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

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

Dispersion Relations and Rescattering Effects in B Nonleptonic Decays

Recently, the final state strong interactions in nonleptonic B decays were investigated in a formalism based on hadronic unitarity and dispersion relations in terms of the off-shell mass squared of the $B$ meson. We consider an heuristic derivation of the dispersion relations in the mass variables using the reduction LSZ formalism and find a discrepancy between the spectral function and the dispersive variable used in the recent works. The part of the unitarity sum which describes final state interactions is shown to appear as spectral function in a dispersion relation based on the analytic continuation in the mass squared of one final particles. As an application, by combining this formalism with Regge theory and SU(3) flavour symmetry we obtain constraints on the tree and the penguin amplitudes of the decay $B^0\to \pi^+\pi^-$.Comment: 17 pages, Latex, 2 figure

Bound States and Threshold Resonances in Quantum Wires with Circular Bends

We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high curvature. We determine the bound state energies as well as the transmission and reflection matrices, ${\cal T}$ and ${\cal R}$ and focus on the nature of the resonances which occur in the vicinity of channel thresholds. We explore the dependence of these solutions on the curvature of the tube and angle of the bend and discuss several limiting cases where our numerical results confirm analytic predictions.Comment: 24 pages, revtex file, one style file and 17 PostScript figures include

Toward a unified description of hadro- and photoproduction: S-wave pi- and eta-photoproduction amplitudes

The Chew-Mandelstam parameterization, which has been used extensively in the two-body hadronic sector, is generalized in this exploratory study to the electromagnetic sector by simultaneous fits to the pion- and eta-photoproduction S-wave multipole amplitudes for center-of-mass energies from the pion threshold through 1.61 GeV. We review the Chew-Mandelstam parameterization in detail to clarify the theoretical content of the SAID hadronic amplitude analysis and to place the proposed, generalized SAID electromagnetic amplitudes in the context of earlier employed parameterized forms. The parameterization is unitary at the two-body level, employing four hadronic channels and the gamma-N electromagnetic channel. We compare the resulting fit to the MAID parameterization and find qualitative agreement though, numerically, the solution is somewhat different. Applications of the extended parameterization to global fits of the photoproduction data and to global fits of the combined hadronic and photoproduction data are discussed.Comment: 9 pages, 9 figures; added figures and tex

Reconstruction of the optical potential from scattering data

We propose a method for reconstruction of the optical potential from scattering data. The algorithm is a two-step procedure. In the first step the real part of the potential is determined analytically via solution of the Marchenko equation. At this point we use a diagonal Pad\'{e} approximant of the corresponding unitary $S$-matrix. In the second step the imaginary part of the potential is determined via the phase equation of the variable phase approach. We assume that the real and the imaginary parts of the optical potential are proportional. We use the phase equation to calculate the proportionality coefficient. A numerical algorithm is developed for a single and for coupled partial waves. The developed procedure is applied to analysis of $^{1}S_{0}$ $NN$, $^{3}SD_{1}$ $NN$, $P31$ $\pi^{-} N$ and $S01$ $K^{+}N$ data.Comment: 26 pages, 8 figures, results of nucl-th/0410092 are refined, some new results are presente

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

Dilaton Interactions and the Anomalous Breaking of Scale Invariance of the Standard Model

We discuss the main features of dilaton interactions for fundamental and effective dilaton fields. In particular, we elaborate on the various ways in which dilatons can couple to the Standard Model and on the role played by the conformal anomaly as a way to characterize their interactions. In the case of a dilaton derived from a metric compactification (graviscalar), we present the structure of the radiative corrections to its decay into two photons, a photon and a $Z$, two $Z$ gauge bosons and two gluons, together with their renormalization properties. We prove that, in the electroweak sector, the renormalization of the theory is guaranteed only if the Higgs is conformally coupled. For such a dilaton, its coupling to the trace anomaly is quite general, and determines, for instance, an enhancement of its decay rates into two photons and two gluons. We then turn our attention to theories containing a non-gravitational (effective) dilaton, which, in our perturbative analysis, manifests as a pseudo-Nambu Goldstone mode of the dilatation current ($J_D$). The infrared coupling of such a state to the two-photons and to the two-gluons sector, and the corresponding anomaly enhancements of its decay rates in these channels, is critically analyzed.Comment: Revised version, 42 pages, 5 figure

Parity-Violating Interaction Effects in the np System

We investigate parity-violating observables in the np system, including the longitudinal asymmetry and neutron-spin rotation in np elastic scattering, the photon asymmetry in np radiative capture, and the asymmetries in deuteron photo-disintegration d(gamma,n)p in the threshold region and electro-disintegration d(e,e`)np in quasi-elastic kinematics. To have an estimate of the model dependence for the various predictions, a number of different, latest-generation strong-interaction potentials--Argonne v18, Bonn 2000, and Nijmegen I--are used in combination with a weak-interaction potential consisting of pi-, rho-, and omega-meson exchanges--the model known as DDH. The complete bound and scattering problems in the presence of parity-conserving, including electromagnetic, and parity-violating potentials is solved in both configuration and momentum space. The issue of electromagnetic current conservation is examined carefully. We find large cancellations between the asymmetries induced by the parity-violating interactions and those arising from the associated pion-exchange currents. In the np capture, the model dependence is nevertheless quite small, because of constraints arising through the Siegert evaluation of the relevant E1 matrix elements. In quasi-elastic electron scattering these processes are found to be insignificant compared to the asymmetry produced by gamma-Z interference on individual nucleons.Comment: 65 pages, 26 figures, submitted to PR