Véronique Bernard

Chiral structure of the nucleon

Abstract We analyze the structure of QCD Green functions with one external nucleon, treated as a very massive field. We discuss the matching conditions and relations of various nucleon matrix elements of quark currents to the relativistic approach. Particular emphasis is put on the forward Compton amplitudes. Besides the nucleon electromagnetic polarizabilities we consider the spin-flip amplitude ƒ 2 (ω 2 ) to one-loop order. We predict the slope parameter of ƒ 2 (ω 2 ) which can be determined from the absorption cross sections of circularly polarized photons on polarized nucleons.

Strangeness Mixing and Quenching in the Nambu-Jona-Lasinio Model

Abstract We study the mixing of quarks of one flavor into the wavefunction of constituent quarks of a different flavor when chiral symmetry breaks dynamically in the Nambu-Jona-Lasinio model. First we generalize the Nambu-Jona-Lasino model to N ƒ flavors including U(1) A symmetry breaking by a 2N ƒ - fermion interaction. In the Hartree-Fock approximation, this term is entirely responsible for flavor mixing. We specialize to three flavors and use meson properties and vacuum quark condensates to fix the three parameters of the model. We show that there are generically two different regimes in the broken chiral symmetry phase. Non-linearities in the strange quark mass are strong in the “barely broken regime”, allowing for a large Σ-term and a small s-quark content of the proton. In the “firmly broken regime”, non-linearities in m s , are small, chiral perturbation theory is likely to be reliable and the Σ-term is small. We also study deep inelastic scattering and demonstrate that dynamical chiral symmetry breaking gives rise to a non-negligible s-parton distribution.

Axial structure of the nucleon

We review the current status of experimental and theoretical understanding of the axial nucleon structure at low and moderate energies. Topics considered include (quasi)elastic (anti)neutrino–nucleon scattering, charged pion electroproduction off nucleons and ordinary as well as radiative muon capture on the proton.

Properties of vector and axial-vector mesons from a generalized Nambu-Jona-Lasinio model

Abstract We construct a generalized Nambu-Jona-Lasinio lagrangian including scalar, pseudoscalar, vector and axial-vector mesons. We specialize to the two-flavor case. The properties of the structured vacuum as well as meson masses and coupling constants are calculated giving an overall agreement within 20% of the experimental data. We investigate the meson properties at finite density. In contrast to the mass of the scalar σ-meson, which decreases sharply with increasing density, the vector meson masses are almost independent of density. Furthermore, the vector-meson-quark coupling constants are also stable against density changes. We point out that these results imply a softening of the nuclear equation of state at high densities. Furthermore, we discuss the breakdown of the KFSR relation on the quark level as well as other deviations from phenomenological concepts such as universality and vector meson dominance.

Effects of collective modes on the single-particle states and the effective mass in 208Pb

Abstract A microscopic particle-vibration model is used to study the single-particle energies, spectroscopic factors and nucleon effective mass in 208 Pb. The relevant quantities are deduced from the knowledge of the mass operator which is the sum of a Hartree-Fock term and an energy-dependent term coming from the coupling to RPA vibrations. The results are discussed and compared with experimental data. The main conclusions are: (i) the gap between the occupied and unoccupied shells is substantially decreased by the coupling to the vibrations; (ii) the spectroscopic factors in the valence shells are of the order of 0.7–0.8, and in some cases smaller; (iii) the value of the effective mass near the Fermi level is about 1.1–1.2.

The form factors of the nucleon at small momentum transfer

Abstract We study the low energy expansion of the nucleons electroweak form factors in the framework of an effective chiral Lagrangian including pions, nucleons and the Δ(1232). We work to third order in the so-called small scale expansion and compare the results with the ones previously obtained in the chiral expansion. In addition, these calculations serve as a first exploratory study of renormalization and decoupling within the small scale expansion.

πK scattering in chiral perturbation theory to one loop

Abstract We evaluate the πK scattering amplitude at next-to-leading order in the framework of chiral perturbation theory. All low-energy constants appearing in the effective lagrangian of the pseudoscalars have previously been determined. We calculate the scattering lengths of the S- and P-waves as well as the expansion parameters around the point v ≡ (s - u)/4MK = t = 0 in the unphysical region. Furthermore, phase-shifts of the low partial waves are presented and compared to the data. In most cases, the chiral predictions are comparable to the trends set by the empirical information. For a precise comparison, however, more accurate experimental determinations of the πK scattering process at low and moderate energies would be necessary. We urge the experimenters to perform these.

Neutral pion photoproduction at threshold

Abstract We evaluate the neutral pion photoproduction amplitude at threshold to one loop in chiral perturbation theory. Virtual pions generated infrared singularities in the scattering amplitude and modify the familiar low-energy expansion of the electric dipole amplitude Eo+ at next-to-leading order.

Resonance properties from the finite-volume energy spectrum

A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the Δ-resonance a clear resonance structure emerges in such an analysis. Consequently, measuring the volume-dependence of the energy levels in lattice QCD will allow to determine the mass and the width of the Δ with reasonable accuracy.

Critical analysis of baryon masses and sigma terms in heavy baryon chiral perturbation theory

We present an analysis of the octet baryon masses and the πN andKN σ-terms in the framework of heavy baryon chiral perturbation theory. At next-to-leading order,O(q3), knowledge of the baryon masses and σπN(0) allows to determine the three corresponding finite low-energy constants and to predict the twoKN σ-terms σKN(1,2)(0). We also include the spin-3/2 decuplet in the effective theory. The presence of the non-vanishing energy scale due to the octet-decuplet splitting shifts the average octet baryon mass by an infinite amount and leads to infinite renormalizations of the low-energy constants. The first observable effect of the decuplet intermediate states to the baryon masses starts out at orderq4. We argue that it is not sufficient to retain only these but no other higher order terms to achieve a consistent description of the three-flavor scalar sector of baryon CHPT. In addition, we critically discuss anSU (2) result which allows to explain the large shift σπN(2Mπ2)-σπN(0) via intermediate Δ (1232) states.