Inelastic Sum Rules

The history and present status of several sum rules for deep-inelastic lepton scattering are reviewed, with particular attention to the discovery of scaling, partons, quarks and QCD. Two outstanding issues are then discussed in more detail: the singlet (Ellis-Jaffe) nucleon spin sum rule and the Drell-Hearn-Gerasimov-Iddings sum rule

The Shifted Coupled Cluster Method: A New Approach to Hamiltonian Lattice Gauge Theories

It is shown how to adapt the non-perturbative coupled cluster method of many-body theory so that it may be successfully applied to Hamiltonian lattice $SU(N)$ gauge theories. The procedure involves first writing the wavefunctions for the vacuum and excited states in terms of linked clusters of gauge invariant excitations of the strong coupling vacuum. The fundamental approximation scheme then consists of i) a truncation of the infinite set of clusters in the wavefunctions according to their geometric {\em size}, with all larger clusters appearing in the Schr\"odinger equations simply discarded, ii) an expansion of the truncated wavefunctions in terms of the remaining clusters rearranged, or ``shifted'', to describe gauge invariant {\em fluctuations} about their vacuum expectation values. The resulting non-linear truncated Schr\"odinger equations are then solved self-consistently and exactly. Results are presented for the case of $SU(2)$ in $d=3$ space-time dimensions.Comment: 13 pages + 5 postscript figures, plain Late

Cancellation of the Chiral Anomaly in a Model with Spontaneous Symmetry Breaking

A perturbatively renormalized Abelian Higgs-Kibble model with a chirally coupled fermion is considered. The Slavnov identity is fulfilled to all orders of perturbation theory, which is crucial for renormalizability in models with vector bosons. BRS invariance, i.e. the validity of the identity, forces the chiral anomaly to be cancelled by Wess-Zumino counterterms. This procedure preserves the renormalizability in the one-loop approximation but it violates the Froissart bounds for partial wave amplitudes above some energy and destroys renormalizability from the second order in h bar onwards due to the counterterms. (The paper has 3 figs. in postscript which are not included; send request to the author's e-mailbox with subject: figures . The author is willing to mail hard copies of the paper.)Comment: 13 pages, plain TeX, SI 92-1

Behavioural susceptibility theory: the role of appetite in genetic susceptibility to obesity in early life

Excess weight gained during the early years and, in particular, rapid weight gain in the first 2 years of life, are a major risk factors for adult obesity. The growing consensus is that childhood obesity develops from a complex interaction between genetic susceptibility and exposure to an ‘obesogenic’ environment. Behavioural susceptibility theory (BST) was developed to explain the nature of this gene–environment interaction, and why the ‘obesogenic’ environment does not affect all children equally. It hypothesizes that inherited variation in appetite, which is present from birth, determines why some infants and children overeat, and others do not, in response to environmental opportunity. That is, those who inherit genetic variants promoting an avid appetite are vulnerable to overeating and developing obesity, while those who are genetically predisposed to have a smaller appetite and lower interest in food are protected from obesity—or even at risk of being underweight. We review the breadth of research to-date that has contributed to the evidence base for BST, focusing on early life, and discuss implications and future directions for research and theory

Cut Vertices and Semi-Inclusive Deep Inelastic Processes

Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic processes in the target fragmentation region is explicitly constructed. The problem of factorization is discussed in detail.Comment: LaTex2e, 24 pages including 17 postscript figure

Analytic Estimates of the QCD Corrections to Neutrino-Nucleus Scattering

We study the QCD corrections to neutrino deep-inelastic scattering on a nucleus, and analytically estimate their size. For an isoscalar target, we show that the dominant QCD corrections to the ratio of the neutral- to charged-current events are suppressed by sin^4 theta_W, where theta_W is the weak mixing angle. We then discuss the implications for the NuTeV determination of sin^2 theta_W.Comment: 16 pages, Late

The Coupled Cluster Method in Hamiltonian Lattice Field Theory

The coupled cluster or exp S form of the eigenvalue problem for lattice Hamiltonian QCD (without quarks) is investigated. A new construction prescription is given for the calculation of the relevant coupled cluster matrix elements with respect to an orthogonal and independent loop space basis. The method avoids the explicit introduction of gauge group coupling coefficients by mapping the eigenvalue problem onto a suitable set of character functions, which allows a simplified procedure. Using appropriate group theoretical methods, we show that it is possible to set up the eigenvalue problem for eigenstates having arbitrary lattice momentum and lattice angular momentum.Comment: LaTeX, no figur

Positivity constraints for lepton polarization in neutrino deep inelastic scattering

We consider the spin polarization of leptons produced in neutrino and antineutrino nucleon deep inelastic scattering, via charged currents, and we study the positivity constraints on the spin components in a model independent way. These results are very important, in particular in the case of $\tau^{\pm}$ leptons, because the polarization information is crucial in all future neutrino oscillation experiments.Comment: 14 pages, 4 figure

The Coupled Cluster Method in Hamiltonian Lattice Field Theory: SU(2) Glueballs

The glueball spectrum within the Hamiltonian formulation of lattice gauge theory (without fermions) is calculated for the gauge group SU(2) and for two spatial dimensions. The Hilbert space of gauge-invariant functions of the gauge field is generated by its parallel-transporters on closed paths along the links of the spatial lattice. The coupled cluster method is used to determine the spectrum of the Kogut-Susskind Hamiltonian in a truncated basis. The quality of the description is studied by computing results from various truncations, lattice regularisations and with an improved Hamiltonian. We find consistency for the mass ratio predictions within a scaling region where we obtain good agreement with standard lattice Monte Carlo results.Comment: 13 pages, 7 figure

On a class of embeddings of massive Yang-Mills theory

A power-counting renormalizable model into which massive Yang-Mills theory is embedded is analyzed. The model is invariant under a nilpotent BRST differential s. The physical observables of the embedding theory, defined by the cohomology classes of s in the Faddeev-Popov neutral sector, are given by local gauge-invariant quantities constructed only from the field strength and its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the journa