The string of variable density: perturbative and non-perturbative results

We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which hold regardless of the inhomogeneity of the string. Working on specific examples we obtain very accurate approximations which are compared both with the results of WKB method and with the numerical results obtained with a collocation approach. Finally, we show that the asymptotic behaviour of the energies of the string obtained with perturbation theory, worked to second order in the inhomogeinities, agrees with that obtained with the WKB method and implies a different functional dependence on the density that in two and higher dimensions.Comment: 28 pages, 3 tables, 6 figure

Hadronic interactions from effective chiral Lagrangians of quarks and gluons

Effective chiral Lagrangians involving constituent quarks, Goldstone bosons and long-distance gluons are believed to describe the strong interactions in an intermediate energy region between the confinement scale and the chiral symmetry breaking scale. Baryons and mesons in such a description are bound states of constituent quarks. We discuss the combined use of the techniques of effective chiral field theory and of the field theoretic method known as Fock-Tani representation to derive effective hadron interactions. The Fock-Tani method is based on a change of representation by means of a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation on the microscopic quark-quark interaction derived from a chiral effective Lagrangian leads to chiral effective interactions describing all possible processes involving hadrons and their constituents. The formalism is illustrated by deriving the one-pion-exchange potential between two nucleons using the quark-gluon effective chiral Lagrangian of Manohar and Georgi. We also present the results of a study of the saturation properties of nuclear matter using this formalism

Production of charmed baryons in pˉp\bar p p collisions close to their thresholds

Cross sections for the charm-production reactions $\bar p p \to \bar \Lambda_c^- \Sigma_c^+$, $\bar \Sigma_c\Sigma_c$, $\bar \Xi_c\Xi_c$, and $\bar \Xi_c'\Xi_c'$ are presented, for energies near their respective thresholds. The results are based on a calculation performed in the meson-exchange framework in close analogy to earlier studies of the J\"ulich group on the strangeness-production reactions $\bar p p \to \bar \Lambda\Sigma$, $\bar \Sigma\Sigma$, $\bar \Xi\Xi$ by connecting the two sectors via SU(4) flavor symmetry. The cross sections are found to be in the order of $0.1 - 1$ $\mu b$ at energies of $100$ MeV above the respective thresholds, for all considered channels. Complementary to meson-exchange, where the charmed baryons are produced by the exchange of $D$ and $D^*$ mesons, a charm-production potential derived in a quark model is employed for assessing uncertainties. The cross sections predicted within that picture turned out to be significantly smaller.Comment: 17 pages, 7 figure

Charm production in antiproton-proton annihilation

We study the production of charmed mesons (D) and baryons (Lambda_c) in antiproton-proton (app) annihilation close to their respective production thresholds. The elementary charm production process is described by either baryon/meson exchange or by quark/gluon dynamics. Effects of the interactions in the initial and final states are taken into account rigorously. The calculations are performed in close analogy to our earlier study on app -> antiLambda-Lambda and app -> antiK-K by connecting the processes via SU(4) flavor symmetry. Our predictions for the antiLambda_c-Lambda_c production cross section are in the order of 1 to 7 mb, i.e. a factor of around 10-70 smaller than the corresponding cross sections for antiLambda-Lambda However, they are 100 to 1000 times larger than predictions of other model calculations in the literature. On the other hand, the resulting cross sections for antiD-D production are found to be in the order of 10^{-2} -- 10^{-1} microbarn and they turned out to be comparable to those obtained in other studies.Comment: 5 pages, 2 figures, Contribution to the proceedings of the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, 30 August - 3 September 201

The ψ\psi(3770) resonance and its production in pˉp→DDˉ\bar pp \to D \bar D

The production of a $D\bar D$ meson-pair in antiproton-proton ($\bar p p$) annihilation close to the production threshold is investigated, with special emphasis on the role played by the $\psi$(3770) resonance. The study is performed in a meson-baryon model where the elementary charm production process is described by baryon exchange. Effects of the interactions in the initial and final states are taken into account rigorously, where the latter involves also those due to the $\psi$(3770). The predictions for the $D\bar D$ production cross section are in the range of 30 -- 250 nb, the contribution from the $\psi$(3770) resonance itself amounts to roughly 20 -- 80 nb.Comment: 6 pages, 6 figure

Production of charmed pseudoscalar mesons in antiproton-proton annihilation

We study the production of charmed mesons (D, D_s) in antiproton-proton annihilation close to the reaction thresholds. The elementary charm production process is described by baryon exchange and in the constituent quark model, respectively. Effects of the interactions in the initial and final states are taken into account rigorously. The calculations are performed in close analogy to our earlier study on pbarp to KbarK by connecting the processes via SU(4) flavor symmetry. Our predictions for the DDbar production cross section are in the order of 10^{-2} -- 10^{-1} mu b. They turned out to be comparable to those obtained in other studies. The cross section for a D_sD_s pair is found to be of the same order of magnitude despite the fact that its production in pbarp scattering requires a two-step process.Comment: 15 pages, 13 figures, some typos corrected, some comments adde

Scattering of charmed baryons on nucleons

Chiral effective field theory is utilized for extrapolating results on the $\Lambda_c N$ interaction, obtained in lattice QCD at unphysical (large) quark masses, to the physical point. The pion-mass dependence of the components that constitute the $\Lambda_c N$ potential up to next-to-leading order (pion-exchange diagrams and four-baryon contact terms) is fixed by information from lattice QCD simulations. No recourse to SU(3) or SU(4) flavor symmetry is made. It is found that the results of the HAL QCD Collaboration for quark masses corresponding to $m_\pi = 410$--$570$ MeV imply a moderately attractive $\Lambda_c N$ interaction at $m_\pi = 138$ MeV with scattering lengths of $a\approx -1$ fm for the $^1S_0$ as well as the $^3S_1$ partial waves. For such an interaction the existence of a charmed counterpart of the hypertriton is unlikely but four- and/or five-baryons systems with a $\Lambda_c$ baryon could be indeed bound.Comment: 7 pages, 2 figures; table added, several comments adde

The Gerasimov-Drell-Hearn sum rule and the single-pion photoproduction multipole E0+ close to threshold

The long-standing discrepancy between the Gerasimov-Drell-Hearn sum rule and the analysis of pion photoproduction multipoles is greatly diminished by use of s-wave multipoles that are in accord with the predictions of chiral perturbation theory and describe the experimental data in the threshold region. The remaining difference may be due to contributions of channels with more pions and/or heavier mesons whose contributions to the sum rule remain to be investigated by a direct measurement of the photoabsorption cross sections.Comment: 9 pages, latex, 1 figure, to appear in Phys. Rev.