The Theta+ (1540) as a heptaquark with the overlap of a pion, a kaon and a nucleon

We study the very recently discovered Theta+ (1540) at SPring-8, at ITEP and at CLAS-Thomas Jefferson Lab. We apply the same RGM techniques that already explained with success the repulsive hard core of nucleon-nucleon, kaon-nucleon exotic scattering, and the attractive hard core present in pion-nucleon and pion-pion non-exotic scattering. We find that the K-N repulsion excludes the Theta+ as a K-N s-wave pentaquark. We explore the Theta+ as a heptaquark, equivalent to a N+pi+K borromean bound-state, with positive parity and total isospin I=0. We find that the kaon-nucleon repulsion is cancelled by the attraction existing both in the pion-nucleon and pion-kaon channels. Although we are not yet able to bind the total three body system, we find that the Theta^+ may still be a heptaquark state. We conclude with predictions that can be tested experimentally.Comment: 5 pages, 5 figures, 2 tables, submitted to Phys. Rev. D, rapid communicatio

Spontaneous chiral symmetry breaking in the linked cluster expansion

We investigate dynamical chiral symmetry breaking in the Coulomb gauge Hamiltonian QCD. Within the framework of the linked cluster expansion we extend the BCS ansatz for the vacuum and include correlation beyond the quark-antiquark paring. In particular we study the effects of the three-body correlations involving quark-antiquark and transverse gluons. The high momentum behavior of the resulting gap equation is discussed and numerical computation of the chiral symmetry breaking is presented.Comment: 13 pages, 9 figure

Chiral Extrapolation, Renormalization, and the Viability of the Quark Model

The relationship of the quark model to the known chiral properties of QCD is a longstanding problem in the interpretation of low energy QCD. In particular, how can the pion be viewed as both a collective Goldstone boson quasiparticle and as a valence quark antiquark bound state where universal hyperfine interactions govern spin splittings in the same way as in the heavy quark systems. We address this issue in a simplified model which; however, reproduces all features of QCD relevant to this problem. A comparison of the many-body solution to our model and the constituent quark model demonstrates that the quark model is sufficiently flexible to describe meson hyperfine splitting provided proper renormalization conditions and correct degrees of freedom are employed consistently.Comment: 6 pages, 2 eps figures, uses revtex. Version to appear in Phys. Rev. Let

Fermion family recurrences in the Dyson-Schwinger formalism

We study the multiple solutions of the truncated propagator Dyson-Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant $g$, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These ``recurrences'' appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to a question about the value of the Yukawa coupling, and has no special profound significance in the Standard Model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation $E=\sqrt{p^2+M(p^2)^2}$ for the charged lepton member of each family. This requires three independent measurements of the charged lepton's energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton

From Current to Constituent Quarks: a Renormalization Group Improved Hamiltonian-based Description of Hadrons

A model which combines the perturbative behavior of QCD with low energy phenomenology in a unified framework is developed. This is achieved by applying a similarity transformation to the QCD Hamiltonian which removes interactions between the ultraviolet cutoff and an arbitrary lower scale. Iteration then yields a renormalization group improved effective Hamiltonian at the hadronic energy scale. The procedure preserves the standard ultraviolet behavior of QCD. Furthermore, the Hamiltonian evolves smoothly to a phenomenological low energy behavior below the hadronic scale. This method has the benefit of allowing radiative corrections to be directly incorporated into nonperturbative many-body techniques. It is applied to Coulomb gauge QCD supplemented with a low energy linear confinement interaction. A nontrivial vacuum is included in the analysis via a Bogoliubov-Valatin transformation. Finally, the formalism is applied to the vacuum gap equation, the quark condensate, and the dynamical quark mass.Comment: 36 pages, RevTeX, 5 ps figures include

Chiral Symmetry Breaking with Scalar Confinement

Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulting in the several successful theorems of PCAC. On the other hand scalar confinement is suggested both by the spectroscopy of hadrons and by the string picture of confinement. However these two evidences are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we reformulate the coupling of the quarks to the string, and we are able to comply with chiral symmetry breaking, using scalar confinement. The results are quite encouraging.Comment: 4 pages, 5 figures, contribution to the XXXVIIIth Rencontres de Moriond QCD and High Energy Hadronic Interaction

Chiral Lagrangian for strange hadronic matter

A generalized Lagrangian for the description of hadronic matter based on the linear $SU(3)_L \times SU(3)_R$ $\sigma$-model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale invariance is incorporated. The observed values for the vacuum masses of the baryons and mesons are reproduced. In mean-field approximation, vector and scalar interactions yield a saturating nuclear equation of state. We discuss the difficulties and possibilities to construct a chiral invariant baryon-meson interaction that leads to a realistic equation of state. It is found that a coupling of the strange condensate to nucleons is needed to describe the hyperon potentials correctly. The effective baryon masses and the appearance of an abnormal phase of nearly massless nucleons at high densities are examined. A nonlinear realization of chiral symmetry is considered, to retain a Yukawa-type baryon-meson interaction and to establish a connection to the Walecka-model.Comment: Revtex, submitted to Phys. Rev.

Linear square-mass trajectories of radially and orbitally excited hadrons in holographic QCD

We consider a new approach towards constructing approximate holographic duals of QCD from experimental hadron properties. This framework allows us to derive a gravity dual which reproduces the empirically found linear square-mass trajectories of universal slope for radially and orbitally excited hadrons. Conformal symmetry breaking in the bulk is exclusively due to infrared deformations of the anti-de Sitter metric and governed by one free mass scale proportional to Lambda_QCD. The resulting background geometry exhibits dual signatures of confinement and provides the first examples of holographically generated linear trajectories in the baryon sector. The predictions for the light hadron spectrum include new relations between trajectory slopes and ground state masses and are in good overall agreement with experiment.Comment: 33 pages, 5 figures, updated to the extended version published in JHEP, vector meson bulk potential and metric corrected, comments and references added, phenomenology and conclusions unchange