Hard pions and axial meson exchange current effects in negative muon capture in deuterium

The contribution of the axial meson exchange current effects to the doublet transition rate in the reaction μ^? +d → 2n+ ν_μ is calculated by using the minimal, chiral and approximately gauge invariant Lagrangian model for the A₁ρπ system. The contribution from the ρ-π weak decay process current usually considered is found to be nearly cancelled by that from the A₁ pole graph which is prescribed by the underlying invariance principles. Correct treatment of the N¹ propagator in the N¹ excitation current of the pion range leads to ≈ 30 % suppression of the N¹ effect.     

Axial Properties of Baryon Ground and Resonant States

We report results from a study of axial charges of baryon ground and resonant states with relativistic constituent quark models. In particular, we consider the axial charges of the octet and decuplet baryons N, ??, ??, ??, ??*, and ??*. The theoretical predictions are compared to experiment, in the case of the N, and to results from other approaches, especially from lattice quantum chromodynamics and chiral perturbation theory. Some remarks are also made regarding the role of axial charges for spontaneous breaking of chiral symmetry.     

The structure of the gauge theory vacuum

The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.     

One-loop corrections to the baryon axial vector current

The symmetry breaking corrections to the pion?Cbaryon couplings vanish to first order in 1/N _c, where N _c is the number of colours. Loop graphs with octet and decuplet intermediate states cancel to various orders in N _c as a consequence of the large-N _c spin-flavour symmetry of QCD baryons. The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large N _c limit. 1/N _c corrections in the case of g _A in QCD are presented here.     

Topologically non-trivial chiral transformations

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu-Jona-Lasinio model the hidden gauge and massive Yang-Mills approaches to vector mesons are linked by a special chiral transformation which removes the chiral field from the scalar-pseudoscalar sector. The chirally rotated axial vector meson field (à _μ ) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu-Jona-Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important feature, which usually is generated by non-vanishing axial vector profiles, is thus maintained by the simplificationà _μ = 0.     

Spontaneous chiral symmetry breaking for a U(N) gauge theory on a lattice

We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.     

Current algebra of quarks confined to a cavity

Equal-time commutators of fields with charges are calculated in a cavity approximation to the MIT bag model, with N flavours of non-interacting quarks confined to a rigid spherical cavity and SU(N) symmetry arbitrarily broken by mass terms. It is proved that inside the cavity the algebra is identical with that of free field theory, whilst on the boundary quark fields commute with axial charges. Vector divergences and sigma commutators belong to a $\text{(N,}\text{N}\text{) + (}\text{N}\text{, N)}$ multiplet of chiral SU(N) × SU(N). Axial divergences contain additional surface terms which do not contribute to sigma commutators. A non-strange quark mass in the range 20–44 MeV is required to give a value 30–70 MeV for the nucleon matrix element of the sigma commutator relevant to pion-nucleon scattering.     

Hard pions and axial meson exchange currents in nuclear physics

Starting from the hard meson method we develop a consistent approach to the problem of the axial meson exchange currents (MEC). This method incorporates the current algebra and PCAC together with the vector dominance and allows one to study the pion as well as heavy-meson exchanges on an equal footing. Using a minimal, chiral and approximately gauge-invariant phenomenological Lagrangian (PL) model for the A_1ρπ system we construct the two-nucleon axial MEC operator in the tree approximation. This operator automatically possesses the correct chiral SU(2) × SU(2) transformation properties and has the smoothest momentum dependence which is allowed within the combined current algebra and vector dominance approaches. In the given model, we consider the non-Born part of the amplitude N + J^A → n + π and demonstrate that in the soft pion limit, it exactly coincides with the PCAC prediction.     

Saddle-points in the twisted reduced chiral model

It is shown that the abnormal behaviour found in numerical simulations of twisted reduced SU(N→∞) chiral model in two dimensions results from fluctuations around a non-trivial extremum of the action. The possible rôle of such saddle-points in the crossover to the strong coupling regime is discussed.     

Dynamical breakdown of supersymmetry and chiral symmetry in 1+1 dimensions

Dynamical breakdown of supersymmetry and chiral symmetry is studied through a 1+1 dimensional field theoretical model in the large-N limit in 1/N expansion. The study is based on the calculation of bilinear field condensates in an effective potential approach. It is shown that the condition for supersymmetry breaking is related to the values of the parameters in the model and chiral symmetry breaking exists in most cases.     

An effective lagrangian with no U(1) problem in CPn−1 models and QCD

We write an effective lagrangian which gives two-point Green's functions satisfying the anomalous Ward identities for the U(1) axial vector current with a singlet particle that has a non-vanishing mass in the chiral limit. We show that the mechanism that has been postulated by Witten and Veneziano for solving the U(1) problem in the framework of the 1/n expansion in QCD is fully active in the two-dimensional CP^n? model where the 1/n expansion can be explicitly performed.     

Consistent quantization of a two-dimensional non-abelian chiral theory

A two-dimensional SU(N) gauge model coupled to Weyl fermions is studied following recent suggestions for the quantization of potentially anomalous chiral theories. The Weyl fermion determinant is evaluated and the fermionic current is shown to be conserved due to the gauge invariance of the resulting quantum theory. As in the abelian case, the vector meson acquires a mass and the model is consistent provided a regularization parameter is conveniently chosen.     

Approaching the large-N limit: A renormalization group approach to large-N field theories

A technique is developed for finding recursive solutions to field theories that take values in SU(N). The approach can be used as a method of solving the large-N limit as well as calculating finite-N effects. This is illustrated with examples of the anharmonic oscillator, SU(N) chiral model and two-dimensional lattice QCD.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

The large-N phase transition in the U(N) chiral models

We prove the existence of a large-N phase transition in the d = 2 chiral model and calculate via strong-coupling methods the phase-transition point. The critical coupling constant is 0.324. We also treat the chiral model chains (equivalent to the gauge model on polyhedrons) and our approximate calculations come very close to the exact results for the solvable cases.     

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N _c expansion scheme. It is found that the 1/N _c corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N _c expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.     

Effective chiral lagrangians with baryons—the mass splitting of the spin 1/2 parity partners

There are two inequivalent spin 1/2 baryon field operators that can be constructed directly out of three quark field operators. These are associated with a pair of parity partners. Their chiral transformation properties yield some unexpected results. In particular.U(1) axial transformations can mix the two operators. With these chiral transformation properties the spin 1/2 baryon parity partners are incorporated in an effective chiral lagrangian together with the spin 0 meson fields. The mass splitting of these parity partners is then found to be related to their coupling to the flavour singlet pseudoscalar, $$M_ - - M_ + \simeq F_\pi g_{\mathop {flavour}\limits_{singlet} N_ - N_ + } $$ The further selection rule, in the exact chiral limit, $$g_{\pi N_ + N_ - } = 0$$ is also found. Using these results, and their extension to the non-chiral limit, the enhancement of the decay ofN _? intoN ₊ η, as opposed toN ₊ π, is elucidated even though it is suppressed by phase space. Two flavours is given principle consideration although three flavours is also briefly discussed.     

Magnetic moment and radius of the nucleon in a nonlocal model of meson-nucleon interaction

Magnetic moment and radius of the nucleon are calculated in a nonlocal extension of the chiral linear σ-model. Properties of the nonlocal model under the vector and axial transformations are considered. The conserved electromagnetic and vector currents, and partially conserved axial vector current are obtained. In the calculation of the nucleon electromagnetic vertex the π- and σ-loop diagrams are included. Contribution from vector mesons is added in the vector meson dominance model with a gauge-invariant photon-meson coupling. The nonlocality parameter associated with the πN interaction is fixed from the experimental magnetic moment of the neutron. Other parameters (nonlocality parameter for the σN interaction and the mass of the σ-meson) are constrained by the magnetic moment of the proton. The calculated electric and magnetic mean-square radii of the proton and neutron are in satisfactory agreement with experiment. Received: 12 February 2001 / Accepted: 4 September 2001     

Meson-exchange corrections to the nuclear weak axial charge density in the hard pion model and 0+ 3 0− transitions in A = 16 nuclei

Starting with the hard-pion model based on a minimal chiral invariant phenomenological lagrangian, the two-body part of the time component of the weak axial-vector current is constructed in the tree approximation. Pion, rho- and A₁-meson exchanges are considered. The mesonic exchange operator obtained is applied to describe the purely weak axial 0⁺?0^?, ΔT = 1 transition in the nuclear A = 16 system. In order to treat nuclear structure correlation effects, explicit use of shell-model wave functions with configuration mixing is made. We confirm the large enhancement of the nuclear weak axial charge density with respect to impulse approximation.     

Axial polarizability and weak currents in nuclei

The effect of the isobaric excitations on the weak axial coupling constants in nuclei is studied through P.C.A.C. We first establish the Klein-Gordon equation for the virtual pion field in the nucleus; it takes into account pion rescattering. The influence of isobar excitation is contained in the axial polarizability coefficient which is linked to the p-wave π-N scattering volume. The derivation of this equation stresses its analogies with electromagnetism. We give then a basic relation between the axial current and the pionic field. It incorporates the effects of the isobars in the axial polarizability, which leads naturally to an electromagnetic analog. We show that this relation leads in heavy nuclei to a quenching of the axial coupling constant by the Lorentz-Lorenz factor, which may originate from the short range or the Pauli correlations, depending on the range of the π-N forces. Hence this quenching may have a different origin than the existence of short-range correlations and may arise from a Pauli blocking effect. On the other hand, the pseudoscalar coupling constant is found to be strongly suppressed. In finite nuclei, these basic quenchings can be masked by surface effects, the general features of which are studied with the help of a solvable model. This model is further used to obtain the asymptotic pion field which is linked to the effective pion-nucleus coupling constant and can be determined experimentally through π-nucleus dispersion relations. We find that this quantity is quenched, in agreement with recent experimental data.