arXiv subjects
Publications and source records attributed to Jean-Marc Richard.
Positivity constraints have proved to be important for spin observables of exclusive reactions involving polarized initial and final particles. Attention is focused in this note on the photoproduction of pseudoscalar mesons from spin 1/2 baryons, more specifically gamma+ N -> K+ Lambda, gamma+ N -> K Sigma, for which new experimental data are becoming available.
The chromomagnetic interaction, with full account for flavour-symmetry breaking, is applied to S-wave configurations containing two quarks and two antiquarks. Phenomenological implications are discussed for light, charmed, charmed and strange, hidden-charm and double-charm mesons, and extended to their analogues with beauty.
A presentation and a generalisation are given of the phenomenon of level rearrangement, which occurs when an attractive long-range potential is supplemented by a short-range attractive potential of increasing strength. This problem has been discovered in condensate-matter physics and has also been studied in the physics of exotic atoms. A similar phenomenon occurs in a situation inspired by quantum dots, where a short-range interaction is added to an harmonic confinement.
The positivity conditions of the spin density matrix constrain the spin observables of the reaction antiproton-proton to AntiLambda-Lambda, leading to model-independent, non-trivial inequalities. The formalism is briefly presented and examples of inequalities are provided.
The dynamics of the strangeness-exchange reactions antiproton-proton to AntiLambda-Lambda, AntiLambda-Sigma or AntiSigma-Sigma is discussed, either at the hadron level, in terms of strange-meson exchange, or at the quark level, in terms of quark--antiquark creation or annihilation.
The binding energy of three identical bosons is estimated by coupled differential equations which generalise the Feshbach--Rubinow approximation. This method turns out to be rather efficient, especially in the limit of vanishing binding.
A review is first presented of the Hall--Post inequalities relating $N$-body to $(N-1)$-body energies of quantum bound states. These inequalities are then applied to delimit, in the space of coupling constants, the domain of Borromean binding where a composite system is bound while smaller subsystems are unbound.
We discuss model-independent inequalities for the spin observables in the reaction $\bar\mathrm{p}\mathrm{p}\to\barΛΛ$, which have been measured at CERN with a polarised proton target.
The $(p,d,\bar{p},\bar{d})$ molecule, with a proton, a deuteron and their antiparticles, is stable againt spontaneous dissociation, but none of its three-body subsystems are stable. This molecule should be built by combining two atoms, for instance a protonium $(p\bar{p})$ and its heavier analogue $(d\bar{d})$. Most other four-body molecules have at least one stable three-body subsystem and thus can be built by adding the constituents one by one.
We review the weak-decay and spectroscopy properties of baryons with two charmed quarks. We also present the convergent speculations on exotic mesons $(QQ\bar{q}\bar{q})$ with two heavy quarks and two light antiquarks.
For some values of the constituent masses m_i, the hydrogen-like molecule (m_1^+,m_2^+,m_3^-,m_4^-) is stable with respect to spontaneous dissociation into two neutral atoms, while none of its three-body subsystems such as (m_1^+,m_2^+,m_3^-) is stable. This occurs in particular in the neighbourhood of the (M^+,m^+,M^-,m^-) configuration with M/m=2, as for instance for the molecule (p,d,\bar{p},\bar{d}) involving an antiproton and an antideuteron.
A brief review is presented of the stability domain of three- and four-charge ground-states when the constituent masses vary. Rigorous results are presented, based on the scaling behavior and the convexity properties deduced from the variational principle. They are supplemented by accurate numerical computations.
The Hall--Post inequalities provide lower bounds on $N$-body energies in terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to be tested with exactly-solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for $N$ spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillator
We re-examine V. Gribov's theorem of 1960 according to which the total cross-section cannot approach a finite non-zero limit with, at the same time, a diffraction peak having a finite slope. We are very close to proving by an explicit counter-example that elastic unitarity in the elastic region is an essential ingredient of the proof. By analogy, we raise the question of the saturation of the Froissart-Martin bound, for which no examples incorporating elastic unitarity exist at the present time.
Some rigorous results can be derived using a very simple approach to hadron spectroscopy, in which a static potential is associated with non-relativistic kinematics. Several regularities of the experimental spectrum are explained by such models. It is underlined that certain methods developed for hadronic physics have found applications in other fields, in particular atomic physics. A few results can be extended to cases involving spin-dependent forces or relativistic kinematics.
We estimate the ratio $R=g_{3}/g_{2}$ of the critical coupling constants $g_{2}$ and $g_{3}$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give $R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the other hand, for an attractive well protected by an external repulsive barrier, the ratio approaches the rigorous lower bound $R=2/3$. We also present results for N=4 bosons, sketch the extension to $N>4$, and discuss various consequences.
We review ideas and speculations concerning possible bound states or resonances coupled to the nucleon-antinucleon channel.
It is recalled that spin-observables in the strangeness-exchange reaction $\bar{p}{p} \to \barΛΛ$ are not independent but are related to each other by simple algebraic relations. This provides constraints on the existing data on polarization and spin-correlation coefficients, and also on the forthcoming data obtained using a polarized proton target.