120349764
Electroproduction and photoabsorption in a model of higher baryon couplings
We have studied the two related problems of inelastic e - -N scattering and the total photoabsorption cross section in a relativistic SU(6) × O(3) model of higher baryon couplings developed over the last few years. The hypothesis of duality is incorporated for both these photonic processes by summing over an infinite sequence of s-channel resonances, the facility for which is provided in this model of B L B(P,V) couplings through a simple structure of the form factor for the supermultiplet transition (L P →0 + ) and a "Regge universality" condition on the "reduced" coupling constants. A slight variant of this form factor, which has been applied successfully to several two-body processes recently, is found to give rather good fits to the resonance-production region of inelastic e - -N scattering over a wide range of input data. The difference (Δσ T ) of the total photoabsorption cross section on the proton and the neutron targets is also reproduced quite accurately over the whole range of available data. For these two processes, the higher-spin (J=L+1/2, J=L+3/2) states are found to produce dominant contributions over those of the lower-spin (J = L-1/2) states. A comparison of this pattern with a corresponding one operative for the evaluation of electromagnetic masses within this model prompts us to infer almost a "causal" relationship between the positive value of Δσ T on the one hand and the traditional negative value of (δm p -δm n ) on the other. However, an important shortcoming of this model is its inability to reproduce the scaling region of deep-inelastic e - -N scattering for very high incident electron energies (e>10 GeV). This is presumably because of the absence in this model of a mechanism for the inclusion of daughter trajectories, whose contributions are expected to be progressively more important as the energy is increased.
117884842
THREE-BODY VERTICES WITH TWO-BODY TECHNIQUES,
Publisher Summary This chapter discusses three-body vertices with two-body techniques. It has long been recognized that vertex functions for few particle systems provide a convenient medium for the analysis of reactions in the language of Feynman diagrams, analogously to elementary particle processes. The development of three-particle theory has provided considerably more impetus for the use of the language of three-body vertex functions through the possibility of their exact evaluation with only two-body input. While three-body vertices are probably superfluous for the description of only three-body processes, their practical usefulness often extends to reactions involving more than three-particle systems, as long as such systems can be meaningfully described in terms of not more than three particles playing the active role. This chapter reviews a simplified construction of three-body vertices. For a four system, the problem of normalization of the corresponding wave functions is so much more involved that at the present state of computer technology, there appears little chance of the exact evaluation of αdd and αtN vertex functions in terms of overlap integrals if wave functions calculated entirely in terms of N-N input potentials are to be used.
15889809
On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer-Duffin β-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard “trace” techniques. The results are compared with a recent derivation due to Bosanac.
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
61725309
The three-body problem: third generation and beyond?
123745795
*recoil effects* in a model of higher baryon couplings. i. photoproduction
A recently proposed model (MM) of higher baryon couplings for P and V mesons is reformulated by reviewing the fuller possibilities of the "recoil term" in the primitive quark-meson interaction. While this introduces no basic change in the P-meson coupling structures, it yields an entirely new (L-1)-wave coupling of V mesons to J = L+12 baryons, which is capable of generating helicity-flip amplitudes. The advantage of this new coupling structure over the earlier one is demonstrated through the excellent reproduction of (i) the E1 angular distribution in Y * →Λγ decay and (ii) the appreciable magnitudes as well as energy variations of the asymmetry parameter ∑(θ) in pion photoproduction. In addition to a comparison of the two coupling structures (old and new), the present paper is also designed to study the role of still another parametric structure for the form factor - one which exhibits better convergence properties at higher energies than those discussed in MM. The additional processes studied in this connection are (i) η and X 0 photoproduction at intermediate energies (> 2 GeV), (ii) polarization of the recoil proton in η and π photoproduction, and (iii) π 0 photoproduction at high energies (∼ 6 GeV), in accordance with our earlier scheme of s-channel resonances. In connection with η photoproduction the roles of some pertinent I =12 resonances such as S 11 , P 11 , and G 17 are discussed, especially in relation to supermultiplet assignments.
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.