HADRON PHYSICS: Effective Theories of Low Energy QCD Second International Workshop on Hadron Physics

Mesons at Large N_{C}
View Description Hide DescriptionThe N_{C} → ∞ limit of QCD gives a useful approximation scheme to the physical hadronic world. A brief overview of the mesonic sector is presented. The large‐N_{C} constraints on the low‐energy couplings of Chiral Perturbation Theory are summarized and the role of unitarity corrections is discussed.

QCD string and chiral symmetry
View Description Hide DescriptionWe assume that QCD can be described in a certain kinematical regime by an effective string theory. This hadronic string must couple to background chiral fields in a chirally invariant manner, taking into account the true chirally non‐invariant QCD vacuum. By requiring conformal symmetry of the string and the unitarity constraint on chiral fields we reconstruct the equations of motion for the latter ones. These provide a consistent background for the propagation of the string. By further requiring locality of the effective action we recover the Lagrangian of non‐linear sigma model of pion interactions. The prediction is totally unambiguous and parameter‐free. The estimated chiral structural constants of Gasser and Leutwyler fit very well the phenomenological values.

Dispersive treatment of Κ → ππ
View Description Hide DescriptionWe write a set of dispersion relations for the Κ → ππ amplitude in which the weak Hamiltonian carries momentum. A soft pion theorem relates this amplitude to the Κ → π amplitude, and can be used to determine one of the two subtraction constants — the second constant is at present known only to leading order in chiral perturbation theory. We solve the dispersion relations numerically and express the result in terms of the unknown higher order corrections to this subtraction constant. We present preliminary results of an analysis of the effect of inelastic channels.

Meson‐Baryon Interactions in Unitarized Chiral Perturbation Theory
View Description Hide DescriptionMeson‐Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The s‐wave meson‐baryon scattering amplitude is analyzed in a Bethe‐Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off‐shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic resonances of the N(1535), N(1670), Λ(1405) and Λ(1670) resonances which compare well with accepted numbers.

Excited Baryon Spectroscopy in the 1/N_{ c } Expansion
View Description Hide DescriptionWe analyze the masses of the negative parity SU (6) 70‐plet baryons using the 1/N_{c} expansion to order 1/N_{c} and to first order in SU (3) breaking. At this level of precision there are twenty predictions which include the well known Gell‐Mann Okubo and equal spacing relations together with four new relations involving SU (3) breaking splittings in different SU (3) multiplets. Although the breaking of SU (6) symmetry occurs at zeroth order in 1/N_{c} , it turns out to be small. The dominant source of the breaking is the hyperfine interaction which is of order 1/N_{c} . The spin‐orbit interaction, of zeroth order in 1/N_{c} , is entirely fixed by the splitting between the singlet states Λ(1405) and Λ(1520), and the spin‐orbit puzzle is solved by the presence of other zeroth order operators involving flavor exchange.

Generalized Heat Kernel Coefficients for a New Asymptotic Expansion
View Description Hide DescriptionThe method which allows for asymptotic expansion of the one‐loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M ^{2} depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger ‐ DeWitt, the more general case with the nongenerate mass matrix M = diag(m _{1}, m _{2}, …) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley ‐ DeWitt coefficients is clarified.

’t Hooft Determinant: fluctuations and the structure of the vacuum
View Description Hide DescriptionThe ’t Hooft six quark flavor mixing interaction (N_{f} = 3) is bosonized by the path integral method. The considered complete Lagrangian is constructed on the basis of the combined ’t Hooft and U(3) × U(3) extended chiral four fermion Nambu — Jona‐Lasinio interactions. The method of the steepest descents is used to derive the effective mesonic Lagrangian. Additionally to the known lowest order stationary phase (SP) result of Reinhardt and Alkofer we obtain the contribution from the small quantum fluctuations of bosonic configurations around their stationary phase trajectories. Fluctuations give rise to multivalued solutions of the gap equations. Using the gap equations we construct the effective potential, from which the structure of the vacuum can be settled. We obtain that from the several extremal solutions, only one is a minimum. The others are either maxima or a saddle point. The effective potential reveals furthermore the existence of logartithmically divergent attractive wells at certain field expectation values, signalizing caustic regions.

Models of color confinement based on dual superconductors
View Description Hide DescriptionRecently, the relatively old speculation that the physical QCD vacuum might be a kind of dual superconductor, in which color‐magnetic monopoles have condensed, seems to have received some “experimental” confirmation in lattice calculations. The lattice calculations do not dictate, however, the form of the effective low‐energy theory. And indeed, a rather wide panoply of possible effective theories has been proposed. The purpose of this talk is to review them in order to contrast their properties.

Casimir Energies in the Light of Renormalizable Quantum Field Theories
View Description Hide DescriptionEffective hadron models commonly require the computation of functional determinants. In the static case these are one‐loop vacuum polarization energies, known as Casimir energies. In this talk I will present general methods to efficiently compute renormalized one‐loop vacuum polarization energies and energy densities and apply these methods to construct soliton solutions within a variational approach. This calculational method is particularly useful to study singular limits that emerge in the discussion of the classical Casimir problem which is usually posed as the response of a fluctuating quantum field to externally imposed boundary conditions.

Light meson resonances from unitarized Chiral Perturbation Theory
View Description Hide DescriptionWe report on our recent progress in the generation of resonant behavior in unitarized meson‐meson scattering amplitudes obtained from Chiral Perturbation Theory. These amplitudes provide simultaneously a remarkable description of the resonance region up to 1.2 GeV as well as the low energy region, since they respect the chiral symmetry expansion. By studying the position of the poles in these amplitudes it is possible to determine the mass and width of the associated resonances, as well as to get a hint on possible classification schemes, that could be of interest for the spectroscopy of the scalar sector.

Nucleon‐Nucleon interactions from effective field theory
View Description Hide DescriptionWe have established a new convergent scheme to treat analytically nucleon‐nucleon interactions from a chiral effective field theory. The Kaplan‐Savage‐Wise (KSW) amplitudes are resummed to fulfill the unitarity or right hand cut to all orders below pion production threshold. This is achieved by matching order by order in the KSW power counting the general expression of a partial wave amplitude with resummed unitarity cut, with the inverses of the KSW amplitudes. As a result, a new convergent and systematic KSW expansion is derived for an on‐shell interacting kernel in terms of which the partial waves amplitudes are computed. The agreement with data for the S‐waves is fairly good up to laboratory energies around 350 MeV and clearly improves and reestablishes the phenomenological success of the KSW amplitudes when treated within this scheme.

Criterium for the index theorem on the lattice
View Description Hide DescriptionWe study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We propose a new criterion for solutions of the Ginsparg‐Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d = 2 is m _{0} = 1.1 ± 0.1.

Off‐shell effects in nuclear matter from an EFT point of view
View Description Hide DescriptionEffective field theory requires all observables to be independent of the representation used for the quantum field operators. Off‐shell parts of the in‐medium vertex functions depend on the partucular representation so that off‐shell properties of the interactions should not lead to any observable effects. We analyse this issue in the context of many‐body approaches to nuclear matter, where it should be possible to shift into three‐body force the contributions from purely off‐shell two‐body interactions. We show that none of the commonly used truncations of the two‐body scattering amplitude such as the ladder, Brueckner‐Hartree‐Fock or parquet approximations respect this requirement.

Thermal Meson properties within Chiral Perturbation Theory
View Description Hide DescriptionWe report on our recent work about the description of a meson gas below the chiral phase transition within the framework of Chiral Perturbation Theory. As an alternative to the standard treatment, we present a calculation of the quark condensate which combines the virial expansion and the meson‐meson scattering data. We have also calculated the full one‐loop elastic pion scattering amplitude at finite temperature and we have unitarized the amplitude using the Inverse Amplitude Method in order to reproduce the temperature effects on the mass and width of the ρ and σ resonances. Our results show a clear increase of the thermal ρ width, as expected from previous analysis. The results for the σ are consistent with Chiral Symmetry Restoration. We comment on the relevance of our results within the context of Relativistic Heavy Ion Collisions.

Theta Term in QCD sum rules at Finite Temperature and the Neutron Electric Dipole Moment
View Description Hide DescriptionBy using thermal QCD sum rules to investigate the θ̄ induced neutron electric dipole moment d_{n} , we have examined the behaviour of broken CP symmetry at finite temperature. We find that, below the critical temperature, the ratio slightly decreases but survives at temperature effects, implying T nonrestoration of CP‐invariance [1].

Thermal model for RHIC, part I: particle ratios and spectra
View Description Hide DescriptionA simple thermal model with single freeze‐out and flow is used to analyze the ratios of hadron yields and the hadron transverse‐mass spectra measured in Au+Au collisions at RHIC. An overall very good agreement between the model predictions and the data is achieved for all measured hadron species including hyperons.

Thermal model for RHIC, part II: elliptic flow and HBT radii
View Description Hide DescriptionWe continue the analysis of the preceding talk with a discussion of the elliptic flow and the Hanbury‐Brown‐Twiss pion correlation radii. It is shown that the thermal model can be extended to describe these phenomena. The description of the elliptic flow involves an appropriate deformation of the freeze‐out hyper‐surface and flow velocity. The obtained results agree reasonably with the data for soft (< 2 GeV) transverse momenta. For the pionic HBT correlation radii the experimental feature that R _{out}/R _{side} ≃ 1 is naturally obtained. The reproduction of individual R _{side} and R _{out} can be achieved with the inclusion of the excluded volume corrections, which effectively increase the radii by ∼ 30%.

Diquark Condensation in Electrically and Color Neutral Quark Matter
View Description Hide DescriptionWe discuss the possible phase structure of strongly interacting matter in the regime of high densities and low temperatures where the quarks are expected to be in a color superconducting state. We focus on the additional constraints imposed by the requirement of electric and color neutrality which is essential for the description of neutron star interiors. To that end we employ a 3‐flavor NJL‐type quark model, which treats the diquark condensates and the quark‐antiquark condensates on an equal footing. The resulting phase diagram at zero temperature and the various independent chemical potentials turns out to be very rich, containing at least five different color superconducting phases. We search for regions of electrically and color neutral matter and also discuss the possibility of mixed phases with zero net charge. Neglecting surface and Coulomb effects we find nine different mixed phases with up to four components. Preliminary estimates indicate, however, that the mixed phases become unstable if surface and Coulomb effects are included.

Effects of quark matter and color superconductivity in compact stars
View Description Hide DescriptionThe equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation. We investigate the effects of a variation of the form factors of the interaction on the phase diagram of quark matter under the condition of β‐ equilibrium and charge neutrality. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state. We calculate the quark star configurations by solving the Tolman‐ Oppenheimer‐ Volkoff equations and obtain for the transition from a hot, normal quark matter core of a protoneutron star to a cool diquark condensed one a release of binding energy of the order of ΔMc ^{2} ∼ 10^{53} erg. We study the consequences of antineutrino trapping in hot quark matter for quark star configurations with possible diquark condensation and discuss the claim that this energy could serve as an engine for explosive phenomena. A “phase diagram” for rotating compact stars (angular velocity‐baryon mass plane) is suggested as a heuristic tool for obtaining constraints on the equation of state of QCD at high densities. It has a critical line dividing hadronic from quark core stars which is correlated with a local maximum of the moment of inertia and can thus be subject to experimental verification by observation of the rotational behavior of accreting compact stars.

Effects of the ρ − ω mixing interaction in relativistic models
View Description Hide DescriptionThe effects of the ρ − ω mixing term in infinite nuclear matter and in finite nuclei are investigated with the non‐linear Walecka model in a Thomas‐Fermi approximation. For infinite nuclear matter the influence of the mixing term in the binding energy calculated with the NL3 and TM1 parametrizations can be neglected. Its influence on the symmetry energy is only felt for the TM1 with a unrealistically large value for the mixing term strength. For finite nuclei the contribution of the isospin mixing term is very large as compared with the expected value to solve the Nolen‐Schiffer anomaly.