Electromagnetic interactions for the two-body spectator equations

This paper presents a new non-associative algebra which is used to (i) show how the spectator (or Gross) two-body equations and electromagnetic currents can be formally derived from the Bethe-Salpeter equation and currents if both are treated to all orders, (ii) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (iii) prove that the currents so derived are exactly gauge invariant when truncated consistently to any finite order. In addition to presenting these new results, this work complements and extends previous treatments based largely on the analysis of sums of Feynman diagrams.Comment: 44 pages, 14 figure

Decay widths in the massive Schwinger model

By a closer inspection of the massive Schwinger model within mass perturbation theory we find that, in addition to the $n$-boson bound states, a further type of hybrid bound states has to be included into the model. Further we explicitly compute the decay widths of the three-boson bound state and of the lightest hybrid bound state.Comment: 8 pages, Latex file, no figure

A second Higgs from the Higgs portal

In the Higgs portal framework, the Higgs field generally mixes with the Standard Model singlet leading to the existence of two states, one of which is identified with the 125 GeV scalar observed at the LHC. In this work, we analyse direct and indirect constraints on the second mass eigenstate and the corresponding mixing angle. The existence of the additional scalar can be beneficial as it can stabilise the otherwise-metastable electroweak vacuum. We find parameter regions where all of the bounds, including the stability constraints, are satisfied. We also study prospects for observing the decay of the heavier state into a pair of the 125 GeV Higgs-like scalars.Comment: 16 pages, updated figures 3 and 4 with new limits from Higgs-searches at the LHC, minor text adjustments, references adde

A comprehensive treatment of electromagnetic interactions and the three-body spectator equations

We present a general derivation the three-body spectator (Gross) equations and the corresponding electromagnetic currents. As in previous paper on two-body systems, the wave equations and currents are derived from those for Bethe-Salpeter equation with the help of algebraic method using a concise matrix notation. The three-body interactions and currents introduced by the transition to the spectator approach are isolated and the matrix elements of the e.m. current are presented in detail for system of three indistinguishable particles, namely for elastic scattering and for two and three body break-up. The general expressions are reduced to the one-boson-exchange approximation to make contact with previous work. The method is general in that it does not rely on introduction of the electromagnetic interaction with the help of the minimal replacement. It would therefore work also for other external fields

Lagrangian with off-shell vertices and field redefinitions

Meson exchange diagrams following from a lagrangian with off-shell meson-nucleon couplings are compared with those generated from conventional dynamics. The off-shell interactions can be transformed away with the help of a nucleon field redefinition. Contributions to to the $NN$- and $3N$-potentials and nonminimal contact e.m. meson-exchange currents are discussed, mostly for an important case of scalar meson exchange. (pacs 11.10.Lm, 13.75.Cs, 21.30.-x, 24.10.Jv)Comment: 18 pages (Revtex), 4 eps figure

Quark-Antiquark Bound States in the Relativistic Spectator Formalism

The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an earlier work is proven to give vanishing meson$\to$ $q+\bar{q}$ decay amplitudes, as required by confinement. The regularization of the singularities in the linear potential that are associated with nonzero energy transfers (i.e. $q^2=0,q^{\mu}\neq0$) is improved. Quark mass functions that build chiral symmetry into the theory and explain the connection between the current quark and constituent quark masses are introduced. The formalism is applied to the description of pions and kaons with reasonable results.Comment: 31 pages, 16 figure

Effects of Relativistic Dynamics in pp→ppπ0pp \to pp \pi^0 near Threshold

The cross-section for threshold $\pi^0$ production in proton-proton collisions is evaluated in the framework of the covariant spectator description. The negative energy intermediate states are included non-perturbatively and seen to yield a considerably smaller contribution, when compared to perturbative treatments. A family of OBE-models with different off-shell scalar coupling is considered.Comment: 10 pages, 3 figures, 1 tabl

Intrinsic operators for the electromagnetic nuclear current

The intrinsic electromagnetic nuclear meson exchange charge and current operators arising from a separation of the center-of-mass motion are derived for a one-boson-exchange model for the nuclear interaction with scalar, pseudoscalar and vector meson exchange including leading order relativistic terms. Explicit expressions for the meson exchange operators corresponding to the different meson types are given in detail for a two-nucleon system. These intrinsic operators are to be evaluated between intrinsic wave functions in their center-of-mass frame.Comment: 54 pages revtex, no figure