20 research outputs found

    Charge specific baryon mass relations with deformed SU_q(3) flavor symmetry

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    The quantum group SUq(3)=Uq(su(3))SU_q(3)=U_q(su(3)) is taken as a baryon flavor symmetry. Accounting for electromagnetic contributions to baryons masses to zeroth order, new charge specific qq-deformed octet and decuplet baryon mass formulas are obtained. These new mass relations have errors of only 0.02\% and 0.08\% respectively; a factor of 20 reduction compared to the standard Gell-Mann-Okubo mass formulas. A new relation between the octet and decuplet baryon masses that is accurate to 1.2\% is derived. An explicit formula for the Cabibbo angle, taken to be Ο€14\frac{\pi}{14}, in terms of the deformation parameter qq and spin parity JPJ^P of the baryons is obtained.Comment: 14 page

    Deformations of spacetime and internal symmetries

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    Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group SU(3)SU(3) to the quantum group SUq(3)≑Uq(su(3))SU_q(3)\equiv U_q(su(3)) (a Hopf algebra) and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly with experimental data.Comment: 5th International Conference on New Frontiers in Physics, Crete, Greece, July 6-14, 201

    The Standard Model particle content with complete gauge symmetries from the minimal ideals of two Clifford algebras

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    Building upon previous works, it is shown that two minimal left ideals of the complex Clifford algebra Cβ„“(6)\mathbb{C}\ell(6) and two minimal right ideals of Cβ„“(4)\mathbb{C}\ell(4) transform as one generation of leptons and quarks under the gauge symmetry SU(3)CΓ—U(1)EMSU(3)_C\times U(1)_{EM} and SU(2)LΓ—U(1)YSU(2)_L\times U(1)_Y respectively. The SU(2)LSU(2)_L weak symmetries are naturally chiral. Combining the Cβ„“(6)\mathbb{C}\ell(6) and Cβ„“(4)\mathbb{C}\ell(4) ideals, all the gauge symmetries of the Standard Model, together with its lepton and quark content for a single generation are represented, with the dimensions of the minimal ideals dictating the number of distinct physical states. The combined ideals can be written as minimal left ideals of Cβ„“(6)βŠ—Cβ„“(4)β‰…Cβ„“(10)\mathbb{C}\ell(6)\otimes\mathbb{C}\ell(4)\cong \mathbb{C}\ell(10) in a way that preserves individually the Cβ„“(6)\mathbb{C}\ell(6) structure and Cβ„“(4)\mathbb{C}\ell(4) structure of physical states. This resulting model includes many of the attractive features of the Georgi and Glashow SU(5)SU(5) grand unified theory without introducing proton decay or other unobserved processes. Such processes are naturally excluded because they do not individually preserve the Cβ„“(6)\mathbb{C}\ell(6) and Cβ„“(4)\mathbb{C}\ell(4) minimal ideals.Comment: 13 Page

    Three generations of colored fermions with S3S_3 family symmetry from Cayley-Dickson sedenions

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    An algebraic representation of three generations of fermions with SU(3)CSU(3)_C color symmetry based on the Cayley-Dickson algebra of sedenions S\mathbb{S} is constructed. Recent constructions based on division algebras convincingly describe a single generation of leptons and quarks with Standard Model gauge symmetries. Nonetheless, an algebraic origin for the existence of exactly three generations has proven difficult to substantiate. We motivate S\mathbb{S} as a natural algebraic candidate to describe three generations with SU(3)CSU(3)_C gauge symmetry. We initially represent one generation of leptons and quarks in terms of two minimal left ideals of Cβ„“(6)\mathbb{C}\ell(6), generated from a subset of all left actions of the complex sedenions on themselves. Subsequently we employ the finite group S3S_3, which are automorphisms of S\mathbb{S} but not of O\mathbb{O} to generate two additional generations. Given the relative obscurity of sedenions, efforts have been made to present the material in a self-contained manner.Comment: 18 pages, 1 figur
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