arXiv subjects

Judith A. McGovern

Publications and source records attributed to Judith A. McGovern.

44 records · Page 3Linked to original sources

arXiv1999

A renormalisation-group treatment of two-body scattering

Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the linearised renormalisation group are used to assign a systematic power-counting to terms in the potential near each of these fixed points. The expansion around the nontrivial fixed point is shown to be equivalent to the effective-range expansion.

hep-ph↗

arXiv1998

On the absence of fifth-order contributions to the nucleon mass in heavy-baryon chiral perturbation theory

(New version with some expanded discussion; figures and minor typos corrected.) We have calculated the contribution proportional to the fifth power of the pion mass in the chiral expansion of the nucleon mass in two flavour HBCPT. Only one irreducible two-loop integral enters, and this vanishes. All other corrections in the heavy-baryon limit can be absorbed in the physical pion-nucleon coupling constant which enters in the third order term, and so there are no contributions at fifth order. Including finite nucleon mass corrections, the only contribution agrees with the expansion of the relativistic one-loop graph in powers of the ration of the pion and nucleon masses, and is only 0.3% of the third order term. This is an encouraging result for the convergence of two-flavour heavy-baryon chiral perturbation theory.

hep-ph↗

arXiv1998

The Wilson Renormalisation Group Applied to the Potential in NN Scattering

Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the linearised renormalisation group are used to assign a systematic power-counting to terms in the potential near each of these fixed points. The expansion around the nontrivial fixed point defines a power counting scheme which is equivalent to the effective-range expansion.

hep-ph↗

arXiv1997

A self-consistent approach to the Wigner-Seitz treatment of soliton matter

We propose a self-consistant approach to the treatment of nuclear matter as a crystal of solitons in the Wigner-Seitz approximation. Specifically, we use a Bloch-like boundary condition on the quarks at the edge of a spherical cell which allows the dispersion relation for a given radius to be calculated self-consistently along with the meson fields; in previous work some ansatz for the dispersion relation has always been an input. Results in all models are very sensitive to the form of the dispersion relation, so our approach represents a significant advance. We apply the method to both the Friedberg Lee model and the chiral quark-meson model of Birse and Banerjee. Only the latter shows short range repulsion; in the former the transition to a quark plasma occurs at unrealistically low densities.

nucl-th↗

arXiv1997

Renormalisation and power counting in effective field theories for nucleon-nucleon scattering

The renormalisation of NN scattering in theories with zero-range interactions is examined using a cut-off regularisation and taking the cut-off to infinity. Inclusion of contact interactions that depend on energy as well as momentum allows the effective range to be fitted to experiment with any desired sign or magnitude. However, power counting breaks down: terms of different orders in the potential can contribute to the scattering amplitude at the same order.

hep-ph↗

arXiv1997

Relations Among Correlation Functions in the High Temperature Phase of QCD with Broken SU(3)

Group-theoretic arguments are used to determine the dependence of two-point correlators of quark bilinears on the current quark masses. The leading difference between $π$ and $δ$ correlators is found to be of order $m_s$ times a U(1)$_{\scriptscriptstyle A}$-violating correlator. These general arguments are consistent with Schaefer's observation that if U(1)$_{\scriptscriptstyle A}$ violation persists to high enough temperatures then the strange $η$ can be lighter than the non-strange one.

hep-ph↗

arXiv1996

U(1) Axial Symmetry and Correlation Functions in the High Temperature Phase of QCD

Simple group-theoretical arguments are used to demonstrated that in the high temperature (chirally restored) phase of QCD with N massless flavours, all n-point correlation functions of quark bilinears are invariant under U(1) axial transformations provided n < N. In particular this implies that the two-point correlation function in the eta' channel is identical to that in the pion channel for N > 2. Unlike previous work, this result does not depend on the topological properties of QCD and can be formulated without explicit reference to functional integrals.

hep-ph↗

arXiv1995

Magnetic Moments of the Octet Baryons in the Colour-Dielectric Model

Baryon magnetic moments are calculated in the colour-dielectric model with pion and kaon loops. The only free parameter of the model is determined from the nucleon isoscalar radius, and all SU(3) symmetry breaking, including that in the quark sector, is determined by mesonic masses and decay constants. Good agreement with experiment is obtained for the ratios of the magnetic moments, but the inclusion of kaons does not improve the results. The results obtained in this approach are significantly better than any that have been obtained in hedgehog-based models.

hep-ph↗