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For gauge theory, the matrix element for any physical process is independent of the gauge used. Since this is a formal statement and examples are known where gauge invariance is violated, for any specific process this gauge invariance needs to be checked by explicit calculation. In this paper, gauge invariance is found to hold for a large non-trivial class of processes described by tree diagrams in the standard model -- tree diagrams with two external $W$ bosons and any number of external Higgs bosons. This verification of gauge invariance is quite complicated, and is based on a direct study of the difference between different gauges through induction on the number of external Higgs bosons.

The application of fermion-boson symmetry to the standard model leads to the following: first, there are three generations of scalar quarks and scalar leptons in addition to the known quarks and leptons, and, secondly, the divergences in the perturbation series for the standard model are reduced. In the light of experimental data from LEP, Tevatron Collider, and LHC, some consequences of these two statements taken together are discussed. A series of experiments are proposed to search for the scalar quarks and scalar leptons at the Large Hadron Collider. The first step in this search is to look for new fermions by analyzing events with a pair of oppositely changed leptons both with large transverse momenta. The scalar quarks and the scalar leptons are then searched for through their decays into these new fermions plus a known quark or lepton.

We prove the general theorem that the real part of the forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite energy., Comment: 4 pages

We will recall the main feaatures of an accurate phenomenological model to describe successfully near-forward elastic scattering in a wide energy range, including ISR, SPS and Tevatron colliders. A large step in energy domain is accomplished with the LHC collider, presently running, giving the opportunity to confront the new data with the predictions of our theoretical approach., Comment: 4 pages, 3 figures, Invited talk presented by Jacques Soffer at DIFFRACTION 2014, September 10 - 15, 2014, Primosten, Croatia (To be published in the AIP Conference Proceedings)

In 1970, on purely theoretical grounds, all total hadronic total cross sections were predicted to increase without limit for higher and higher energies. This was contrary to the conventional belief at that time. In 1978, an accurate phenomenological model was formulated for the case of proton-proton and antiproton-proton interactions. The parameters for this model were slightly improved in 1984 using the additional available experimental data. Since then, for thirty years these parameters have not changed. This development, including especially the difficult task of formulating this phenomenological model and the comparison of the predictions of this model with later experimental results, is summarized., Comment: 14 pages, 6 figures, Contribution to the special issue of the International Journal of Modern Physics A on "Elastic and diffractive scattering" coordinated by Christophe Royon

The properties of scalar quarks are studied, especially the formation of fermionic mesons with an anti-quark. On the basis of this theoretical investigation together with the experimental data, both from last year and from this year, of the ATLAS Collaboration and the CMS Collaboration at the Large Hadron Collider, it is proposed that the standard model of Glashow, Weinberg, and Salam should be augmented by scalar quarks, scalar leptons, and additional fermions. If these scalar quarks and scalar leptons are in one-to-one correspondence with the ordinary quarks and ordinary leptons, either in number or in the degrees of freedom, then there may be a fermion-boson symmetry. The fermion-boson symmetry obtained this way is of a different nature from that of supersymmetry., Comment: 7 pages, 1 figure

Some time ago, an accurate phenomenological approach, the BSW model, was developed for proton-proton and antiproton-proton elastic scattering cross sections at center-of-mass energies above 10 GeV. This model has been used to give successful theoretical predictions for these processes, at successive collider energies. The BSW model involves a combination of integrals that, while computable numerically at fairly high energies, require some mathematical analysis to reveal the high-energy asymptotic behavior. In this paper we present a high-energy asymptotic representation of the scattering amplitude at moderate momentum transfer, for the leading order in an expansion parameter closely related to the logarithm of the center-of-mass energy. The fact that the expansion parameter goes as the logarithm of the energy means that the asymptotic behavior is accurate only for energies greatly beyond any foreseeable experiment. However, we compare the asymptotic representation against the numerically calculated model for energies in a less extreme region of energy. The asymptotic representation is given by a simple formula which, in particular, exhibits the oscillations of the differential cross section with momentum transfer. We also compare the BSW asymptotic behavior with the Singh-Roy unitarity upper bound for the diffraction peak., Comment: 27 pages, 11 figures,revised version to appear in Physical Review D

The one-loop calculation of the amplitude for the Higgs decay H-->\gamma\gamma\ due to virtual W's in the unitary gauge is presented. As the Higgs does not directly couple to the massless photons, the one-loop amplitude is finite. The calculation is performed in a straightforward way, without encountering divergences. In particular, artifacts like dimensional regularization are avoided. This is achieved by judiciously routing the external momenta through the loop and by combining the integrands of the amplitudes before carrying out the integration over the loop momentum. The present result satisfies the decoupling theorem for infinite Higgs mass, and is thus different from the earlier results obtained in the \xi=1 gauge using dimensional regularization. The difference between the results is traced to the use of dimensional regularization., Comment: 20 pages, 2 figures

Since the photon has no mass, it does not couple directly to the Higgs particle. This implies that the one-loop correction to the decay H --> \gamma\gamma\ is necessarily finite. Therefore, this correction should be calculable without introducing either regularization or ghosts. Such a calculation is carried out in this paper for the case of one W loop. The result obtained this way turns out not to agree with the previous, well-known one, and it is argued that the present result is to be preferred because it satisfies the decoupling theorem. The discrepancy can be traced to the use of dimensional regularization in the previous result., Comment: 12 pages, 4 figures

Recently Andr\'e Martin has proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ at high energy which is one-fourth of the known Froissart-Martin-Lukaszuk upper bound on $\sigma_{tot}$. Here we obtain an upper bound on $\sigma_{inel}$ in terms of $\sigma_{tot}$ and show that the Martin bound on $\sigma_{inel}$ is improved significantly with this added information., Comment: 4 pages

Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a function of the momentum is also derived for longer-range power-law potentials which do not fulfill these conditions., Comment: 19 pages, pdflatex, 3 figures, refs. added, typos corrected, to appear in JMP

In the framework of the impact picture we compute the analyzing power $A_N$ for $pp$ elastic scattering at high energy and in the very forward direction. We consider the full set of Coulomb amplitudes and show that the interference between the hadronic non-flip amplitude and the single-flip Coulomb amplitude is sufficient to obtain a good agreement with the present experimental data. This leads us to conclude that the single-flip hadronic amplitude is small in this low momentum transfer region and it strongly suggests that this process can be used as an absolute polarimeter at the BNL-RHIC $pp$ collider., Comment: 6 pages, 6 figures, to appear Physical Review D

For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f(\vec{k}', \vec{k})$. The result is $f=\sqrt{\frac{\pi}{2}}\{1/log k)+O(1/(log k)^2)$. The only exceptions occur if $V$ happens to have a zero energy bound state. Our new result includes as a special subclass the case of rotationally symmetric potentials, $V(|\vec{x}|)$., Comment: 65 pages, Latex, significant changes, new sections and appendices

We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_i's for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation., Comment: Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-84-ER40158

For semisimple groups, possibly multiplied by U(1)'s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for non-semisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical consequences worth studying. The non-semisimple group with only two generators that do not commute is studied in detail., Comment: 16 pages, no figures, prepared with ReVTeX4

If three right-handed neutrinos are added to the Standard Model, then, for the three known generations, there are six quarks and six leptons. It is then natural to assume that the symmetry considerations that have been applied to the quark matrices are also valid for the lepton mass matrices. Under this assumption, the solar and atmospheric neutrino data can be used to determine the individual neutrino masses. Using the \chi^2 fit, it is found that the mass of the lightest neutrino is (2-5)\times10^{-3} eV, that of the next heavier neutrino is (10-13)\times10^{-3} eV, while the mass of the heaviest neutrino is (52-54)\times10^{-3} eV., Comment: 27 pages, LaTeX, including several figures

We present an extension to $\pi^{\pm} p$ and $K^{\pm} p$ elastic scattering at high energies of the impact-picture phenomenology we first proposed more than twenty years ago, for $p p$ and $\bar p p$ elastic scattering. We show, in particular, that the analytic form of the opacity function for the proton obtained previously is compatible with the experimental results on $\pi p$ and $K p$ elastic scattering at high energies. It is proposed that $\pi^{\pm}$ and $K^{\pm}$ external beams be provided from CERN-LHC, so that their elastic scattering from protons can be studied at higher energies. Our phenomenology for $p p$ and $\bar p p$ elastic scattering is updated by including new data and we give predictions for future experiments at BNL-RHIC and CERN-LHC., Comment: 28 pages, 18 eps figures

A model is presented for the quantum memory, the content of which is a pure quantum state. In this model, the fundamental operations of writing on, reading, and resetting the memory are performed through scattering from the memory. The requirement that the quantum memory must remain in a pure state after scattering implies that the scattering is of a special type, and only certain incident waves are admissible. An example, based on the Fermi pseudo-potential in one dimension, is used to demonstrate that the requirements on the scattering process are consistent and can be satisfied. This model is compared with the commonly used model for the quantum memory; the most important difference is that the spatial dimensions and interference play a central role in the present model., Comment: RevTeX4, 7 pages, no figures

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer., Comment: RevTeX4, 32 pages, no figures

We review recent work on analytical solutions to the MSW equations for three neutrino flavours, for exponential and linear potentials. An application to a particular mass matrix is also discussed. The three neutrino masses are determined, respectively, to be 0.001--0.004, and roughly 0.01 and 0.05 eV., Comment: 7 pages, presented at Scandinavian Neutrino Workshop, Uppsala, February 8-10, 2001, to appear in the proceedings, Physica Scripta. Conference info at http://www3.tsl.uu.se/~damet/neutrino/first.html

When the electron density is a linear function of distance, it is known that the MSW equations for two neutrino species can be solved in terms of known functions. It is shown here that more generally, for any number of neutrino species, these MSW equations can be solved exactly in terms of single integrals. While these integrals cannot be expressed in terms of known functions, some of their simple properties are obtained. Application to the solar neutrino problem is briefly discussed., Comment: 14 pages

If three right-handed neutrinos are added to the Standard Model, then, for the three known generations, there are six quarks and six leptons. It is then natural to assume that the symmetry considerations that have been applied to the quark matrices are also valid for the lepton mass matrices. Under this assumption, the solar and atmospheric neutrino data can be used to determine the individual neutrino masses. Three minima have been found, using the chi^2 fit, and, from these minima, it is determined that the mass of the lightest neutrino is 1.3\times10^-3 eV, that of the next heavier neutrino is 1.3\times10^-2 eV, while the mass of the heaviest neutrino is 3.4\times10^-2, 5.8\times10^-2 or 9.4\times10^-2 eV., Comment: 10 pages

Under the assumption that the density variation of the electrons can be approximated by an exponential function, the solar Mikheyev-Smirnov-Wolfenstein effect is treated for three generations of neutrinos. The generalized hypergeometric functions that result from the exact solution of this problem are studied in detail, and a method for their numerical evaluation is presented. This analysis plays a central role in the determination of neutrino masses, not only the differences of their squares, under the assumption of universal quark-lepton mixing., Comment: 22 pages, LaTeX, including 2 figures

We show that the rising total cross section $\sigma(\gamma\gamma \to hadrons)$ recently observed by the L3 and OPAL Collaborations at LEP are fully consistent with the impact-picture for high-energy scattering. The impact picture is then used to predict this total cross section at higher energies. These experimental results confirm once more the success of the theoretical approach, which predicted for the first time, nearly thirty years ago, the universal increase of total cross sections at high energies., Comment: 5 pages, Latex, 1 figure. Revised version

We prove that, in (2+1) dimensions, the S-wave phase shift, $ \delta_0(k)$, k being the c.m. momentum, vanishes as either $\delta_0 \to {c\over \ln (k/m)} or \delta_0 \to O(k^2)$ as $k\to 0$. The constant $c$ is universal and $c=\pi/2$. This result is established first in the framework of the Schr\"odinger equation for a large class of potentials, second for a massive field theory from proved analyticity and unitarity, and, finally, we look at perturbation theory in $\phi_3^4$ and study its relation to our non-perturbative result. The remarkable fact here is that in n-th order the perturbative amplitude diverges like $(\ln k)^n$ as $k\to 0$, while the full amplitude vanishes as $(\ln k)^{-1}$. We show how these two facts can be reconciled., Comment: 23 pages, Latex

We show that the rising total photoproduction cross section recently observed at HERA is entirely consistant with the impact-picture in the theory of expanding protons which was proposed more than twenty years ago. More accurate data, which is expected to be forthcoming soon, will give this prediction a stringent test., Comment: 4 pages, CPT-94/P.3060,LaTex,2 fig available on cpt.univ-mrs.fr directory pub/preprints/94/fundamental-interactions/94-P.3060