSTRACT

Limits on the Higgs boson mass restrict CKM mixing of a possible fourth family beyond the constraints previously obtained from precision electroweak data alone. Existing experimental and theoretical bounds on the Higgs mass already significantly restrict the allowed parameter space. Zero CKM mixing is excluded and mixing of order the Cabibbo angle is allowed. Upper and lower limits on 3-4 CKM mixing are exhibited as a function of the Higgs mass. We use the default inputs of the Electroweak Working Group and also explore the sensitivity of both the three and four family fits to alternative inputs.

Motivation & Objective

• To determine the allowed parameter space for CKM mixing in a four-family Standard Model (SM4) using precision electroweak (PEW) data and Higgs mass constraints.
• To assess how Higgs mass limits from the Tevatron (CDF/D0) and theoretical unitarity bounds affect the viability of SM4 with non-zero fourth-family mixing.
• To evaluate the sensitivity of CKM mixing constraints to alternative inputs, including ∆α(5), data set composition, and hadronic asymmetry uncertainties.
• To explore whether tuning quark masses or lepton mass splittings can extend the allowed mixing region beyond the Cabibbo angle scale.

Proposed method

• Global fits to PEW data using the ZFITTER code with two-loop electroweak radiative corrections, incorporating EWWG default inputs and alternative parameter sets.
• Incorporation of Higgs mass constraints from CDF and D0 (95% CL exclusion for 131 ≤ mH ≤ 204 GeV) into the SM4 fit framework.
• Application of non-decoupling two-loop corrections to the oblique parameters T and Zbb vertex, proportional to mQ₄² and CKM mixing angles.
• Use of RG/stability analysis (Hashimoto) to derive theoretical lower bounds on mH relative to fourth-family quark masses, assuming perturbative validity of SM4.
• Systematic variation of input parameters: two alternative determinations of ∆α(5), inclusion of low-energy measurements, and exclusion of hadronic asymmetry data to test robustness.
• Comparison of χ² minimization across models with varying mQ₄, mν′, mℓ′, and |s₃₄| to identify best-fit mixing angles and 95% CL upper limits.

Experimental results

Research questions

• RQ1 What are the upper and lower bounds on 3-4 CKM mixing in SM4 when combined Higgs mass and electroweak precision data are applied?
• RQ2 How do Higgs mass constraints from the Tevatron (CDF/D0) and theoretical unitarity bounds affect the allowed range of fourth-family quark mixing?
• RQ3 To what extent do alternative inputs—particularly ∆α(5) and data set composition—affect the constraints on CKM mixing in SM4?
• RQ4 Can tuning quark and lepton mass splittings in SM4 extend the allowed parameter space for non-zero CKM mixing beyond the Cabibbo angle scale?
• RQ5 Does the global fit to SM4 prefer non-zero mixing even when the χ² minimum occurs at zero mixing, due to Higgs mass and stability constraints?

Key findings

• Zero CKM mixing in the fourth family is excluded by the combination of Higgs mass limits and theoretical unitarity bounds, even when the SM3 fit prefers mH ≈ 50 GeV.
• Non-zero CKM mixing of order the Cabibbo angle is allowed, with 95% CL upper limits of |s₃₄| < 0.27 for quark masses near the Tevatron’s 500 GeV lower limit.
• For quark masses near the perturbative unitarity bound (~1 TeV), the 95% CL upper limit on mixing tightens to |s₃₄| < 0.175.
• Theoretical stability bounds from Hashimoto’s RG analysis require mH > mQ₄ for perturbative validity, which excludes small or vanishing mixing when combined with Higgs mass data.
• Tightening the Higgs mass constraint via exclusion of hadronic asymmetry data leads to significantly reduced allowed parameter space and tighter mixing limits.
• Despite a deeper χ² minimum at |s₃₄| = 0, the allowed mixing range is not extended by tuning masses to shift the minimum away from zero; the upper limit remains around |s₃₄| < 0.175.