Tsou Sheung Tsun

Diffractive scattering in the dual model

Abstract A method is suggested for calculating the elastic amplitude as the shadow of multiparticle processes. This does not require explicit formulae for the production amplitudes, but depends only on the following assumptions: (a) Regge behaviour, (b) semi-local duality, (c) exchange degeneracy. The system is multiperipheral in general structure but because of the assumption (a)-(c), it incorporates such features as the clustering of final particles and provides a proper treatment of quantum numbers, phases, and resonance spins. As a result, the unitarity sum separates automatically into two components corresponding respectively to pomeron and ordinary reggeon exchange, each of which is seen to have the correct qualitative dependence on the quantum numbers, the energy s , and the momentum transfer t . Quantitatively, the elastic amplitude is given in terms of a triple-Regge vertex, for which we suggest a simple parametization based on a detailed study of existing experiment and the Veneziano model. The method is then applied to calculate the elastic amplitudes for π ± p, K ± p and pp within the range 6 s t > −0.5 GeV 2 . Semi-quantitative agreement is obtained with experiment with essentially no free parameter. Although the investigation is restricted at present to elastic scattering as the shadow of only the non-diffractive component satisfying (a)-(c), the method is believed to apply also to other diffractive processes, and may be regarded as the first step in an iterative solution of the full unitarity equation.

Regge parameters from duality and unitarity

From s-channel unitarity, two coupled integral equations are derived for the reggeon and pomeron propagators using a method developed in an earlier work. The first (R) is a consistency equation constraining the reggeon parameters, while the second (P) gives the pomeron trajectory in terms of the solutions of the first. Starting then from the empirical information on the reggeon intercept (αR∼0.5) and the t-dependence of the triple-reggeon vertex obtained in inclusive reactions, one is able to calculate the strength of reggeon couplings g and the parameters of the pomeron by solving these equations. Two approximate solutions are given, one asymptotically and one at finite energies. The first gives g = 8.6, αP(0) = 1.12 and α′P(0) = 0.1 GeV−2 while the second gives g = 7.0, αP(0) = 0.95 and α′P(0) = 0.5 GeV−2. These are to be compared with the empirical values g∼6.3, αP(0)∼1.0 and α′P(0)∼0.25 GeV−2. In addition, one predicts the relative normalisation of the pomeron and reggeon propagators at t = 0 to be PR = 1.0 which is quite close to the values between 0.9 and 1.2 obtained from phenomenological fits to σT. The pomeron pole is generated here as the shadow of amplitudes which are dominated by the multiperipheral production of resonant clusters. A crude estimate with our solution yields at NAL-ISR energies an average charge multiplicity of about 2.3 per cluster as compared with the value of 2.2±0.2 obtained from a recent experiment.

Half-string oscillator approach to string field theory

Abstract We give an operator formulation of the string field theory proposed by E. Witten using half-string oscillator modes. This formalism, identifying the physical string states as infinite matrices, is developed in such a way that interactions at the level of vertices can be calculated in terms of products and traces of these matrices without relying on ill-defined manipulations of functional integrals.

't Hooft's order-disorder parameters and the dual potential

It is shown that the operator B(C) = Tr[P exp ig̃ ∮ Ãi(x)dx ] constructed with the recently derived dual potential Ã(x) and a coupling g̃ related to g by the Dirac quantization condition satisfies the correct commutation relation with the Wilson operator Tr[P exp ig ∮ Ai(x)dx ] as required by ’t Hooft for his order-disorder parameters. chanhm@v2.rl.ac.uk tsou @maths.ox.ac.uk In his study of the confinement problem in nonabelian gauge theories, ’t Hooft introduced 2 loop-dependent operators A(C) and B(C) with the following commutation relations: [1] A(C)B(C ′) = B(C ′)A(C) exp(2πin/N) (1) for su(N) gauge symmetry, and any two spatial loops C and C ′ with linking number n between them. A(C) was explicitly given as: A(C) = Tr [

Circumstantial evidence for rotating mass matrix from fermion mass and mixing data

Abstract. It is shown that existing data on the mixing between up and down fermion states and on the hierarchical mass ratios between fermion generations, as far as can be so analyzed at present, are all consistent with the two phenomena being both consequences of a mass matrix rotating in generation space with changing energy scale. As a result, the rotating mass matrix can be traced over some 14 orders of magnitude in energy from the mass scale of the t quark at 175 GeV to below that of the atmospheric neutrino at 0.05 eV.

On loop space formulation of gauge theories

Abstract In attempting to formulate gauge theories entirely in terms of loop variables, it is found convenient to work in the function space of parametrised loops with the loop space connection F μ (C¦s) as field variables. Equivalence to the conventional formulation in terms of the gauge potential Aμ(x) is ensured by imposing on F μ (C¦s) certain conditions implying the local absence of “magnetic sources” or monopoles. These conditions are reminiscent of the Poincare lemma in electromagnetism, and establish a one-one correspondence between F μ (C¦s) so constrained and Aμ(x) up to gauge equivalence. We use this approach to reformulate the action principle for pure gauge theories and to derive field equations from it completely in terms of loop variables. We believe that the formalism is useful in the theory of monopoles and may also find application in lattice calculations.

Neutrino oscillations in the dualized standard model

A method developed from the dualized standard model for calculating the quark CKM matrix and masses is applied to the parallel problem in neutrino oscillations. Taking the parameters determined from quarks and the masses of two neutrinos:

Monopoles in Superloop Space

{m}_{3}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}2}\char21{}{10}^{\ensuremath{-}3} {\mathrm{eV}}^{2}

Flavor changing neutral currents in the dualized standard model

suggested by atmospheric neutrino data and

Polyakov Loops for the ABJ Theory

{m}_{2}^{2}\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{eV}}^{2}