Narrow Results

Motivated by the recent experimental evidence of the exotic B=S=+1 baryonic state Θ (1540), we examine the older existing data on K⁺N elastic scattering through the time delay method. We find positive peaks in time delay around 1.545 and 1.6 GeV in the D₀₃ and P₀₁ partial waves of K⁺N scattering respectively, in agreement with experiments. We also find an indication of the J=3/2 Θ* spin-orbit partner to the Θ, in the P₀₃ partial wave at 1.6 GeV. We discuss the pros and cons of these findings in support of the interpretation of these peaks as possible exotics.

We study the properties of the color triplet quark cluster when flavor symmetry is broken. The relevance of such a cluster for some models of pentaquarks is then examined in the light of recent experimental signals.

The relativistic generalization of Faddeev–Yakubovsky approach is constructed in the form of the dispersion relations. The five-quark amplitudes for the low-lying pentaquarks including the u-, d-, s-quarks are calculated. The poles of these amplitudes determine the masses and widths of θ-pentaquarks.

The effective Lande splitting factor $g^{\ast }$ for heavy pentaquarks has been investigated, where the pentaquarks are described as Composite Fermions (CFs). The effective Lande splitting factor for heavy pentaquarks ${𝜃}_c^0$, $N_c^0$, ${\mathrm{\Xi }}_c^0$ and ${𝜃}_b^{+}$, $N_b^{+}$, ${\mathrm{\Xi }}_b^{+}$ has been extracted. It has been suggested that due to color magnetic field, diquarks behave like CFs and effective masses of the pentaquarks $m^{\ast }$ have been estimated in diquark–diquark–antiquark scheme with the input of effective diquark masses calculated in the framework of Composite Fermion model (CFM). With $m^{\ast }{g}^{\ast }$ as the additional contribution to the energy expression, the variation of $g^{\ast }$ with angular momentum $L$ has been studied. The vacuum value of $g^{\ast }$ has been extracted, which can be attributed to the splitting due to spin contribution of CFs and choromo-electromagnetic character of the QCD vacuum.

I discuss the recent experimental and theoretical developments following the discovery of the Θ⁺ pentaquark – an exotic baryon resonance observed in the KN channel by several experiments, and an exotic Ξ*^-- (ddssū) reported by NA49 at CERN. I focus on the theoretical interpretation of the data, both in terms of quark and chiral degrees of freedom, on the predictions for related exotic states, and on several unresolved questions raised by the experimental data, such why some experiments observe the pentaquarks and other don't, the apparently extremely narrow width of the Θ⁺ and the determination of its parity. I also describe the likely properties of the proposed heavy-quark pentaquarks – an anticharmed exotic baryon and , , which are expected to be extremely narrow or even stable against strong decays. H1 recently reported observation of a possible Θ_c candidate in D*^-p channel. Pentaquarks are also being searched for in e⁺e^- annihilation and γγ collisions in the LEP data and at B-factories.

The pentaquarks are exotic baryons formed of four quarks and an antiquarks. Their existence has been discussed in the literature over the last 30 years or more, first in connection with kaon nucleon scattering data. The subject has been revived by the end of 2002 when experimental evidence of a narrow baryon of strangeness S=+1, and mass M≃1530 MeV has been found. This is interpreted as the lightest member of an SU(3)-flavor antidecuplet. Here we shall mainly review the predictions of pentaquark properties as e.g. mass, spin and parity, within constituent quark models. Both light and heavy pentaquarks will be presented.

In this talk, I address some open problems in hadron physics and stress their importance for a better understanding of QCD in the confinement regime.

Recent results on the study of the electromagnetic structure of nucleon resonances, the spin structure of protons and neutrons at small and intermediate photon virtuality, and the search for exotic pentaquark baryons are presented.

Glueballs and hybrids are predicted to exist but searches for them have failed to provide conclusive evidence. One–gluon exchange is not an important part of strong interactions in this energy regime. Instead, quarks seem to interact indirectly, via changes of the QCD vacuum. Strong interactions seem to be governed by instanton–induced interactions; the chiral soliton model gives a more suitable interpretation of the Θ⁺(1540) than models based on the dynamics of four quarks and one antiquark.

Light and heavy pentaquarks are described within a constituent quark model based on a spin-flavor hyperfine interaction. In this model the lowest state acquires positive parity. The masses of the light antidecuplet members are calculated dynamically using a variational method. It is shown that the octet and antidecuplet states with the same quantum numbers mix ideally due to SU(3)_F breaking. Masses of the charmed antisextet pentaquarks are predicted within the same model.

A model for nuclei described directly in terms of quarks has been developed in both relativistic and non-relativistic forms. It describes nuclear binding energy and structure for small nuclei (A=3,4) systematically correctly, including the EMC effect. With one free parameter each for strange and for nonstrange states, it also well describes low energy baryon-nucleon scattering, phase shifts and potentials. It predicts low mass, narrow dibaryon and pentaquark states. To be consistent with reported states, new physics may be required that is not included in any quark model to date.

Recently the H1 Collaboration observed a narrow peak in D*^-p invariant mass spectrum from what is believed to be an anti-charmed pentaquark baryon state with quark content, produced in deep inelastic scattering in ep collisions at HERA. This new state was tentatively named as being an anti-charmed analog of Θ⁺ pentaquark discovered in 2003 by LEPS Collaboration. The upgraded CDF detector is sensitive to production of charmed pentaquark states in central rapidity region due to ability to trigger on displaced tracks from weakly decaying daughter hadrons. At this conference we report results of searches for anti-charmed pentaquark and its charged isospin partner in collisions at at Tevatron.

A brief review of the latest developments in the spectroscopy of heavy quarks is presented. The current status of the recently 'discovered' pentaquarks is also discussed.

We review lattice calculations of pentaquarks and discuss issues pertaining to interpolation fields, distinguishing the signal of pentaquarks from those of the KN scattering states, chiral symmetry, and ghost state contaminations.

The results of pentaquark searches at the B-factories are reviewed. No pentaquark signal has been seen; the resulting bounds (on pentaquark production rates, branching fractions, and widths) vary in strength, and in their relationship to positive results from other experiments.

FOCUS is a photoproduction experiment designed to reconstruct charm particles and to study their decays. Data was collected at Fermilab during the 1996-97 fixed-target run. We present recent results on semileptonic meson decays and a search for pentaquarks.

We consider an imaginary time functional integral formulation of a two-flavor, 3+1 lattice QCD model with Wilson's action and in the strong coupling regime (with a small hopping parameter, κ > 0, and a much smaller plaquette coupling, , so that the quarks and glueballs are heavy). The model has local SU(3)_c gauge and global SU(2)_f flavor symmetries, and incorporates the corresponding part of the eightfold way particles: baryons (mesons) of asymptotic mass ≈-3 ln κ(≈-2 ln κ). We search for pentaquark states as meson–baryon bound states in the energy–momentum spectrum of the model, using a lattice Bethe–Salpeter equation. This equation is solved within a ladder approximation, given by the lowest nonvanishing order in κ and β of the Bethe–Salpeter kernel. It includes order κ² contributions with a exchange potential together with a contribution that is a local-in-space, energy-dependent potential. The attractive or repulsive nature of the exchange interaction depends on the spin of the meson–baryon states. The Bethe–Salpeter equation presents integrable singularities, forcing the couplings to be above a threshold value for the meson and the baryon to bind in a pentaquark. We analyzed all the total isospin sectors, I = 1/2, 3/2, 5/2, for the system. For all I, the net attraction resulting from the two sources of interaction is not strong enough for the meson and the baryon to bind. Thus, within our approximation, these pentaquark states are not present up to near the free meson–baryon energy threshold of ≈-5 ln κ. This result is to be contrasted with the spinless case for which our method detects meson–baryon bound states, as well as for Yukawa effective baryon and meson field models. A physical interpretation of our results emerges from an approximate correspondence between meson–baryon bound states and negative energy states of a one-particle lattice Schrödinger Hamiltonian.

We have investigated the Regge trajectories of exotic hadrons by considering different possible pentaquark configurations with finite quark mass in the flux tube model. Significant deviation is observed in the linear behavior of the Regge trajectories for pentaquark systems in view of the universal value of the Regge slope parameter for hadrons. The modified Regge trajectories are also compared with the available experimental and lattice data. It is observed that the nonlinear Regge trajectories of such pentaquark systems can be well described by the relativistic corrections in view of the current quark masses and the high rotational speed of the quarks at the end of flux tube structure.

In recent years, many tetraquarks and pentaquarks have been discovered by various experimental groups and $X(3872)$, $Z_c(3900)$, $X(4430)$, $P_c^{+}(4312)$, $P_c^{+}(4457)$ are some of the interesting observed tetraquark and pentaquark states. The Regge trajectories of some such states are studied in view of the flux tube model of hadrons with finite quark masses. The effect of flux tube (or string) length variation on the Regge trajectories of these states is analyzed in detail. It is observed that for a fixed angular momentum, the string length has a constant value. Some other states are also proposed and the results obtained are then compared with the studies by others. Our findings correspond rather well with those of other researchers and with those of the experiment.

In this report, I discuss some of the most recent lattice spectroscopy calculations of hadrons and hadronic resonances involving charm quarks, with special emphasis on those that are relevant from an experimental perspective.