Deep inelastic lepton-hadron scattering in massive vector gauge models

A class of strong interaction models in which the interactions between fractionally charged colored quarks are mediated by massive neutral vector gluons is considered. All the vector gluons acquire masses via the usual Higgs mechanism. The effective coupling constants $\text{g}$ (gauge coupling) and $\text{h}$ (quartic self-coupling) are supposed to approach a limit cycle in the limit of large space-like momenta. The large Q² behavior of the moments of the deep inelastic lepton-hadron structure functions is analysed using this hypothesis. It is shown that Bjorken scaling is violated by power terms of Q² multiplied by an oscillating function of Q².     

Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.     

Regularisation of theP→γγ vertex in the vector meson dominance model

The problem of the PCAC anomaly in the decaysP→γγ (P≡ pseudoscalar meson) is essentially one of regularisation. The constraints deriving there-from, together with similar ones from gauge invariance, typical of a spin 1/2 field theory, are used to define a vector meson dominance approximation for the corresponding amplitudes. The approximation is in this sense dual to the quark model and does indeed reconstruct the high energy quark model behaviour of the amplitudes in the Bjorken-Johnson-Low (BJL) limit. There are interesting new relations for vector meson (V) coupling constants in the decaysV→Pγ and for the PCAC anomaly itself.     

Analysis of the electroproduction structure functions in the lowQ 2 region,combining the vector meson dominance and the parton model with possible scaling violation

The nucleon structure functionF ₂ is constructed and analysed for low values ofQ ² using the generalised vector meson dominance representation with the largeQ ² spectral function calculated from the analytic continuation of the parton model structure function. Various parametrisations of the parton distributions are considered. Possible effects of the largeQ ² scaling violation on the lowQ ² part of the structure function are investigated. The magnitude of the total contribution given by this asymptotic part can be as high as 50% of the vector meson contribution in the low-Q ², low-χ region. The contribution of the valence quarks alone to the structure function at lowQ ² turns out to be at least as important as the corresponding non-Pomeron Regge-pole-like terms coming from the vector meson part. Increase of the structure function with ν coming from the increase of the quark sea in the limit of small χ implied by QCD turns out to be relatively weak at lowQ ². Predictions of the model are compared with available experimental data. The photoproduction cross section and the nuclear effects in the structure function are also briefly discussed.     

Neutrino mass effect on the nuclear muon capture

Multipole expansion of the partial transition amplitude in the nuclear muon capture with massive lefthanded Dirac neutrino has been derived. The multipole amplitudes for the partial nuclear transitions are given as the explicit functions of the neutrino mass parameter. As an example, the capture rate, the recoil asymmetry and the neutrino polarization are investigated in terms of these multipole amplitudes. The transversal neutrino polarization provides a connection between theT-violation and the neutrino mass: ifT-odd component in the neutrino polarization is observed, then neutrino must be a massive particle. It turns out that in the capture rate and recoil polarization, the effects due to very small neutrino mass can be proportional to the square ratio of the neutrino mass to its momentum, while the neutrino transversal polarization is proportional to this ratio only. Under the recent limits on the muon neutrino mass, the observable effects inthe partial transition may be below the order of ?10^?3.     

String theory beyond the Planck scale

The high-energy behavior of string scattering amplitudes is studied to all orders in perturbation theory, with the aim of exploring the short-distance structure of string theory. It is shown that the sum over all Riemann surfaces is dominated by a saddle point. Consequently, the high-energy limit is universal and simple to calculate. In this limit, furthermore, the amplitudes fall off in a stringy way - much faster than that allowed by field theory. The dominant saddle points are identified as coming from world sheets which are Z_G+1 symmetric algebraic curves, and their contribution to the scattering amplitude is evaluated. An interesting spacetime picture of the high-energy limit emerges. The issue of summing the perturbation expansion is addressed.     

Soft gluon corrections to large-pT direct photon and dilepton production

QCD O(α_s²) corrections to large-p_T real and virtual photon production from scattering in the quark-gluon channel are studied in the soft gluon limit. In this limit we carefully preserve the analytic structure of amplitudes in the small-momenta integration regions. The result is a rather large correction to the Born term which significantly improves the agreement with data on p + p → γ + X. The application of the approach to other processes is discussed and the dominant terms of the O(α_s²) correction to e⁺e^? → three jets are reproduced.     

On the low-energy limit of one-loop photon–graviton amplitudes

We present first results of a systematic study of the structure of the low-energy limit of the one-loop photon–graviton amplitudes induced by massive scalars and spinors. Our main objective is the search of KLT-type relations where effectively two photons merge into a graviton. We find such a relation at the graviton–photon–photon level. We also derive the diffeomorphism Ward identity for the 1PI one-graviton–N-photon amplitudes.     

Scaling limit of the one-dimensional attractive Hubbard model: the non-half-filled band case

The scaling limit of the less than half-filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0 < n < 1) while adjusting the interaction and bandwidth in such a way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find that similarly to the half-filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half-filled band and consequently to the chiral invariant SU(2) Gross-Neveu (CGN) model. The structure of the massless sector differs from that of the half-filled band case: the excitations are of particle and hole type, however they are not uniquely defined. The energy and the momentum of this sector exhibits a tower structure corresponding to a conformal field theory with c = 1 and SU(2) × SU(2) symmetry. The energy-momentum spectrum and the zero temperature free energy of the states with finite density coincides with that of the half-filled case supporting the identification of the limiting model with the SU(2) symmetric CGN theory.     

Electroweak tri-boson couplings at LEP II and beyond

Possible non-standard model couplings of electroweak vector bosons are studied inW pair production ine ⁺ e ^? collisions. Helicity amplitudes are calculated in a factorized formalism; the choice of helicity basis suggested by this formalism is shown to increase sensitivity of angular correlations to anomalous couplings. In the course of this analysis, the chi-squared test for finite data samples is more carefully formulated. BothCP-conserving andCP-violating couplings are considered.     

Shackless on linear absorption models

We examine the fundamental constraints that all Linear Absorption Models must possess, independent of the rescattering amplitude. These constraints are most direct in impact parameter space, where the re-scattering appears simply as a multiplicative factor. It is a crucial test of such models that the ratio of two exchanges — for example vector and tensor exchanges — is completely specified in b-space by the ratio of input Regge pole amplitudes. Amplitude analysis exist for vector π exchange, in π⁻p→π^On. Lacking experimental A₂ tensor amplitudes, we use the Linear Absorption Models constraint to calculate A₂ exchange from ? input, and compare the results with π⁻p→η^On data. Both simplicity and duality assumptions for Regge pole couplings are considered. The results suggest that Linear Absorption Models constraint is not fully consistent with data.     

Polarization amplitudes fore + e − →W + W − ande + e − →ZZ

The main purpose of this work is to study the three weak boson vertex. We give explicit formulae for all polarization amplitudes of the processese ⁺ e ^? →W ⁺ W ^? ande ⁺ e ^? →ZZ, with arbitrary couplings between the various intermediate vector bosons. Using these expressions we discuss possible signatures ofC, P andT violation in the three vector boson coupling, as well as the effects of anomalous magnetic dipole and electric quadrupole moments ofW ^±. The amplitudes for the above processes in any SU(2) × U(1) and SU(2)_L × SU(2)_R × U(1) gauge theory are also given, while the special case of the Weinberg-Salam model is studied in detail.     

Regge analysis and dual absorptive model for γN → πN, γN → ηN and related processes

We present a combined Regge-pole Regge-cut analysis of γN → π^oN, γN → ηN and of certain processes related by vector dominance. The magnitude of Regge cuts is constrained to satisfy the requirements of the dual absorptive model. Calculations in terms of the weak cut model are also presented and ways to experimentally distinguish between these two models are discussed. The structure of the real and imaginary parts of the amplitudes is also analyzed.     

On W±, Z0, γ self-interactions: High energy behaviour and tree unitarity bounds

We analyze the high-energy behaviour of vector boson scattering amplitudes within the framework of a recently suggested lagrangian model based on global weak isospin symmetry broken by electromagnetism. Requiring vanishing of the most strongly (as s²) rising contribution to vector boson scattering amplitudes leads to vector boson self-interactions dependent on a single parameter, for which the anomalous W^± magnetic moment, κ, can be chosen. Tree unitarity is violated at about 2 TeV for arbitrary κ as in the SU(2)_L × U(1)_Y theory for m_H → ∞. The model is well suited for significant tests of the vector boson sector of the SU(2)_L × U(1)_Y electroweak theory in processes such as e⁺e⁻ → W⁺W⁻.     

Vector boson pair production in e−e− collisions with polarized beams

The W-boson pair production in e⁻e⁻ collisions with polarized beams is investigated. The helicity amplitudes are derived for general couplings and the conditions for a good high-energy behaviour of the cross-section are given. The results are applied to the heavy vector boson production in the context of the left-right symmetric model. The Ward identities and the equivalence theorem are also discussed.     

Time-reversal invariance-like relations for spin-effects in elastic and inelastic reactions; vector-meson photoproduction versus compton scattering from nucleons

For elastic scattering, relations between spin-effects (for example, the well-known asymmetry-polarization equality) follow from time-reversal invariance. We show that if certain amplitude combinations vanish, there are strikingly similar relations between spin-effects for elastic and also inelastic reactions. This vanishing of amplitude combinations (denoted M-purity) corresponds asymptotically to purely natural or purely unnatural parity in the crossed channel. The M-purity relations hold for spin-configurations much more general than do the corresponding time-reversal invariance relations.The experimental evidence for purely natural parity exchanges in high energy vector meson photoproduction from nucleons is shown to be good for all amplitudes involving nonzero meson helicity, but less conclusive for the zero helicity ones. Using time-reversal invariance and a vector meson-dominance argument, this implies no unnatural parity contributions in high energy Compton scattering from nucleons.Because of this empirical evidence for M-purity in these two processes, a detailed application to spin-effects in Compton scattering and in vector meson photoproduction is made. Some time-reversal invariance relations in Compton scattering resemble the corresponding M-purity relations though the applicability of the two is different, and there are examples where only one of the two exists. Out of our illustrations, the only M-purity relations which change in form due to the extra amplitudes present in the inelastic reaction are the M-purity analogue and extensions of the asymmetry-polarization equality (of Compton scattering) referring to the photon; the change is the appearance of the elements ?⁰⁰ of the vector meson density-matrix ?. Our other examples of M-purity relations do not change in form in going over from the elastic reaction (Compton scattering) to the inelastic reaction (vector meson photoproduction).     

Vector meson production by inelastic scattering of polarized electrons off polarized nucleons

A general analysis of vector meson production by inelastic scattering of polarized electrons (or muons) off polarized nucleons is presented. Cross section and vector meson decay angular distribution are discussed in terms of s-channel helicity amplitudes for natural and unnatural parity exchange. The question of experiments suitable for analyzing the more refined dynamical features of ?⁰-production is discussed in detail. Estimates are given for the effects to be expected from unnatural parity exchange.     

Comparing the p̅p → K − K + and p̅p → π−π+ reactions

A partial wave amplitude analysis of LEAR data on differential cross sections and analyzing powers of p?p → K ^? K ⁺ has been performed in the range p _lab = 360 ? 1000 MeV/c, and compared to the results from the same observables for p?p → π^?π⁺. Contrary to other analyses we see no compelling evidence of resonance behavior in our amplitudes. However, as we discuss, the resulting amplitudes are not unique since a third observable remains to be measured for both reactions. Another remarkable result is that for p?p → K ^? K ⁺ all our solutions in the momentum interval below 900 MeV/c, only partial wave amplitudes including J _max = 2 are necessary. This upper limit on the angular momentum is smaller than J _max = 3 which is required for the data of the reaction p?p → π^?π⁺ in the same momentum interval. This finding is consistent with a model analysis for data above 1 GeV/c. Annihilation models with short range baryon exchange give too small J ≥ 2 amplitudes and final state ππ and K?K interactions are presumably very important.     

Singlet $$\tilde V$$ correlator within the instanton vacuum model

The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of the QCD vacuum. In the chiral limit, we calculate the longitudinal w _L ⁽⁰⁾ and transversal w _T ⁽⁰⁾ , with respect to the axial-vector index, invariant amplitudes at an arbitrary spacelike momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U _A (1) anomaly.