HADRON PHYSICS: Effective Theories of Low Energy QCD

Nonlocal regularization of chiral quark models in the soliton sector
View Description Hide DescriptionA chiral quark model is described which is regularized in terms of Lorentz invariant nonlocal interactions. The model is regularized to all loop orders and it ensures the proper quantization of the baryon number. It sustains bound hedgehog solitons which, after suitable center of mass corrections, can adequately describe the nucleon.

Baryons as solitons
View Description Hide DescriptionChiral lagrangians as effective field theories of QCD are successfully applied to meson physics in the framework of chiral perturbation theory. Because of their nonlinear structure these lagrangians allow for static soliton solutions interpreted as baryons. Their semiclassical quantization, which provides the leading order in an expansion with the number of colors, turned out to be insufficient to obtain satisfactory agreement with empirical baryon observables. However with large corrections are expected in the nexttoleading order carried by mesonic fluctuations around the soliton background, which require renormalization to 1loop. In contrast to chiral perturbation theory, the lowenergy lagrangian proves inapt and terms with an arbitrary number of gradients may in principle contribute. Assumptions about the a priori unknown higher chiral orders are tested by the scaledependence of the results. For example, in the simple SineGordon model with 1 scalar field in dimensions, knowledge of the lowenergy behavior together with the mere existence of an underlying 1loop renormalizable scaleindependent solitonic theory is sufficient to regain the full solution. Baryonic observables calculated within that framework generally lead to better agreement with experiment except for the axial quantities. For these quantities the expansion does not converge sufficiently fast because the current algebra mixes different orders.

Discriminating between chiral models of the nucleon via hard semiinclusive and scattering
View Description Hide DescriptionMeasurements of the flavor asymmetry of the polarized antiquark distributions in the nucleon, would provide a unique opportunity to discriminate between different models of the role of the chiral structure of the nucleon in deepinelastic scattering. In the pion cloud model of the nucleon’s sea quark distributions the polarized flavor asymmetry is zero, while the large picture of the nucleon as a chiral soliton predicts large polarized flavor asymmetries. We discuss the prospects for measuring the polarized antiquark flavor asymmetries in two types of semiinclusive scattering experiments: i) Hadron production in semiinclusive polarized eN scattering (SMC, HERMES); ii) DrellYan lepton pair production in polarized NN scattering at HERA or RHIC energies. In particular, the DrellYan spin asymmetries are shown to be remarkably sensitive to

Stability of multiquark systems
View Description Hide DescriptionWe give a brief review of developments in the field of exotic hadrons formed of more than three quarks and/or antiquarks. In particular we discuss the stability of multiquark systems containing heavy flavors. We show that the gluon exchange model and the chiral constituent quark model based Goldstone boson (pseudoscalar meson) exchange give entirely different results.

Quantum Monte Carlo studies of relativistic effects in and
View Description Hide DescriptionRelativistic effects in and have been studied in the context of Relativistic Hamiltonian Dynamics, using Variational Monte Carlo Methods. Relativistic invariance is achieved through Poincaré group algebra, which introduces a boost interaction term defining the first relativistic effect considered. The second consists in the nonlocalities associated with the relativistic kinetic energy operator and with the relativistic onepion exchange potential (OPEP). These nonlocalities tend to cancel, being the total effect on the binding energy attractive and very small, of the order of 1%. The dominant relativistic effect is due to the boost interaction, whose contribution is repulsive and of the order of 5%. The repulsive term of the nonrelativistic 3body interaction has to be reduced by 37% so that the optimal triton binding energy is recovered, meaning that around 1/3 of this phenomenological term accounts for relativisitic effects. The changes induced on the wave functions of nuclei by these relativistic effetcs are very small and short ranged. Although the nonlocalities of OPEP, resulting in a reduction of 15%, are cancelled by other relativistic contributions, they may have significant effects on pion exchange currents in nuclei.

Computation of the nucleon properties in the chiral quark model
View Description Hide DescriptionUp to now the quark sea contributions to the energy and various physical observables in the chiral quark model have been formulated with the summation of levels. We will present a different technique for computing various physical observables, based on using the Euclidean Green functions and their Kspin partial wave reduction. In this framework it is not necessary to discretize the continuous spectrum by introducing a finite boundary. Besides this technical advantage such an alternative computation scheme makes it possible to obtain the numerical predictions of the model in an entirely independent way. Using this formulation we perform a new selfconsistent computation of the nucleon state in the NambuJonaLasinio model. We use the PauliVillars cutoff to define the model. Our results for the nucleon energy, the mesonic profile, and various observables essentially confirm results obtained by other groups using this regularization. Similar techniques applied to Minkowskian Green functions can be used to compute the nucleon structure functions.

Multibaryons in the Skyrme model
View Description Hide DescriptionLowlying multibaryon configurations are studied within the bound state approach to the Skyrme model. We use approximate ansätze for the static background fields based on rational maps which have the same symmetries of the exact solutions. To determine the explicit form of the collective Hamiltonians and wave functions we only make use of these symmetries. Thus, the expressions obtained are also valid in the exact case. On the other hand, the meson bindings, inertia parameters and hyperfine splitting constants we calculate do depend on the detailed form of the ansätze and are, therefore, approximate. Using these values we compute the lowlying spectra of multibaryons with and strangeness 0, −1 and With these results the stability of some multilambda configurations is discussed.

Form factors of baryons in a confining and covariant diquarkquark model
View Description Hide DescriptionWe treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. This description results as an approximation to the relativistic Faddeev equation for three quarks which yields an effective BetheSalpeter equation. Octet and decuplet masses and fully fourdimensional wave functions have been computed for two cases: assuming an essentially pointlike diquark on the one hand, and a diquark with internal structure on the other hand. Whereas the differences in the mass spectrum are fairly small, the nucleon electromagnetic form factors are greatly improved assuming a diquark with structure. First calculations to the pionnucleon form factor also suggest improvements.

Nucleonnucleon interaction in a chiral constituent quark model
View Description Hide DescriptionWe study the nucleonnucleon (NN) problem as a sixquark system in a nonrelativistic chiral constituent quark model where the Hamiltonian contains a linear confinement and a pseudoscalar meson (Goldstone boson) exchange interaction between the quarks. This interaction has a long range Yukawatype part, depending on the mass of the exchanged meson and a short range part, mainly responsible for the good description of the baryon spectra. We calculate the NN potential in the adiabatic approximation as a function of Z, the separation distance between the centres of the two threequark clusters. The orbital part of the sixquark states is constructed either from the usual cluster model states or from molecular orbital single particle states. The latter are more realistic, having proper axially and reflectionally symmetries. In both cases the potential presents an important hard core at short distances, explained through the dominance of the configuration. However in the molecular orbital basis the core is less repulsive, as a consequence of the fact that this basis gives a better upper bound for the energy of the sixquark system. We calculate the potential for the and channels with two different parametrizations. We find a small (few MeV) attractive pocket for one of these parametrizations. A middle range attraction is simulated by the addition of a σmeson exchange interaction between quarks, of a form similar to that of the pseudoscalar meson exchange. The present study is an intermediate, useful step towards dynamical calculations based on the resonating group method.

Chiral NN interactions in nuclear matter
View Description Hide DescriptionWe consider an effective field theory of NN system in nuclear medium. The shallow bound states, which complicate the effective field theory analysis and lead to the large scattering length in the vacuum case do not exist in matter. We show that the nexttoleading order terms in the chiral expansion of the effective NN potential can be interpreted as corrections so that the expansion is systematic. It is pointed out however that it is still useful to treat the problem nonperturbatively since it may allow for the consideration of the nuclear systems with the density smaller that the normal nuclear matter one. The potential energy per particle is calculated. The possible directions in constructing the chiral theory of nuclear matter are outlined.

A sketch of two and three bodies
View Description Hide DescriptionA cartoon of the Effective Field Theory of many nucleon systems is drawn, concentrating on Compton scattering in the two nucleon system, and on nd scattering in the three body system.

A renormalisationgroup treatment of twobody scattering
View Description Hide DescriptionA Wilsonian renormalisation group is used to study nonrelativistic twobody scattering by a shortranged potential. We identify two fixed points: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the linearised renormalisation group are used to assign a systematic powercounting to terms in the potential near each of these fixed points. The expansion around the nontrivial fixed point is shown to be equivalent to the effectiverange expansion.

QCD dynamics at
View Description Hide DescriptionTaking into account the terms in the effective chiral lagrangian, we show that, at the theory with 2 light quarks of equal mass involves two degenerate vacuum states separated by a barrier. For the energy barrier between two vacua appears already in the leading order in mass. This corresponds to the first order phase transition at The surface energy density of the domain wall separating two different vacua is calculated. In the immediate vicinity of the point two minima of the potential still exist, but one of them becomes metastable. The probability of the false vacuum decay is estimated.

Wilson’s area law and string effective actions for confining gauge theories
View Description Hide DescriptionAfter reviewing the rôle of center vortices and monopoles in Wilson’s area law of confinement, we estimate the string tension for an ensemble of noninteracting center vortices. Next, we discuss the string representations of dual superconductor type  and gauge models and their application to the evaluation of field strength correlators. The largedistance asymptotic behaviors of the latter are shown to be in agreement with the stochastic vacuum model of QCD and existing lattice data.

Magnetic monopoles, center vortices, confinement and topology of gauge fields
View Description Hide DescriptionThe vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum YangMillstheory. For this purpose the continuum analog of the maximum center gauge is constructed.

How could quark polarization be measured
View Description Hide DescriptionThe perspectives of two new nonstandard methods of transversal quark polarization measurement are considered: the jet handedness and the socalled “Collins effect” due to spin dependent Todd fragmentation function responsible for the leftright asymmetry in fragmenting of transversally polarized quarks. Recent experimental indications in favor of these effects are observed: 1. The correlation of the Todd oneparticle fragmentation functions found by DELPHI in jet decay. Integrated over the fraction of longitudinal and transversal momenta, this correlation is of 1.6% order, which means order of 13% for the analyzing power. 2. A rather large (≈10%) handedness transversal to the production plane observed in the diffractive production of triples from nuclei by the beam. It shows a clear dynamic origin and resembles the single spin asymmetry behavior. All this makes us hope to use these effects in polarized DIS experiments for transversity measurement. The first estimation of transversity was done by using the azimuthal asymmetry in semiinclusive DIS recently measured by HERMES and SMC.

Heavy flavor contributions to QCD sum rules and the running coupling constant
View Description Hide DescriptionWe have calculated first and second order corrections to several sum rules measured in deep inelastic leptonhadron scattering. These corrections, which are due to heavy flavors only, are compared with the existing perturbation series which is computed for massless quarks up to third order in the strong coupling constant A study of the perturbation series reveals that the large logarithms of the type dominate the perturbation series at much larger values than those given by the usual matching conditions imposed on the Therefore these matching conditions cannot be used to extrapolate the running coupling constant from small μ to very large scales like An alternative description of the running coupling constant in the MOMscheme is proposed.

Colorflavor transformations and QCD lowenergy effective action
View Description Hide DescriptionThe colorflavor transformation is applied in the QCD strong coupling limit to construct the effective chiral Lagrangian. The calculations are performed by placing the fermions onto two different sublattices and by making use of the longdistance approximation and gradient expansion. The saddle point approximation could be applied on such a double lattice. In this framework the effect of the spontaneous chiral symmetry breaking is described and the numerical values of the chiral condensate, pion decay constant and pion mass are estimated by using the only parameter of model, the lattice spacing a. The effective chiral Lagrangian of QCD is recovered up to the terms of order

Chiral QCD dynamics: Recent results
View Description Hide DescriptionI review recent chiral perturbation theory results for the electromagnetic hyperon and the strange nucleon form factors. I also present a precise chiral nucleonnucleon potential based on a modified Weinberg power counting and discuss the pertinent results and implications.

Up to twoloop calculations in HBCPT
View Description Hide DescriptionWe start with a brief introduction to HBCPT, and discuss spindependent forward Compton scattering both as a pedagogic example and to present our recent results for the fourthorder contribution. We then present two recent twoloop calculations in HBCPT; the fifthorder contribution to the nucleon mass and the lowestorder contribution of the WessZuminoWitten anomalous Lagrangian to forward spindependent Compton scattering. In both cases there are checks on the results which confirm the consistency of HBCPT at twoloop level. While the smallness of the mass correction is encouraging for the convergence of the theory, the fourthorder contribution to the spin polarizability turns out to be very large.