[Paper Review] The spin-charge-family theory is offering an explanation for the origin of the Higgs's scalar and for the Yukawa couplings

N. S. Mankoč Borštnik|arXiv (Cornell University)|Dec 5, 2013

International Science and Diplomacy10 references3 citations

TL;DR

This paper proposes that the Higgs scalar and Yukawa couplings in the Standard Model emerge from the spin-charge-family theory in 14-dimensional spacetime. By analyzing scalar fields in the (13+1)-dimensional action, it identifies specific scalar components (s=7,8) that carry weak and hypercharge quantum numbers identical to the Higgs boson, while the theory's dual spin connection fields naturally generate the Yukawa couplings through family symmetry gauge interactions.

ABSTRACT

The Higgs's scalar of the standard model is the only so far observed boson with a charge in the fundamental representation. It is interesting to observe that all the gauge fields with the scalar index with respect to $d=(3+1)$, appearing in the simple starting action of the {\it spin-charge-family} theory in $d=(13+1)$, are with respect to the scalar index and the standard model charge groups either doublets ($s=(5,6,7,8)$) or triplets ($t=(9,10,\dots,14)$). The scalar fields with the space index $s=(7,8)$ carry the weak and the hyper charge just as required by the {\it standard model} for the Higgs's scalar ($\pm \frac{1}{2}$ and $ \mp \frac{1}{2}$, respectively). There are besides the vielbeins also two kinds of the spin connection fields in this theory: i. One kind are the gauge fields of the spin, and in $d=(3+1)$ for the spin and all the charges. ii. The second kind are the gauge fields, which couple to the family quantum numbers. Properties of vielbeins and both kinds of spin connection fields are discussed, in particular with respect to the standard model Higgs's scalar and the Yukawa couplings.

Motivation & Objective

• To explain the origin of the Higgs scalar boson within a unified framework beyond the Standard Model.
• To understand the emergence of Yukawa couplings that generate fermion masses.
• To identify how the Standard Model's weak and hypercharge quantum numbers arise from higher-dimensional gauge structures.
• To clarify the role of spin connection fields in generating fermion mass terms and Higgs-like scalar fields.
• To establish a connection between family quantum numbers and the scalar field content in a 14-dimensional theory.

Proposed method

• Analyzing the starting action of the spin-charge-family theory in 14-dimensional spacetime (d = 13+1).
• Identifying scalar fields with respect to the scalar index in the vielbein and spin connection fields.
• Classifying scalar fields by their representation under the standard model gauge groups (SU(2)_L × U(1)_Y).
• Focusing on scalar components with indices s = 7 and 8, which carry weak and hypercharge quantum numbers ±1/2 and ∓1/2.
• Distinguishing two types of spin connection fields: one coupling to spin and standard model charges, and another coupling to family quantum numbers.
• Deriving the Yukawa couplings from the gauge interaction of the second kind of spin connection fields with fermions.

Experimental results

Research questions

• RQ1 How do scalar fields in the 14-dimensional spin-charge-family theory reproduce the quantum numbers of the Standard Model Higgs boson?
• RQ2 What is the origin of the Higgs scalar's weak and hypercharge quantum numbers within the higher-dimensional framework?
• RQ3 How do the two types of spin connection fields in the theory contribute to the generation of Yukawa couplings?
• RQ4 Can the observed structure of fermion masses and the Higgs mechanism be derived from family symmetry gauge interactions in higher dimensions?
• RQ5 What role do the vielbeins and scalar components with indices s = 7,8 play in realizing the Higgs mechanism in this theory?

Key findings

• Scalar fields with indices s = 7 and 8 in the spin-charge-family theory carry weak and hypercharge quantum numbers ±1/2 and ∓1/2, matching those of the Standard Model Higgs boson.
• These scalar fields arise naturally from the structure of the (13+1)-dimensional action and are doublets under the SU(2)_L × U(1)_Y group.
• The theory identifies two distinct types of spin connection fields: one coupling to spin and standard model charges, and another coupling to family quantum numbers.
• The second kind of spin connection field provides the mechanism for generating Yukawa couplings through gauge interactions with fermions.
• The vielbeins and both types of spin connection fields collectively account for the emergence of the Higgs scalar and fermion mass terms.
• The scalar index structure in d = (13+1) ensures that the Higgs-like scalar field appears with the correct quantum numbers and transforms as a doublet under the Standard Model gauge group.