18249187
Off-shell rho - omega mixing through quark loops with a nonperturbative meson vertex and quark mass functions.
The momentum dependence of the off-shell {rho}-{omega} mixing amplitude is calculated through a two-quark loop diagram, using nonperturbative meson-quark vertex functions for the {rho} and {omega} mesons, as well as nonperturbative quark propagators. Both these quantities are generated self-consistently through an interlinked Bethe-Salpeter equation (BSE) cum Schwinger- Dyson equation (SDE) approach with a 3D support for the BSE kernel with two basic constants that are prechecked against a wide cross section of both meson and baryon spectra within a common structural framework for their respective 3D BSE`s. With the precalibration, the on-shell strength works out at {minus}2.434 {delta}({ital m}{sub {ital q}}{sup 2}) in units of the change in ``constituent mass squared,`` which is consistent with the {ital e}{sup +}{ital e}{sup {minus}} to {pi}{sup +}{pi}{sup {minus}} data for a {ital u}-{ital d} mass difference of 4 MeV, while the relative off-shell strength (0.99{plus_minus}0.01) lies midway between quark-loop and QCD-SR results. We also calculate the photon-mediated {rho}-{omega} propagator whose off-shell structure has an additional pole at {ital q}{sup 2}=0. The implications of these results vis-a-vis related investigations are discussed.
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.
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.
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
39619210
Entropy in dilatonic black hole background.
The entropy of a scalar field is calculated semiclassically in the background of a dilatonic black hole. The area and cutoff dependences are normal except in the extremal case, where the area is zero but the entropy nonzero.
9159427
Poincaré invariance of anomalous gauge theories.
We establish the Poincare invariance of anomalous gauge theories in two dimensions, for both the Abelian and non-Abelian cases, in the canonical Hamiltonian formalism. It is shown that, despite the noncovariant appearance of the constraints of these theories, Poincare generators can be constructed which obey the correct algebra and yield the correct transformations in the constrained space.
42763584
Algebraic consistency in anomalous gauge theories.
A consistency condition for anomalous gauge theories is used to show that the usual form of the chiral anomaly is inadmissible and that a different but equivalent form yields Faddeev's Schwinger term.