Regge Poles in High-Energy Electron Scattering

The possibility that the photon is described by a Regge trajectory is considered, and the effect of this assumption on the analysis of electron-pion, electron-nucleon, and electron-helium scattering is examined in some detail. Partial-wave projections for the various amplitudes are made in the annihilation channel, and a multiparticle unitarity condition is formally imposed by use of the N/D matrix formulation. Since the photon does not have a fixed spin of one, the spin matrix structure is considerably more complicated than in the conventional theory. The amplitudes are written in terms of the Regge poles corresponding to the photon, ρ-ω meson, etc., and the resulting cross sections are given in the interesting high-energy limit. In contrast to the usual analysis, where form factors depend only on the momentum transfer, we find a larger number of independent functions which depend on the energy as well, however, in a characteristic manner. That is, the essential change due to the Regge behavior of the photon is an over-all nonintegral power of the energy occurring in the cross section. The effect of this factor can be experimentally tested and this possibility is discussed

On the analysis of nucleon-nucleon scattering experiments

A method of perturbation calculation, especially adapted to nucleon-nucleon scattering problems, is described. Any contribution to the energy of the system which is relatively small where the nuclear potential is large may be treated as the perturbation. Two principal examples are discussed. (1) Energy as the perturbation: An expansion of the phase shifts in powers of the energy is written down which extends earlier results of Schwinger, Blatt, and Jackson. (2) The Coulomb field as the perturbation in the proton-proton problem: Expansions are given which relate the nuclear phase shifts in a combined nuclear and Coulomb field to the corresponding phase shifts for a purely nuclear problem. Attention is confined to central forces throughout

KK Gravitons and Unitarity Violation in the Randall-Sundrum Model

We show that perturbative unitarity for $W_LW_L$ scattering places significant constraints on the Randall-Sundrum theory with two 3-branes, with matter confined to the TeV brane. The exchange of massive 4D Kaluza-Klein gravitons leads to amplitudes growing linearly with the CM energy squared. Summing over KK gravitons up to a scale \lbar and testing unitarity at \sqrt s=\lbar, one finds that unitarity is violated for \lbar below the 'naive dimensional analysis' scale, $\Lambda_{NDA}$. We evaluate \lbar as a function of the curvature ratio $m_0/M_{Planck}$ for the pure gravity theory. We then demonstrate that unitarity need not be violated at \lbar in the presence of a heavy Higgs boson. In fact, much larger Higgs masses are consistent with unitarity than if no KK gravitons are present. Observation of the mass and width (or cross section) of one or more KK gravitons at the LHC will directly determine $m_0/M_{Planck}$ and the scale $\hat \Lambda$ specifying the couplings of matter to the KK gravitons. With this information in hand and a measurement of the Higgs boson mass, one can determine the precise scale \lbar below which unitarity will remain valid.Comment: 14 pages, 8 figures, major revisions mad

Some Properties of Domain Wall Solution in the Randall-Sundrum Model

Properties of the domain wall (kink) solution in the 5 dimensional Randall-Sundrum model are examined both {\it analytically} and {\it numerically}. The configuration is derived by the bulk Higgs mechanism. We focus on 1) the convergence property of the solution, 2) the stableness of the solution, 3) the non-singular property of the Riemann curvature, 4) the behaviours of the warp factor and the Higgs field. It is found that the bulk curvature changes the sign around the surface of the wall. We also present some {\it exact} solutions for two simple cases: a) the no potential case, b) the cosmological term dominated case. Both solutions have the (naked) curvature singularity. We can regard the domain wall solution as a singularity resolution of the exact solutions.Comment: Typographical error correction for publication. 16 pages, 4 figure

Application of dispersion relations to low-energy meson-nucleon scattering

Relativistic dispersion relations are used to derive equations for low-energy S-, P-, and D-wave meson-nucleon scattering under the assumption that the (3,3) resonance dominates the dispersion integrals. The P-wave equations so obtained differ only slightly from those of the static fixed-source theory. The conclusions of the static theory are re-examined in the light of their new derivation

Improvements to the Method of Dispersion Relations for B Nonleptonic Decays

We bring some clarifications and improvements to the method of dispersion relations in the external masses variables, that we proposed recently for investigating the final state interactions in the B nonleptonic decays. We first present arguments for the existence of an additional term in the dispersion representation, which arises from an equal-time commutator in the LSZ formalism and can be approximated by the conventional factorized amplitude. The reality properties of the spectral function and the Goldberger-Treiman procedure to perform the hadronic unitarity sum are analyzed in more detail. We also improve the treatment of the strong interaction part by including the contributions of both t and u-channel trajectories in the Regge amplitudes. Applications to the $B^0\to \pi^+\pi^-$ and $B^+\to \pi^0 K^+$ decays are presented.Comment: 16 pages, 4 new figures. modifications of the dispersion representatio

Radion effects on unitarity in gauge-boson scattering

The scalar field associated with fluctuations in the positions of the two branes, the ``radion'', plays an important role determining the cosmology and collider phenomenology of the Randall-Sundrum solution to the hierarchy problem. It is now well known that the radion mass is of order the weak scale, and that its couplings to standard model fields are order 1/TeV to the trace of the energy momentum tensor. We calculate longitudinal vector boson scattering amplitudes to explore the constraints on the radion mass and its coupling from perturbative unitarity. The scattering cross section can indeed become non-perturbative at energies prior to reaching the TeV brane cutoff scale, but only when some curvature-Higgs mixing on the TeV brane is present. We show that the coefficient of the curvature-Higgs mixing operator must be less than about 3 for the 4-d effective theory to respect perturbative unitarity up to the TeV brane cutoff scale. Mass bounds on the Higgs boson and the radion are also discussed.Comment: 17 pages, LaTeX, 5 eps figures, uses epsf.sty and axodraw.st

Elementary particles of conventional field theory as Regge poles. III

It is shown that an elementary particle of conventional field theory may, under certain conditions, lie on a Regge trajectory. These conditions are that the system contain a "nonsense" channel at the angular momentum of the particle and that the Born approximation scattering amplitude factor in a well-defined way. They are satisfied by a spin ½ fermion interacting through a conserved current with a spin one neutral boson. The particle in question is the fermion