181778573
HARMONIC OSCILLATOR IN QUARK PHYSICS: SOME ASPECTS, A REVIEW
122194110
Dynamical basis for spin-½ as well as generation stability of leptons and quarks
Abstract A three-way preon interaction with a spin-dependence of the form σ μν (1) σ νγ (2) σ λμ (3) , is proposed for a two-flavor (t,v) preon model, within a Bethe-Salpeter framework. This mechanism not only eliminates all S = 3 2 states but severely restricts the spatial symmetries of allowed S = 1 2 states to at most three distinct “generations” with very strong selection rules forbidding transitions among them.
61725309
The three-body problem: third generation and beyond?
30997914
Null-plane Bethe-Salpeter dynamics: Mass spectra, decay constants of pseudoscalar mesons, and the pion form factor.
A new relativistic definition of the reduced mass ({mu}{sub 12}) of a {ital q{bar q}} pair, so as to be in conformity with the standard Wightman-Garding definition of its relative four-momenta {ital q}{sub {mu}}, is introduced into the kernel of an ongoing Bethe-Salpeter (BS) program on a two-tier basis. The new definition of {mu}{sub 12} (involving the hadron mass {ital M}) is found to produce a natural Regge asymptotic behavior ({ital M}{sup 2}{approximately}{ital N}) in the hadron mass spectra, while retaining the property of an asymptotically linear ({approximately}{ital r}) confinement in the three-dimensional structure of the BS kernel. The relativistic structure of {mu}{sub 12} is responsible for a significant improvement in the fits to the ground-state masses of {ital q{bar q}} and {ital Q{bar q}} mesons as compared to its nonrelativistic definition {ital m}{sub 1}{ital m}{sub 2}/({ital m}{sub 1}+{ital m}{sub 2}). The leptonic decay constants {ital f}{sub {ital p}} and the charge radii thus calculated are also in excellent agreement with data ({pi},{ital k}) where available, while {ital f}{sub {ital p}} predictions for {ital Q{bar q}} mesons have good overlap with recent lattice predictions. Further, the scaling property ({approximately}{ital k}{sub {mu}}{sup {minus}2}) of the hadron's electromagnetic form factor at largemore » {ital k}{sup 2} is a consequence of the on-shell'' form of its null-plane wave function. All these results (which are indicated in the barest outline) are preceded by a perspective summary of the theoretical premises and practical working of the BS equation with a four-fermion interaction kernel as a necessary background on a two-tier basis.« less
122976930
Strange baryon spectra in a Bethe-Salpeter dynamical model
A Bethe-Salpeter equation (BSE) has been derived using a covariant confining interaction motivated from QCD. Recently, this interaction has been applied to a qqq system under the null plane ansatz (NPA), which reduces the resulting equations to three-dimensional form. For equal mass quarks, encouraging results were obtained for baryon masses and quantum numbers. In the present paper, this formalism is generalized to unequal mass kinematics and applied to the spectroscopy of strange baryons (Λ, Σ, Ξ, Ω). All input parameters are fixed from previous calculations. The reduced qqq equation in the NPA is solved algebraically in a six-dimensional harmonic oscillator basis, on lines analogous to the corresponding techniques developed for the equal mass qqq problem. The results on the Λ, Σ spectra are in good agreement with data, where available, up to levels N=5. Our results are compared with those from another relativized potential of baryon masses.
119338250
BARYON SELF-ENERGY WITH qqq BETHE–SALPETER DYNAMICS IN THE NONPERTURBATIVE QCD REGIME: n-p MASS DIFFERENCE
A qqq BSE formalism based on DBχS of an input four-fermion Lagrangian of "current" u, d quarks interacting pairwise via gluon-exchange-propagator in its nonperturbative regime, is employed for the calculation of baryon self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green function techniques. This is a three-body extension of an earlier (two-body) result on the exact 3D–4D interconnection for the respective BS wave functions under 3D kernel support. The nonperturbative QCD feature of this approach (vis-a-vis chiral perturbation theory — see text for comparison) is preserved through the gluon exchange propagator in the infrared regime (characterized by two parameters C0, ω0), precalibrated to both and qqq spectra plus other observables, together with a DBχ S mechanism to generate the dynamical mass m(p). The quark-loop integrals for the neutron (n) – proton (p) mass difference receive contributions from two sources: (i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); (ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from the d-u effect (+1.71 MeV), which is mildly offset by e.m. effect (-0.44), subject to gauge corrections. For an estimate of the latter a general method for QED gauge corrections to an arbitrary momentum dependent vertex function is outlined (in App. C), and a calculation made for the (two-body) kaon as a test case, indicates an increase by 0.612 MeV in the earlier kaon e.m. value (1.032 MeV). This result is taken as a rough indication of the percentage gauge correction expected for the n-p case. A critical comparison is given with the results from QCD sum rules.
119114701
Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
Newtonian gravity was formulated as a geometrodynamic theory as far back in 1930s by Elie Cartan in what is named aptly as Newton Cartan space time. Though there are several approaches of realizing the algebraic structure of the Newton Cartan geometry from a contraction of the relativistic results, a dynamical (field theoretic) realization of it is lacking. In this paper we present such a realization from the localisation of the Galilean Symmetry of nonrelativistic matter field theories.