Asymptotic Symmetry, Particle Mixing, andKl3-Decay Branching Ratios

Abstract

A concept of asymptotic symmetry is formulated and applied to the determination of mixing parameters between the 7r°, TJ°, and r)'°(958) in broken SU(3) and SU(2) symmetries. One of the solutions gives rise to a rather large violation of the | Al |=\ rule in the K lZ decays which is not inconsistent with present experiment.This paper aims to discuss the particle mixing effects by taking the view of asymptotic symmetry which assumes that the SU(3) and SU(2) symmetries are well realized among particles of extremely high momenta. A similar assumption has been used in deriving several successful sum rules from the chiral SU(3)®SU(3) algebra. 1 ' 2 To derive our result by a short-cut (but instructive) computation, we express the requirement of asymptotic SU(3) symmetry in a simple form. Let us consider the pseudoscalar nonet and denote their annihilation operators as a a (k) 1 where a stands for TT*' 0 , K + »°, K + *°, r]°, and 7?' 0 (958), and k denotes their momenta. It should be noted that a a (k) are not the Heisenberg operators but the operators of the physical (i.e., incoming) particles with mass m a . Denoting the SU(3) generators by V i9 the transformation of physical particles in broken SU(3) symmetry can be expressed

Ω−,Ξ*−,Σ<

“…of the symmetry groups of QCD and can be derived from a simple model L QCD including quark mass terms. However, they are valid even though these symmetries are broken [9][10][11][12][13][14][15][16] and even when the Lagrangian is not known or cannot be constructed. Some examples (summation over the dummy index k is understood) of these ETCRs or constraint algebras follow:…”

“…A fundamental part of the dynamical concept of asymptotic SU F (N) symmetry [9][10][11][12] is the behavior of the vector charge V α when acting on a physical state which has momentum k (| k| → ∞), helicity λ, and SU F (N) index α: The physical annihilation operator a α ( k, λ) of a physical on-mass-shell hadron maintains its linearity [including asymptotic SU F (N ) particle mixings] under flavor transformations generated by the charge V α but only in the limit | k| → ∞. We note that the expression | k| → ∞ is completely synonymous with the expression lim | k|→∞ .…”

“…The dynamical assumption of asymptotic SU F (N ) symmetry [9][10][11][12] then states that (12) implying that…”

“…In this article the infinite momentum frame-in conjunction with the fact that the four-vector electromagnetic current j µ em obeys the equal time commutator [V K 0 , j µ em ] = 0 even * slaughtm@FIU.Edu,Slaughts@PhysicsResearch.Net in the presence of symmetry breaking-is used to calculate the magnetic moments of the physical decuplet U spin = 3 2 quartet members without ascribing any specific form to their quark structure or intraquark interactions [9][10][11][12][13].…”

On the unification of Higgs-Nambu Goldstone boson in the formation of near-brane exotic scalar via Scherk-Shwarz breaking in 5-dimensional SU(6) symmetry

“…Recently a grand gauge-Higgs unification based on 5D SU(6) compactified on an orbifold S 1 /Z 2 with fermions in two 6-plets and one 20-plet shows successful breaking with no proton decay at tree level but a little low compactification scale and heavy Higgs [8]. Other work such as Hosotani mechanism with non-zero VEV being developed by extra-dimensional parameters results in instant gauge symmetry breaking after dimensional deconstruction [25,27,47] and some other works in extra dimension and non-Higgs mechanism have been developed [3,4,13,14,15,21,22,24,26,27,35,40,41,48] including the pioneer one [32,34].…”