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Heavy-quark mass relation from a standard-model boson operator representation in terms of fermions

Jaime Besprosvany, Rebeca Sánchez

TL;DR

This work develops a quantum, second-quantized spin-isospin formulation of the Standard Model's heavy-quark sector, expressing vector and scalar bosons as bilinear fermionic operators and introducing a common mass-generating scalar operator. By computing the vacuum expectation value and constructing a mass operator H_m, it derives key relations m_t = v χ_t / sqrt(2) and m_b = v χ_b / sqrt(2) with a normalization constraint |χ_t|^2+|χ_b|^2+ χ_t^* χ_b + χ_t χ_b^* = 1, and a composite-vev condition χ_t + e^{iθ} χ_b = 1. The framework yields standard-model vector masses M_W^2 = g^2 v^2 / 4 and M_Z^2 = (g^2+g'^2) v^2 / 4, along with a mass-sum relation m_t^2 + m_b^2 = v^2 / 2, and emphasizes a t-dominant hierarchy under plausible parameter choices. These results illuminate a consistent link between electroweak symmetry breaking, Yukawa couplings, and potential composite-scale physics, offering a coherent pathway to beyond-SM extensions such as NJL/top-condensate scenarios.

Abstract

The standard-model can be equivalently represented with its fields in a spin-extended basis, departing from fermion degrees of freedom. The common Higgs operator connects the electroweak and Yukawa sectors, restricting the top and bottom quark masses[Phys. Rev. D 99, 073001, 2019]. Using second quantization, within the heavy-particle sector, electroweak vectors, the Higgs field, and symmetry operators are expanded in terms of bilinear combinations of top and bottom quark operators, considering discrete degrees of freedom and chirality. This is interpreted as either a basis choice or as a description of composite models. The vacuum expectation value is calculated quantum mechanically, which relates to the common mass-generating scalar operator and it reproduces the vector and quark-doublet masses. This also links the corresponding scalar-vector and Yukawa vertices, and restricts the t- and b-quark masses in a hierarchy relation.

Heavy-quark mass relation from a standard-model boson operator representation in terms of fermions

TL;DR

This work develops a quantum, second-quantized spin-isospin formulation of the Standard Model's heavy-quark sector, expressing vector and scalar bosons as bilinear fermionic operators and introducing a common mass-generating scalar operator. By computing the vacuum expectation value and constructing a mass operator H_m, it derives key relations m_t = v χ_t / sqrt(2) and m_b = v χ_b / sqrt(2) with a normalization constraint |χ_t|^2+|χ_b|^2+ χ_t^* χ_b + χ_t χ_b^* = 1, and a composite-vev condition χ_t + e^{iθ} χ_b = 1. The framework yields standard-model vector masses M_W^2 = g^2 v^2 / 4 and M_Z^2 = (g^2+g'^2) v^2 / 4, along with a mass-sum relation m_t^2 + m_b^2 = v^2 / 2, and emphasizes a t-dominant hierarchy under plausible parameter choices. These results illuminate a consistent link between electroweak symmetry breaking, Yukawa couplings, and potential composite-scale physics, offering a coherent pathway to beyond-SM extensions such as NJL/top-condensate scenarios.

Abstract

The standard-model can be equivalently represented with its fields in a spin-extended basis, departing from fermion degrees of freedom. The common Higgs operator connects the electroweak and Yukawa sectors, restricting the top and bottom quark masses[Phys. Rev. D 99, 073001, 2019]. Using second quantization, within the heavy-particle sector, electroweak vectors, the Higgs field, and symmetry operators are expanded in terms of bilinear combinations of top and bottom quark operators, considering discrete degrees of freedom and chirality. This is interpreted as either a basis choice or as a description of composite models. The vacuum expectation value is calculated quantum mechanically, which relates to the common mass-generating scalar operator and it reproduces the vector and quark-doublet masses. This also links the corresponding scalar-vector and Yukawa vertices, and restricts the t- and b-quark masses in a hierarchy relation.

Paper Structure

This paper contains 10 sections, 68 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Vector-scalar and fermion-scalar mass components
  3. Standard-model limits and its composite extensions
  4. Second-quantized field expansion
  5. Particle Masses
  6. W$^\pm$ mass
  7. Z mass
  8. Top, bottom quark masses
  9. Composite-scalar vacuum expectation value
  10. Conclusions

Figures (1)

  • Figure 1: $\chi$ component in Eq. \ref{['Chi']}, compared with expected value 1, as obtained in $M_Z$, $M_W$, Eqs. \ref{['Wmass']}, \ref{['NeutralMassOperator']}, constrained by Eq. \ref{['ConstrainChitChib']}, as function of $\theta$ phase and $\chi_t$, favoring, e. g., $0\leq|\chi_b|\ll 1$, and so $0 \ll |\chi_t|\leq 1$.