Michael C. Birse

A nonlocal, covariant generalisation of the NJL model

Abstract We solve a nonlocal generalisation of the NJL model in the Hartree approximation. This model has a separable interaction, as suggested by instanton models of the QCD vacuum. The choice of form factor in this interaction is motivated by the confining nature of the vacuum. A conserved axial current is constructed in the chiral limit of the model and the pion properties are shown to satisfy the Gell-Mann-Oakes-Renner relation. For reasonable values of the parameters the model exhibits quark confinement.

Soliton models for nuclear physics

Abstract Nontopological soliton models have been successfully used to incorporate the quark structure of hadrons into nuclear physics. These are phenomenological field theories which can be motivated from QCD, but are simple enough to permit calculations of nucleon structure and interactions. Three types of model are covered here: soliton bag models, chiral quark-meson models, and colour dielectric models. All involve quarks interacting with various phenomenological boson fields. The forms of their mean-field solutions (solitons) are presented. Arguments relating the models to QCD are outlined. For quark-meson models these go via intermediate NJL-type models. These suggest that that the nonlocalities of the effective action may be well described by the valence quarks alone; the effect of the Dirac sea is to generate kinetic and potential energies for the mesons. Unlike the Skyrme model, the quark-meson models have explicit quark degrees-of-freedom. Their quantisation is thus not restricted to 1/ N c expansions, and they can retain the nonlocal nature of the effective action. A colour-dielectric field can be obtained by a block-spinning approach to QCD. This can give absolute confinement provided the dielectric field vanishes in the vacuum. Dynamical calculations in these models are described, many of which are based on the use of coherent states to provide quantum states corresponding to these solitons. These calculations include recoil corrections, derivation of an effective wave equation for a composite nucleon, and calculations of NN scattering. In models with strong pion fields states of good spin and isospin are constructed from hedgehog solitons. Excited states can be treated with an extension of the random-phase approximation. This is applied to breathing-mode excitations, as well as to strange baryons. A possible way to treat nuclear matter in these models is outlined.

Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory

We calculate the amplitude T1 for forward doubly virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the

Power counting with one-pion exchange

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Meson properties in an extended non-local NJL model

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Chiral symmetry in nuclei: Partial restoration and its consequences

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Spin polarisabilities of the nucleon at NLO in the chiral expansion

form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions of the Born and structure parts of the amplitude. Our result leaves no room for any effect large enough to explain the discrepancy between proton charge radii as determined from muonic and normal hydrogen.

A Renormalization group approach to two-body scattering in the presence of long range forces

Techniques developed for handing inverse-power-law potentials in atomic physics are applied to the tensor one-pion exchange potential to determine the regions in which it can be treated perturbatively. In

Effective theories of scattering with an attractive inverse-square potential and the three-body problem

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ABSENCE OF FIFTH-ORDER CONTRIBUTIONS TO THE NUCLEON MASS IN HEAVY-BARYON CHIRAL PERTURBATION THEORY

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