[Paper Review] A parametrization of the CKM mixing matrix from a scheme of S3L x S3R symmetry breaking

A. Mondragón, E. Rodrı́guez-Jáuregui|ArXiv.org|Apr 10, 1998

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes a parametrization of the CKM mixing matrix using a flavor symmetry scheme based on S3L × S3R breaking, where the hierarchical quark masses and mixing angles arise from the representation structure (1 + 2) of S3. By fitting to experimental CKM matrix elements, the model constrains the CP-violating phase and identifies a preferred symmetry breaking pattern, yielding a four-parameter fit in terms of quark mass ratios and the CP phase with excellent agreement to data.

ABSTRACT

Recent interest in flavour or horizontal symmetry building (mass textures) has been spurred mainly by the large top mass and, hence, the strong hierarchy in quark masses. Recently, various symmetry breaking schemes have been proposed based on the discrete, non-Abelian group S3L x S3R, which is broken according to S3L x S3R > S3_diag > S2_diag. The group S3 treats three objects symmetrically, while the hierarchical nature of the Yukawa matrices is a consequence of the representation structure, 1 + 2, of S3, which treats the generations differently. Different ansaetze for the breaking of the sub-nuclear democracy give different Hermitian mass matrices, M, of the same modified Fritzsch type which differ in the numerical value of the ratio M_23/M_22. A fit to the experimentally determined absolute values of the elements of the CKM matrix gives bounds on the possible values of the CP violating phase and gives a clear indication on the preferred symmetry breaking scheme. A parametrization of the CKM mixing matrix in terms of four quark mass ratios and one CP violating phase in very good agreement with the absolute value of the experimentally determined values of the CKM matrix elements is obtained.

Motivation & Objective

• To explain the observed hierarchy in quark masses and mixing angles using a non-Abelian flavor symmetry based on S3L × S3R.
• To derive a parametrization of the CKM matrix from a specific scheme of S3L × S3R symmetry breaking, particularly through the chain S3L × S3R → S3_diag → S2_diag.
• To constrain the CP-violating phase and identify the preferred symmetry breaking pattern by fitting to experimental values of CKM matrix elements.
• To provide a phenomenologically viable model of quark mixing that reproduces the observed absolute values of CKM matrix elements with minimal assumptions.

Proposed method

• Utilizes the S3L × S3R flavor symmetry group, broken via the chain S3L × S3R → S3_diag → S2_diag, to generate hierarchical Yukawa couplings.
• Applies the S3 representation structure (1 + 2) to construct Hermitian mass matrices of modified Fritzsch type, differing in the ratio M_23/M_22.
• Imposes a specific ansatz for the breaking of sub-nuclear democracy, leading to distinct mass matrix textures.
• Fits the resulting CKM matrix to experimentally measured absolute values of its elements to constrain the CP-violating phase and the mass ratio parameters.
• Uses four quark mass ratios and one CP-violating phase as free parameters in the parametrization.
• Compares the model predictions with experimental data to identify the preferred symmetry breaking scheme.

Experimental results

Research questions

• RQ1 Which specific pattern of S3L × S3R symmetry breaking best reproduces the observed CKM matrix elements?
• RQ2 How do the quark mass ratios and the CP-violating phase influence the predicted values of the CKM matrix elements in this symmetry-based model?
• RQ3 Can a flavor symmetry based on S3L × S3R reproduce the hierarchical structure of quark masses and mixing angles without fine-tuning?
• RQ4 What constraints does the experimental data impose on the CP-violating phase in this framework?
• RQ5 Which of the possible Hermitian mass matrix textures derived from the S3 representation structure yields the best fit to the observed CKM matrix?

Key findings

• The model successfully reproduces the absolute values of the CKM matrix elements with a parametrization based on four quark mass ratios and one CP-violating phase.
• The fit to experimental data provides strong constraints on the allowed range of the CP-violating phase.
• A clear preference emerges for one specific symmetry breaking scheme among the possible ansätze, based on the fit quality.
• The ratio M_23/M_22 in the mass matrix is identified as a key parameter distinguishing different breaking patterns.
• The resulting parametrization is in very good agreement with the experimentally determined values of the CKM matrix elements.
• The model demonstrates that the hierarchical structure of quark masses and mixing angles can be naturally explained via the representation theory of S3L × S3R symmetry.