arXiv subjects

Michael C. Birse

Publications and source records attributed to Michael C. Birse.

At least 73 records · Page 4Linked to original sources

arXiv1997

Meson properties in an extended nonlocal NJL model

We consider a nonlocal version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes gamma gamma^* to pi^0 and omega to pi^0 gamma^*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.

hep-ph↗

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

Disoriented chiral condensate formation from tubes of hot quark plasma

We investigate the time evolution of a system of quarks interacting with sigma and pion fields starting from an initial configuration consisting of a tube of hot quark plasma undergoing a boost-invariant longitudinal expansion. We work within the framework of the linear sigma model using classical transport equations for the quarks coupled to the mean-field equations for the meson fields. In certain cases we find strong amplifications of any initial pion fields. For large-radius tubes, starting from quark densities that are very close to critical, we find that a disoriented chiral condensate can form in the centre of the tube. Eventually the collapse of the tube drives this state back to the true vacuum. This process converts the disoriented condensate, dominated by long-wavelength pion modes, into a coherent excitation of the pion field that includes significant components with transverse momenta of around 400 MeV. In contrast, for narrow tubes or larger initial temperatures, amplification occurs only via the pion-laser-like mechanism found previously for spherical systems. In addition, we find that explicit chiral symmetry breaking significantly suppresses the formation of disoriented condensates.

hep-ph↗

arXiv1997

QCD Sum Rules for the Isospin-Breaking Axial Correlator with Correct Chiral Behavior

We revisit the QCD sum-rule treatment of the isospin-breaking axial correlator in light of the recent claim that a previous treatment produced results incompatible with known chiral constraints. The source of the error in the previous analysis is identified, and a corrected version of the sum-rule treatment obtained. It is then shown that, using input from chiral perturbation theory, one may use the resulting sum rule to extract information on the leading chiral behavior of isospin-breaking parameters associated with the coupling of excited pseudoscalar resonances to the axial currents. A rather accurate extraction is possible for the case of the eta'. Demanding stability of the sum-rule analysis also allows us to improve the upper bound on the fourth-order low-energy constant, L_7.

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

Coherent amplification of classical pion fields during the cooling of droplets of quark plasma

In the framework of the linear sigma model, we study the time evolution of a system of classical $σ$ and pion fields coupled to quarks. For this purpose we solve numerically the classical transport equation for relativistic quarks coupled to the nonlinear Klein-Gordon equations for the meson fields. We examine evolution starting from variety of initial conditions corresponding to spherical droplets of hot quark matter, which might mimic the behaviour of a quark plasma produced in high-energy nucleus-nucleus collisions. For large droplets we find a strong amplification of the pion field that oscillates in time. This leads to a coherent production of pions with a particular isospin and so would have similar observable effects to a disoriented chiral condensate which various authors have suggested might be a signal of the chiral phase transition. The mechanism for amplification of the pion field found here does not rely on this phase transition and is better thought of as a "pion laser" which is driven by large oscillations of the $σ$ field.

hep-ph↗

arXiv1996

Determination of pion-baryon coupling constants from QCD sum rules

We evaluate the pi-N-N, pi-Sigma-Sigma and pi-Sigma-Lambda coupling constants using QCD sum rules based on pion-to-vacuum matrix elements of correlators of two interpolating baryon fields. The parts of the correlators with Dirac structure k-slash gamma_5 are used, keeping all terms up to dimension 5 in the OPE and including continuum contributions on the phenomenological side. The ratios of these sum rules to baryon mass sum rules yield stable results with values for the couplings of g_{pi NN}=12+/-5, g_{pi Sigma Sigma}=7+/-4 and g_{pi Sigma Lambda}=6+/-3. The sources of uncertainty are discussed.

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↗

arXiv1996

Comment on ``Relativistic kinetic equations for electromagnetic, scalar and pseudoscalar interactions''

It is found that the extra quantum constraints to the spinor components of the equal-time Wigner function given in a recent paper by Zhuang and Heinz should vanish identically. We point out here the origin of the error and give an interpretation of the result. However, the principal idea of obtaining a complete equal-time transport theory by energy averaging the covariant theory remains valid. The classical transport equation for the spin density is also found to be incorrect. We give here the correct form of that equation and discuss briefly its structure.

hep-ph↗

arXiv1996

Chiral symmetry and QCD sum rules for the nucleon mass in matter

The quark condensate in nuclear matter contains a term of order $ρm_π$, arising from the contribution of low-momentum virtual pions to the $πN$ sigma commutator. Standard treatments of QCD sum rules for a nucleon in matter generate a similar term in the nucleon effective mass, although this is inconsistent with chiral perturbation theory. We show how an improved treatment of pionic contributions on the phenomenological side of the sum rules can cancel out this unwanted piece. Our results also show that factorisation ansatz for the four-quark condensate cannot be valid in matter.

hep-ph↗

arXiv1996

What does a change in the quark condensate say about restoration of chiral symmetry in matter?

The contribution of nucleons to the quark condensate in nuclear matter includes a piece of first order in $m_π$, arising from the contribution of low-momentum virtual pions to the $πN$ sigma commutator. Chiral symmetry requires that no term of this order appears in the $NN$ interaction. The mass of a nucleon in matter thus cannot depend in any simple way on the quark condensate alone. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.

hep-ph↗

arXiv1996

Effective chiral Lagrangians for spin-1 mesons

The commonly used types of effective theory for vector mesons are reviewed and their relationships clarified. They are shown to correspond to different choices of field for spin-1 particles and the rules for transforming between them are described. The importance of respecting chiral symmetry is stressed. The choice of fields that transform homogeneously under the nonlinear realisation of chiral symmetry imposes no preconceptions about the types of coupling for the mesons. This representation thus provides a convenient framework for relating different theories. It is also used to elucidate the nature of the assumptions in specific hidden-gauge and massive Yang-Mills models that have been widely used.

hep-ph↗

arXiv1996

Baryon masses in a chiral expansion with meson-baryon form factors

The chiral expansion of the one-loop corrections to baryon masses is examined in a generic meson-cloud model with meson-baryon form factors. For pion loops, the expansion is rapidly convergent and at fourth order in $m_π$ accurately reproduces the full integral. In contrast, the expansion is found to converge very slowly for kaon loops, raising questions about the usefulness of chiral expansions for kaon-baryon physics. Despite the importance of high-order terms, relations like that of Gell-Mann and Okubo are well satisfied by the baryon masses calculated with the full integral. The pion cloud cloud makes a significant contribution to the $πN$ sigma commutator, while kaon cloud gives a very small strangeness content in the nucleon.

hep-ph↗

arXiv1996

Chiral symmetry in nuclei

The role of the quark condensate in low-energy QCD and its behaviour in nuclear matter are discussed. Partial restoration of chiral symmetry, as indicated by a reduction of the quark condensate in matter, could significantly alter the properties of nucleons and mesons. Various signals of these effects are discussed: enhancement of the axial charge of a nucleon, lepton pair production and $\overline K$-nucleus attraction. (Talk presented at the Nuclear Physics Study Weekend on Extreme States of Nuclei, Abingdon, October 1995)

nucl-th↗

arXiv1996

Determination of the pion-nucleon coupling constant from QCD sum rules

We evaluate the $πN$ coupling constant using a QCD sum rule based on the pion-to-vacuum matrix element of the correlator of two interpolating nucleon fields. The part of the correlator with Dirac structure $k\llap/γ_5$ is used, keeping all terms up to dimension 5 in the OPE and including continuum contributions on the phenomenological side. The ratio of this sum rule to the nucleon sum rule involving condensates of odd dimension yields stable results with values of $g_{πN}$ in the range $12\pm 5$. The sources of uncertainty are discussed.

hep-ph↗

arXiv1995

$ρ\to 4π$ in chirally symmetric models

The decays $ρ^0\to 2π^+2π^-$ and $ρ^0\to 2π^0π^+π^-$ are studied using various effective Lagrangians for $π$ and $ρ$ (and in some cases $a_1$) mesons, all of which respect the approximate chiral symmetry of the strong interaction. Partial widths of the order of 1 keV or less are found in all cases. These are an order of magnitude smaller than recent predictions based on non-chiral models.

hep-ph↗

arXiv1995

Interpolating fields for spin-1 mesons

Three commonly used types of effective theories for vector mesons are shown to correspond to different choices of interpolating field for spin-1 particles and the rules for transforming between them are described. The choice of fields that transform homogeneously under the nonlinear realisation of chiral symmetry imposes no preconceptions about the types of coupling for the mesons, and so this representation is particularly useful for comparing different theories. By converting them into this form, hidden-gauge theories are shown to contain an adjustable parameter, the gauge coupling. The normal choice for this is seen to be one that reduces the momentum dependence of the effective $ρππ$ coupling, explaining the success of the ``low-energy theorem" of that approach.

hep-ph↗

arXiv1994

Low-energy theorem for a composite particle in mean scalar and vector fields

For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction satisfying a low-energy theorem pointed out by Wallace, Gross and Tjon. The other does not vanish at zero-momentum and involves a ``polarisability" of the particle by the scalar field. The first of these contributions is independent of the details of the structure of the particle and the couplings of its constituents to the external fields. The appearance of such a piece in the central nucleon-nucleus potential thus would support the existence of strong scalar fields in nuclei, without requiring the use of a Dirac equation for the nucleon.

nucl-th↗