arXiv subjects
Publications and source records attributed to Jean-Marc Richard.
We revisit the role of color mixing in the quark-model calculation of tetraquark states, and compare simple pairwise potentials to more elaborate string models with three- and four-body forces. We attempt to disentangle the improved dynamics of confinement from the approximations made in the treatment of the internal color degrees of freedom.
In several mechanisms proposed for multiquark binding, the flavor content of the quark configuration plays a very important role. We shall review some past or recent results on multiquarks dealing with the chromomagnetic interaction and with the spin-independent potential among quarks.
The strong-isospin violation in $ψ(3770)\rightarrow J/ψ+ π^0$ via intermediate $D$ meson loops is investigated in an effective Lagrangian approach. In this process, there is only one $D$-meson loop contributing to the absorptive part, and the uncertainties due to the introduction of form factors can be minimized. With the help of QCD spectral sum rules (QSSR), we extract the $J/ψDD^*$ form factor as an implement from the first principle of QCD. The $DD^*π^0$ form factor can be well determined from the experimental data for $D\rightarrowπlν$. The exploration of the dispersion relation suggests the dominance of the dispersive part via the intermediate $D$ meson loops even below the open charm threshold. This investigation could provide further insights into the puzzling question on the mechanisms for $ψ(3770)\to$ non-$D\bar{D}$ transitions.
This document contains a review on the quark model, prepared for lectures at the Niccolo Cabeo School at Ferrara in May 2012. It includes some historical aspects, the spectral properties of the 2-body and 3-body Schroedinger operators applied to mesons and baryons, the link between meson and baryon spectra, the role of flavour independence, and the speculations about stable or metastable multiquarks. The analogies between few-charge systems and few-quark bound states will be underlined.
The stability of systems containing six quarks or antiquarks is studied within a simple string model inspired by the strong-coupling regime of quantum chromodynamics and used previously for tetraquarks and pentaquarks. We discuss both six-quark $(q^6)$ and three-quark--three-antiquark $ (q^3\bar q{}^3)$ states. The quarks are assumed to be distinguishable and thus not submitted to antisymmetrization. It is found that the ground state of $(q^6)$ is stable against dissociation into two isolated baryons. For the case of $ (q^3\bar q{}^3)$, our results indicate the existence of a bound state very close to the threshold. The investigations are extended to $(q^3Q^3)$ and $(Q^3\bar q^3)$ systems with two different constituent masses, and their stability is discussed as a function of the mass ratio.
Two topics are briefly reviewed in this talk: the decay of flavored hadrons or quarkonium states involving a baryon--antibaryon pair, and the spectroscopy of heavy baryons containing one, two or three heavy quarks. Some prospects for exotic heavy baryons are also discussed.
A brief review is first presented of attempts to predict stable multiquark states within current models of hadron spectroscopy. Then a model combining flip-flop and connected Steiner trees is introduced and shown to lead to stable multiquarks, in particular for some configurations involving several heavy quarks and bearing exotic quantum numbers.
The pentaquark is studied in a simple model of confinement where the quarks and the antiquark are linked by flux tubes of minimal cumulated length, and the Coulomb-like interaction, the spin-dependent terms and the antisymmetrization constraints are neglected.. The ground-state is found to be stable against spontaneous dissociation into a meson and a baryon, both in the case of five equal-mass constituents and for a static quark or antiquark surrounded by four equal masses.
About 120 baryons and baryon resonances are known, from the abundant nucleon with $u$ and $d$ light-quark constituents up to the recently discovered $Ω_b^-=bss$, and the $Ξ_b^-=bsd$ which contains one quark of each generation. In spite of this impressively large number of states, the underlying mechanisms leading to the excitation spectrum are not yet understood. Heavy-quark baryons suffer from a lack of known spin-parities. In the light-quark sector, quark-model calculations have met with considerable success in explaining the low-mass excitations spectrum but some important aspects like the mass degeneracy of positive-parity and negative-parity baryon excitations are not yet satisfactorily understood. At high masses, above 1.8 GeV, quark models predict a very high density of resonances per mass interval which is not observed. In this review, issues are identified discriminating between different views of the resonance spectrum; prospects are discussed how open questions in baryon spectroscopy may find answers from photo- and electro-production experiments which are presently carried out in various laboratories.
We discuss model-independent constraints on spin observables in exclusive and inclusive reactions, with special attention to the case of photoproduction.
We investigate the domain of masses for which a state with total orbital momentum L=1 and unnatural parity $P=+1$ exists for the Coulomb systems $(m_1^+,m_2^-,m_3^-)$.
The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$, cannot be achieved using a mere product of individual electron wave functions, and requires instead an explicit account for the anticorrelation among the two electrons. The wave function proposed by Chandrasekhar is revisited, where the permutation symmetry is first broken and then restored by a counter-term. More delicate problems can be studied using the same strategy: the stability of hydrogen-like ions $(M^+,m^-,m^-)$ for any value of the proton-to-electron mass ratio $M/m$; the energy of the lowest spin-triplet state of helium and helium-like ions; the stability of the doubly-excited hydrogen ion with unnatural parity. The positronium molecule $(e^+,e^+,e^-,e^-)$, which has been predicted years ago and discovered recently, can also be shown to be stable against spontaneous dissociation, though the calculation is a little more involved. Emphasis is put on symmetry breaking which can either spoil or improve the stability of systems.
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a function of the momentum is also derived for longer-range power-law potentials which do not fulfill these conditions.
The linear confinement in quarkonium is generalised as a minimal tree, with interesting geometrical properties. This model binds tetraquarks more easily than the additive model used in earlier investigations.
The linear potential binding a quark and an antiquark in mesons is generalized to baryons and multiquark configurations as the minimal length of flux tubes neutralizing the color, in units of the string tension. For tetraquark systems, i.e., two quarks and two antiquarks, this involves the two possible quark--antiquark pairings, and the Steiner tree linking the quarks to the antiquarks. A novel inequality for this potential demonstrates rigorously that within this model the tetraquark is stable in the limit of large quark-to-antiquark mass ratio.
A new investigation is done of the possibility of binding the "dodecatoplet", a system of six top quarks and six top antiquarks, using the Yukawa potential mediated by Higgs exchange. A simple variational method gives a upper bound close to that recently estimated in a mean-field calculation. It is supplemented by a lower bound provided by identities among the Hamiltonians describing the system and its subsystems.
Positivity constrains the allowed domain for sets of spin observables in exclusive or inclusive reactions. Examples are given for strangeness-echange reactions and photoproduction.
Model-independent identities and inequalities relating the various spin observables of a reaction are reviewed in a unified formalism, together with their implications for dynamical models, their physical interpretation, and the quantum aspects of the information carried by spins, in particular entanglement. These constraints between observables can be obtained from the explicit expression of the observables in terms of a set of amplitudes, a non-trivial algebraic exercise which can be preceded by numerical simulation with randomly chosen amplitudes, from anticommutation relations, or from the requirement that any polarisation vector is less than unity. The most powerful tool is the positivity of the density matrices describing the reaction or its crossed channels, with a projection to single out correlations between two or three observables. For the exclusive reactions, the cases of the strangeness-exchange proton-antiproton scattering and the photoproduction of pseudoscalar mesons are treated in some detail: all triples of observables are constrained, and new results are presented for the allowed domains. The positivity constraints for total cross-sections and single-particle inclusive reactions are reviewed, with application to spin-dependent structure functions and parton distributions. The corresponding inequalities are shown to be preserved by the evolution equations of QCD.