We calculate the pion's valence-quark momentum-fraction probability distribution using a DysonSchwinger equation model. Valence-quarks with an active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale q0 = 0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q0 to q = 2 GeV, it yields first, second and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion's momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrisations of extant pionnucleon Drell-Yan data.
Using a quantum kinetic equation coupled to Maxwell's equation we study the possibility that focused beams at proposed X-ray free electron laser facilities can generate electric field strengths large enough to cause spontaneous electron-positron pair production from the QED vacuum. Our approach yields the time and momentum dependence of the single particle distribution function. Under conditions reckoned achievable at planned facilities, repeated cycles of particle creation and annihilation take place in tune with the laser frequency. However, the peak particle number density is insensitive to this frequency and one can anticipate the production of a few hundred particle pairs per laser period. Field-current feedback and quantum statistical effects are small and can be neglected in this application of non-equilibrium quantum mean field theory. The QED vacuum is unstable in the presence of a strong external field and decays by emitting electronpositron pairs. The pair production rate was first calculated for a static, homogeneous electric field in the early part of the last century [1] and since then many aspects have been studied in detail. Using the Schwinger formula [1] one finds that a sizeable rate requires a field: The possibility of spontaneous pair creation from the vacuum is of particular interest in ultra-relativistic heavy ion collisions [2,3]. Since the QCD string tension is large ( √ σ ∼ 400 MeV), flux tube models of the collision generate a background field that is easily strong enough to initiate the production process via a Schwinger-like mechanism. Feedback between the external field and the field created by the produced particles' motion drives plasma oscillations. This is the back-reaction phenomenon, which has been much discussed [4,5,6]. While this Vlasov-equation-based approach has met with some phenomenological success, a rigorous justification in QCD is wanting.Pair creation by laser beams in QED has also been discussed [7,8], and proposed X-ray free electron laser (XFEL) facilities at SLAC [9] and DESY [10], which could generate field strengths [11, 12] E ≈ 0.1E cr , promise to provide a means to explore this phenomenon.Vacuum decay is a far-from-equilibrium, time-dependent process and hence kinetic theory provides an appropriate descriptive framework. For spatially homogeneous fields, a rigorous connection between kinetic theory and a mean-field treatment of QED has been established [13,14]. The derivation makes plain that the true kinetic equation's source term is intrinsically nonMarkovian, and this is expressed in properties of the solution [13,14,15,16]. Herein we use this quantum Vlasov equation to obtain a description of the time evolution of the momentum distribution function for particles produced via vacuum decay at the planned XFEL facilities.A gauge and Lorentz invariant description of an electromagnetic (e.m.) field is obtained usingAn e.m. plane wave always fulfills F = G = 0 and such a light-like field cannot produce pairs [17]. Therefore, to produce pairs it is necessary t...
Poincare' covariant Faddeev equations for the nucleon and Delta are solved to illustrate that an internally consistent description in terms of confined-quark and nonpointlike confined-diquark-correlations can be obtained. pi N-loop induced self-energy corrections to the nucleon's mass are analysed and shown to be independent of whether a pseudoscalar or pseudovector coupling is used. Phenomenological constraints suggest that this self-energy correction reduces the nucleon's mass by up to several hundred MeV. That effect does not qualitatively alter the picture, suggested by the Faddeev equation, that baryons are quark-diquark composites. However, neglecting the pi-loops leads to a quantitative overestimate of the nucleon's axial-vector diquark component.Comment: 17 pages, 6 figures, REVTEX
Aspects of the formation and equilibration of a quark-gluon plasma are explored using a quantum kinetic equation, which involves a non-Markovian, Abelian source term for quark and antiquark production and, for the collision term, a relaxation time approximation that defines a time-dependent quasi-equilibrium temperature and collective velocity. The strong Abelian field is determined via the simultaneous solution of Maxwell's equation. A particular feature of this approach is the appearance of plasma oscillations in all thermodynamic observables. Their presence can lead to a sharp increase in the time-integrated dilepton yield.
The electric and magnetic dipole moments of the meson are calculated using the propagators and vertices derived from the QCD Dyson-Schwinger equations. Results obtained from using the Bethe-Salpeter amplitude studied by Chappell, Mitchell, and Tandy, and Pichowsky and Lee, are compared. The meson electric dipole moment is generated through the inclusion of a quark electric dipole moment, which is left as a free variable. These results are compared to the perturbative results to obtain a measure of the effects of quark interactions and confinement. The two dipole moments are also calculated using the phenomenological MIT bag model to provide a further basis for comparison. ͓S0556-2813͑98͒01405-8͔
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