Isospin breaking in the pion–nucleon scattering lengths

We analyze isospin breaking through quark mass differences and virtual photons in the pion–nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory.     

Meson-meson interactions and Regge propagators

By a reformulation of the loop expansion in the Resonance-Spectrum Expansion amplitude for meson-meson scattering, in terms of s-channel exchange of families of propagator modes, we obtain a formalism which allows for a wider range of applications. The connection with the unitarized amplitudes employed in some chiral theories is discussed. We also define an alternative for the Regge spectra and indicate how this may be observed in experiment.     

Chiral symmetry and light resonances in hot and dense matter

We present a study of the π π scattering amplitude in the σ and ρ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral-symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear-density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar–isoscalar channel to account for finite nuclear-density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear-matter and heavy-ion collision experiments, such as ρ mass scaling versus broadening from dilepton spectra and chiral restoration signals in the σ channel. We also elaborate on the molecular nature of π π resonances.     

Screened potential and quarkonia properties at high temperatures

We perform a quark model calculation of the quarkonia b and c spectra using smooth and sudden string breaking potentials. The screening parameter is scale dependent and can be related to an effective running gluon mass that has a finite infrared fixed point. A temperature dependence for the screening mass is motivated by lattice QCD simulations at finite temperature. Qualitatively different results are obtained for quarkonia properties close to a critical value of the deconfining temperature when a smooth or a sudden string breaking potential is used. In particular, with a sudden string breaking potential quarkonia radii remain almost independent of the temperature up to the critical point, only well above the critical point the radii increase significantly. Such a behavior will impact the phenomenology of quarkonia interactions in medium, in particular for scattering dissociation processes.     

Is chiral symmetry restored in the excited meson spectrum?

The large degeneracy observed in the excited meson spectrum by the Cristal Barrel Collaboration in the experimental data on proton–antiproton annihilation in flight into mesons in the range 1.9–2.4 GeV has been interpreted as a signal of chiral symmetry restoration. In this work we suggest that such degeneracy may be an indication of the confinement potential modification by color screening. The experimental data can be fairly well reproduced in a constituent quark model with a screened linear confinement potential without changing the dynamical quark mass. Observables that could discriminate our model from those which explicitly restore the chiral symmetry are proposed.     

ππ S-wave phase shifts and non-perturbative chiral approach

We extend a recent non-perturbative chiral approach to ππ S-wave scattering of Oller and Oset by including the couplings to the ηη-channel. We find that the isospin-zero and isospin-two ππ S-wave phase shifts of the model deviate considerably from a recent solution of the Roy-equations. Including the couplings with the ηη-channel does not improve the situation. In particular, no σ-meson like enhancement structure shows up in the Roy-equation solution. We also consider the ππ-scattering lengths in this approach. Received: 17 August 1998 / Revised version: 21 September 1998     

Unitarity constraints and role of geometrical effects in deep-inelastic scattering and vector meson electroproduction

Deep-inelastic scattering at low x and elastic vector meson electroproduction are analyzed on the basis of the s-channel unitarity extended to off-shell particle scattering. It appeared that the role of unitarity is important, but contrary to the case of on-shell scattering it does not rule out a power-like behavior of the total cross sections. We discuss the behavior of the total cross section of virtual photon–proton scattering in the geometrical approach and obtain the result that the exponent of the power-like energy dependence of is related to the constituent quark interaction radius. The mass effects and energy dependence of vector meson electroproduction are discussed along with the angular distributions at large momentum transfers in these processes. Received: 10 September 2001 / Published online: 7 December 2001     

<Emphasis Type="Italic">ππ</Emphasis> scattering in a nonlocal chiral quark model

We consider a nonlocal version of the Nambu and Jona-Lasinio model with the SU(2) × SU(2) chiral symmetry broken by the current-quark-mass term. The nonlocality is contained in the quark-antiquark bilinears of the four-quark vertices as a form factor of the Gaussian type. The model has three parameters which can be fixed in favor of the values of the pion mass mπ, the pion decay constant fπ, and the current quark mass m _c . It is shown that, in the model, the main low-energy theorems which are known for pions are fulfilled. The s-, p-, and d-wave scattering lengths in all isotopic channels and the s-wave slope parameters are calculated, and the results are in satisfactory agreement with phenomenological data. The text was submitted by the authors in English.     

Forward dispersion relations and Roy equations in <Emphasis Type="Italic">ππ</Emphasis> scattering

We first review the results of an analysis of ππ interactions in S, P and D waves for the two-pion effective mass from threshold to about 1.4GeV. In particular, we show a recent improvement of this analysis above the Kˉ threshold using more data for phase shifts and including the S0-wave inelasticity from ππ→Kˉ. In addition, we have improved the fit to the f ₂(1270)-resonance and used a more flexible P-wave parametrization above the Kˉ threshold and included an estimation of the D2-wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42GeV. Finally, in this work we check that the ππ scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy's equations.     

Probing top anomalous couplings at the Tevatron and the Large Hadron Collider

Chromomagnetic and chromoelectric dipole interactions of the top quark are studied in a model-independent framework. Limits are set on the scale of new physics that might lead to such contributions using latest Tevatron measurements of the t[`(t)]t{\bar t} cross-section. It is demonstrated that the invariant mass distribution is a sensitive probe. Prospects at the LHC are examined. It is shown that, for unitarized amplitudes, an increase in the LHC energy is of little importance, while the accumulation of luminosity plays a crucial role.     

Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm _d—m _u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m _d—m _u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN _c counting and furthermore provides an alternative interpretation of the Borel mass.     

The cusp effect in <Emphasis Type="Italic">η</Emphasis>′→<Emphasis Type="Italic">η</Emphasis><Emphasis Type="Italic">π</Emphasis><Emphasis Type="Italic">π</Emphasis> decays

Strong final-state interactions create a pronounced cusp in η′→η π ⁰ π ⁰ decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of π π scattering lengths from K→3π decays to this case. The cusp effect is predicted to have an effect of more than 8% on the decay spectrum below the π ⁺ π ⁻ threshold.     

Isospin violating mass differences of baryons and hadronic loops

Isospin violating mass splittings of the ground state baryons are discussed within the frame-work of the unitarized quark model. It is shown that the long-distance, nonperturbative unitarity effects are important, and that a good agreement with the observed mass splittings can be retained. The importance of six mass sum rules which hold independently of dynamical assumptions is emphasized.     

On a possible estimation of the constituent-quark parameters from Jefferson Lab experiments on the pion form factor

The charge form factor of the pion is calculated for the momentum transfer range of the Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for the quark wave function in the pion is weak, while the dependence on the constituent-quark mass is rather significant. It is possible to estimate the mass of the constituent quark and the sum of the anomalous magnetic moments of the u- and -quarks from the JLab experiments. Received: 3 April 2000 / Revised version: 25 February 2001 / Published online: 25 April 2001     

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector, we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitly, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long-range van der Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.     

On the temperature dependence of quarkonium correlators

I discuss the temperature dependence of quarkonium correlators calculated in lattice QCD. I show that the dominant source of the temperature dependence comes from the zero-mode contribution, while the temperature dependence associated with the melting of bound states is quite small. I study the zero-mode contribution quantitatively for various quark masses and show that it is well described by a quasi-particle model with temperature-dependent heavy quark mass. As a byproduct, an estimate of the medium dependence of the heavy-quark mass is obtained.     

Baryon masses in large N c chiral perturbation theory

We analyse the baryon mass spectrum in a framework which combines the 1/N _c expansion with chiral perturbation theory. Meson loop contributions involving the full SU(3) octet of pseudoscalar Goldstone bosons are evaluated, and the influence of explicit chiral and flavor symmetry breaking by non-zero and unequal quark masses is investigated. We also discuss sigma terms and the strangeness contribution to the nucleon mass. Received: 29 June 1998 / Revised version: 25 November 1998     

Determination of vector meson properties by matching resonance saturation to a constituent quark model

The properties of mesonic resonances can be calculated in terms of the low-energy coefficients of chiral perturbation theory ( PT) by extending unitarized PT to higher energies. On the other hand, these low-energy coefficients can be calculated in two different models, namely i) by assuming resonance saturation and ii) within a constituent quark model. By matching the expressions of the two models combined with the results of unitarized PT and the Weinberg sum rules, the properties of vector and axial-vector mesons can be calculated in the combined large-N _c and chiral limit.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Fe Phenomenological quark models: Chiral Lagrangians - 14.40.Cs Properties of specific particles: Other mesons with S = C = 0, mass < 2.5 GeV     

On size and shape of the average meson fields in the semibosonized Nambu & Jona-Lasinio model

We consider the bosonized form of a two-flavor Nambu & Jona-Lasinio model involving scalar-isoscalar and pseudoscalar-isovector quark-quark interaction. Solitonic meson fields are obtained by minimizing the effective Euclidean action. In dependence on the constituent quark mass, which is the only free parameter in the model, we evaluate a series of meson profiles and compare them with a properly parameterized reference profile. We show that the self-consistent fields do in fact practically not depend on the constituent quark mass. Their shape can be very well approximated by this reference profile which interpolates between the correct asymptotic behavior for small and large radii. To demonstrate the accuracy of the approximation we evaluate several static properties like energy, mean square radius, axial-vector constant and delta-nucleon mass splitting using both self-consistent and reference profiles. The agreement is found to be very well in the physically relevant mass region.