20 research outputs found

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

The quantum group $SU_q(3)=U_q(su(3))$ is taken as a baryon flavor symmetry.
Accounting for electromagnetic contributions to baryons masses to zeroth order,
new charge specific $q$-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 $\frac{\pi}{14}$, in terms of the deformation parameter $q$ and
spin parity $J^P$ of the baryons is obtained.Comment: 14 page

### Deformations of spacetime and internal symmetries

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 $SU(3)$ to the quantum
group $SU_q(3)\equiv U_q(su(3))$ (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

Building upon previous works, it is shown that two minimal left ideals of the
complex Clifford algebra $\mathbb{C}\ell(6)$ and two minimal right ideals of
$\mathbb{C}\ell(4)$ transform as one generation of leptons and quarks under the
gauge symmetry $SU(3)_C\times U(1)_{EM}$ and $SU(2)_L\times U(1)_Y$
respectively. The $SU(2)_L$ weak symmetries are naturally chiral. Combining the
$\mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$ 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 $\mathbb{C}\ell(6)\otimes\mathbb{C}\ell(4)\cong
\mathbb{C}\ell(10)$ in a way that preserves individually the
$\mathbb{C}\ell(6)$ structure and $\mathbb{C}\ell(4)$ structure of physical
states. This resulting model includes many of the attractive features of the
Georgi and Glashow $SU(5)$ grand unified theory without introducing proton
decay or other unobserved processes. Such processes are naturally excluded
because they do not individually preserve the $\mathbb{C}\ell(6)$ and
$\mathbb{C}\ell(4)$ minimal ideals.Comment: 13 Page

### Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions

An algebraic representation of three generations of fermions with $SU(3)_C$
color symmetry based on the Cayley-Dickson algebra of sedenions $\mathbb{S}$ 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 $\mathbb{S}$ as a
natural algebraic candidate to describe three generations with $SU(3)_C$ gauge
symmetry. We initially represent one generation of leptons and quarks in terms
of two minimal left ideals of $\mathbb{C}\ell(6)$, generated from a subset of
all left actions of the complex sedenions on themselves. Subsequently we employ
the finite group $S_3$, which are automorphisms of $\mathbb{S}$ but not of
$\mathbb{O}$ 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