Nuclear pairing from chiral pion-nucleon dynamics

We use a recently improved version of the chiral nucleon-nucleon potential at next-to-next-to-leading order to calculate the ¹S₀ pairing gap in isospin-symmetric nuclear matter. The pairing potential consists of the long-range one- and two-pion exchange terms and two short-distance NN-contact couplings. We find that the inclusion of the two-pion exchange at next-to-next-to-leading order reduces substantially the cutoff dependence of the ¹S₀ pairing gap determined by solving a regularised BCS equation. Our results are close to those obtained with the universal low-momentum nucleon-nucleon potential V_low-k or the phenomenological Gogny D1S force.     

The charge-dependent Bonn potentials with pseudovector pion-nucleon coupling

In order to use high-precision realistic nucleon-nucleon(NN) potentials in relativistic many-body problems,new versions of the charge-dependent Bonn(CD-Bonn) NN potential are constructed with pseudovector pionnucleon coupling,instead of pseudoscalar coupling used in the original CD-Bonn potential as given by Machleidt~(2)).To describe precisely the charge dependence in the NN scattering data,two effective scalar mesons are introduced,whose coupling constants with nucleons are independently determined for each partial wave and for the total angular momentum J≤4.The coupling constants between the vector and pseudovector mesons and a nucleon are identical in all channels.Three revised CD-Bonn potentials with the pseudovector pion-nucleon coupling(pvCD-Bonn) are generated by fitting the Nijmegen PWA phase shift data and the deuteron binding energy with different pion-nucleon coupling strengths.The potentials reproduce the phase shifts in the spin-single channels and the low-energy NN scattering parameters very well,but result in significantly different mixing parameters in the spin-triplet channels.The Dstate probabilities for the deuteron range from 4.22% to 6.05%,demonstrating that the potentials contain different components of the tensor force,which is useful when considering the role of the tensor force in nuclear few-and many-body systems.     

Quark dynamics and strong meson decays

The strong decays of meson resonances are treated in a dynamical quark model. The model is formulated in the framework of general field theory and therefore all calculations are fully relativistic covariant. Spectrum and wave functions are derived from a Bethe-Salpeter equation describing the binding of heavy quarks by a smooth, very strong interaction. The mesonic vertices are calculated with help of these BS amplitudes in triangle graph approximation, thereby guaranteeing a symmetric treatment of all mesons involved in the process. A particular spin dependence of the interaction has the consequence that the super-strong quark binding forces lead to mesonic forces of moderate strength only (saturation of quark forces!).The applications refer to the decays of vector mesons, tensor mesons, scalar mesons into pseudoscalars and vectors and are extended to resonances in the R region. In particular, we include the decays into two pions of the radial excited ?′(1600). The helicity structure of the decays of the axial vector meson is discussed.     

Comments on the calculation of the pion-nucleon coupling constant and s-wave scattering lengths

It is pointed out that Coulomb barrier effects above 300 MeV may have a significant effect on the calculation of f² and a₁ ? a₃ for pion-nucleon scattering. It is argued that Bugg et al. have overestimated the value of f². Uncertainties in their calculations, which cannot be included in the statistical error, are listed and discussed.     

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: ([(?)\vec] r_p - [(?)\vec] r_n\vec \nabla \rho _p - \vec \nabla \rho _n )² G _d(r \rho) + ([(?)\vec] r_p - [(?)\vec] r_n\vec \nabla \rho _p - \vec \nabla \rho _n ·([(J)\vec]_p - [(J)\vec]_n\vec J_p - \vec J_n )G _so(r \rho) + ([(J)\vec]_p - [(J)\vec]_n\vec J_p - \vec J_n )² G _J(r \rho) pertaining to different proton and neutron densities. Our calculation treats systematically the effects from 1p \pi -exchange, iterated 1p \pi -exchange, and irreducible 2p \pi -exchange with intermediate D \Delta -isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions G _d(r \rho) , G _so(r \rho) and G _J(r \rho) which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.     

Quark dynamics, thermal QCD, and the gravity dual

We perform a holographic renormalization of the supergravity action and compute the stress tensor of the dual gauge theory incorporating the logarithmic running of the gauge coupling. From the stress tensor we obtain the shear viscosity and the entropy of the medium at temperature T, and investigate the ratio η/s.     

Low-energy pion-nucleon scattering

Several topics in pion-nucleon scattering at low energies are addressed. First, we review the predictions of chiral symmetry for the near-threshold region. The pion-nucleon scattering lengths and the Cheng-Dashen theorem with the related issue of the strangeness content of the nucleon are discussed in some detail. Finally, the status of the scalar mesons and the relevance of the pomeron and the concept of duality for pion-nucleon dynamics is pointed out.Lecture given at the 8th Summer School on Intermediate Energy Physics: Hadron Dynamics at Low and Intermediate Energies, Prague, July 10–14, 1995.I would like to thank the organizers of the Praha Indian-summer school for inviting me to this beautiful city. I am indebted to Th. Rijken and J. J. de Swart for discussions about the pomeron, the scalar mesons, and partial-wave analysis, and to U. van Kolck and J. Friar for discussions about chiral symmetry. This work was included in the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).     

Electroweak pion-nucleon constant

The parity-violating pion-nucleon coupling constant for the neutral currents of electroweak interaction is calculated by the method of QCD sum rules. In doing this, operators up to dimension 5 are retained in the operator-product expansion for the correlation function in an external pion field. That the value obtained for the pion-nucleon coupling constant is comparatively small stems from a partial cancellation between the leading perturbative and condensate contributions. This constant is compared with experimental data and with the results of calculations performed by other authors.     

Backward pion-nucleon scattering

A global analysis of the world data on differential cross-sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3GeV is performed in a Regge model. Including the N_a\ensuremath N_{\alpha} , N_g\ensuremath N_{\gamma} , D_d\ensuremath \Delta_{\delta} and D_b\ensuremath \Delta_{\beta} trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable u , in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3GeV. Our analysis suggests a G₃₉\ensuremath G_{39} -resonance with a mass of 2.83GeV as member of the D_b\ensuremath \Delta_{\beta} -trajectory from the corresponding Chew-Frautschi plot.     

Quark dynamics in soft hadronic collisions and fragmentation on nuclear targets

Additive and collective pictures of quark dynamics in hadron-hadron collisions lead to different predictions for attenuation effects on nuclear targets and can be distinguished experimentally.     

Quark dynamics and the weak non-leptonic decays of K and D mesons

Quark model predictions for K → 2π and D → Kπ decays were investigated in dynamical frameworks based on the separable approximation (SA), current algebra (CA), current algebra modified for the meson moment dependence (CAC) and current algebra with final-state interactions (CAF). Relativistic and non-relativistic quark model predictions were compared. The effective weak hamiltonian was modified by changing the relative strengths of its flavour $\text{20}\text{and}\text{84}$ parts. All these approaches were also applied to hyperon and $\text{Ω}{}^{\mathrm{?}}$ non-leptonic decays. When using standard QCD enhancement, the best approximation for K → 2π (CAC) works poorly with D → Kπ. The best approximatiob for D→Kπ (CAF) fails in the case of K → 2π. Only CAC with the $\text{84}$ piece of the hamiltonian quenched might be in agreement with studied weak decays.     

PCAC and the non-relativistic pion-nucleon vertex

The Foldy-Wouthuysen reduction technique is applied to the sigma model and pseudovector coupling pion-nucleon Lagrangians. In contrast to electrodynamics the requirement that the non-relativistic pion-nucleon Lagrangian have an approximate symmetry under the same global transformation as the relativistic theory does not uniquely fix the Foldy-Wouthuysen transformation. It is shown that the partially conserved axial-vector current relation is satisfied by the non-relativistic theory and the implications of this on the form of the effective pion-nucleon vertex are discussed.     

Constant-cutoff approach to pion-nucleon scattering

Pion-nucleon scattering amplitudes as well as Born amplitudes are calculated in a constant-cutoff approach to the canonical quantization of skyrmions, with the subsidiary conditions imposed on the quantum fields and their conjugate momenta such that all infrared singularities from the zero-frequency modes are eliminated. It is shown that the Born terms with recoil corrections are reproduced by the pion-nucleon linear and quadratic interactions.     

The weak pion-nucleon vertex revisited

We evaluate the parity-violating weak pion-nucleon vertex in the framework of a chiral soliton model including pions and the vector mesons ρ and ω. The weak πN coupling constant >G_π is enhanced by a factor of 13.3 for the standard electro-weak model as compared to the Cabbibo model, with its absolute value given by G_π ≈ 2.7 · 10⁻⁸. We compare our results to available data and other theoretical determinations. In particular, we predict the γ-asymmetry in ¹⁸F to be |P(¹⁸F)|= 1.2 · 10⁻⁴. We also discuss calculational differences to standard quark model estimates.