Phenomenological formula for CKM matrix and its physical interpretation

Nishida, Kohzo

doi:10.1093/ptep/ptx138

Cited by 1 publication

(1 citation statement)

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“…These characteristics enable us to construct the CKM matrix, and the fact that mass eigenstates are labeled by the square root mass and not by the mass plays a very important role in correctly determining the values of the CKM angles. An earlier paper on CKM angles which foresaw the significance of square root mass is the one by Nishida [13] and is titled "Phenomenological formula for CKM matrix and its physical interpretation". An even earlier interesting work is by Fritzsch [14,15], who also aimed to derive the mixing angles in terms of quark mass ratios.…”

Section: Introductionmentioning

confidence: 99%

CKM Matrix Parameters from the Exceptional Jordan Algebra

Patel,

Singh

2023

Universe

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We report a theoretical derivation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e., left chiral states) as a superposition of mass eigenstates (i.e., the right chiral states) weighted by the square root of mass. Flavor mixing for quarks is mediated by the square root mass eigenstates, and the mass ratios used are derived from earlier work from a left–right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, and they can be listed as follows: the real numbers R, the complex numbers C, the quaternions H and the octonions O. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high-energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also, the action of various spin groups on these representations can also be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as θ12=11.093∘,θ13=0.172∘,θ23=4.054∘. In comparison, the corresponding experimentally measured values for these angles are 13.04∘±0.05∘,0.201∘±0.011∘,2.38∘±0.06∘. The agreement of theory with experiment is likely to improve when the running of quark masses is taken into account.

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Section: Introductionmentioning

confidence: 99%