Quark-Model Baryon-Baryon Interaction and its Applications to Hypernuclei

The quark-model baryon-baryon interaction fss2, proposed by the Kyoto-Niigata group, is a unified model for the complete baryon octet (B_8=N, Lambda, Sigma and Xi), which is formulated in a framework of the (3q)-(3q) resonating-group method (RGM) using the spin-flavor SU_6 quark-model wave functions and effective meson-exchange potentials at the quark level. Model parameters are determined to reproduce properties of the nucleon-nucleon system and the low-energy cross section data for the hyperon-nucleon scattering. Due to the several improvements including the introduction of vector-meson exchange potentials, fss2 has achieved very accurate description of the NN and YN interactions, comparable to various one-boson exchange potentials. We review the essential features of fss2 and our previous model FSS, and their predictions to few-body systems in confrontation with the available experimental data. Some characteristic features of the B_8 B_8 interactions with the higher strangeness, S=-2, -3, -4, predicted by fss2 are discussed. These quark-model interactions are now applied to realistic calculations of few-body systems in a new three-cluster Faddeev formalism which uses two-cluster RGM kernels. As for the few-body systems, we discuss the three-nucleon bound states, the Lambda NN-Sigma NN system for the hypertriton, the alpha alpha Lambda system for 9Be Lambda, and the Lambda Lambda alpha system for 6He Lambda Lambda.Comment: 20 pages, 12 figures, 18th Nishinomiya Yukawa Memorial Symposium on Strangeness in Nuclear Matter, 4 - 5 December 2003, Nishinomiya, Japan. (to be published in Prog. Theor. Phys. Suppl.

Addendum: Triton and hypertriton binding energies calculated from SU_6 quark-model baryon-baryon interactions

Previously we calculated the binding energies of the triton and hypertriton, using an SU_6 quark-model interaction derived from a resonating-group method of two baryon clusters. In contrast to the previous calculations employing the energy-dependent interaction kernel, we present new results using a renormalized interaction, which is now energy independent and reserves all the two-baryon data. The new binding energies are slightly smaller than the previous values. In particular the triton binding energy turns out to be 8.14 MeV with a charge-dependence correction of the two-nucleon force, 190 keV, being included. This indicates that about 350 keV is left for the energy which is to be accounted for by three-body forces.Comment: 4 pages, 1 figur

Three-Cluster Equation Using Two-Cluster RGM Kernel

We propose a new type of three-cluster equation which uses two-cluster resonating-group-method (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. For bound-state problems, this equation is straightforwardly transformed to the Faddeev equation which uses a modified singularity-free T-matrix constructed from the two-cluster RGM kernel. The approximation of the present three-cluster formalism can be examined with more complete calculation using the three-cluster RGM. As a simple example, we discuss three di-neutron (3d') and 3 alpha systems in the harmonic-oscillator variational calculation. The result of the Faddeev calculation is also presented for the 3' system.Comment: 12 pages, no figur

Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator κ\kappa-(ET)2_2Cu2_2(CN)3_3

The static and dynamic local spin susceptibility of the organic Mott insulator $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$, a model material of the spin- 1/2 triangular lattice, is studied by $^{13}$C NMR spectroscopy from room temperature down to 20 mK. We observe an anomalous field-dependent spectral broadening with the continuous and bipolar shift distribution, appearing without the critical spin fluctuations. It is attributable to spatially nonuniform magnetizations induced in the spin liquid under magnetic fields. The amplitude of the magnetization levels off below 1 K, while the low-lying spin fluctuations survive toward the ground state, as indicated by the temperature profile of the relaxation rates.Comment: 4 pages, 4 figure

Contributions of 2π2\pi-exchange, 1π1\pi-exchange, and contact three-body forces in NNLO ChEFT to Λ3_\Lambda^3H

Faddeev calculations of hypertriton ($_\Lambda^3$H) separation energy are performed, incorporating all next-to-next-to-leading-order $\Lambda$NN three-body forces (3BFs) in chiral effective field theory: $2\pi$-exchange, $1\pi$-exchange, and contact interactions. The $1\pi$-exchange and contact interactions are rewritten in a form suitable for evaluating partial-wave matrix elements. The $\Lambda$-deuteron folding potentials constructed from these 3BFs are evaluated to demonstrate their contributions to \h3t. The $1\pi$-exchange interaction provides an attractive effect in which the d-state component of the deuteron wave function plays an important role. The attractive contribution tends to cancel the repulsive ones from the $2\pi$-exchange and contact 3BFs. Faddeev calculations show that the net effect of the 3BFs to the \h3t separation energy is small in a range between $-5$ to $+20$ keV, depending on the NN interaction used. Although these results are based on speculative low-energy constants, they can serve as a reference for further investigations.Comment: 6 pages, 4 figure

Faddeev Calculation of Λ3_\Lambda^3H Incorporating 2{\pi} Exchange Λ\LambdaNN Interaction

Faddeev calculations of hypertriton ($_\Lambda^3$H) separation energy are performed, incorporating $2\pi$-exchange $\Lambda$NN three-baryon force. Repulsive contributions of the three-baryon force in the order of 50 $-$ 100 keV are found, depending on the NN interactions employed. The effect is not negligible compared with the small separation-energy of $_\Lambda^3$H and is essential to gauge the two-body $\Lambda$N interactions.Comment: 6 pages, 3 Figure

Partial-wave expansion of ΛNN\Lambda NN three-baryon interactions in chiral effective field theory

An expression of partial wave expansion of three-baryon interactions in chiral effective field theory is presented. The derivation follows the method by Hebeler et al. [Phys. Rev. C{\bf 91}, 044001 (2015)], but the final expression is more general. That is, a systematic treatment of the higher-rank spin-momentum structure of the interaction becomes possible. Using the derived formula, a $\Lambda$-deuteron folding potential is evaluated. This information is valuable for inferring the possible contribution of the $\Lambda NN$ three-baryon forces to the hypertriton as the basis of further studies by sophisticated Faddeev calculations. A microscopic understanding of $\Lambda NN$ three-baryon forces together with two-body $\Lambda N$ interactions is essential for the description of hypernuclei and neutron-star matter.Comment: 7 pages, 4 figure

The nonmesonic weak decay of the hypertriton

The nonmesonic decay of the hypertriton is calculated based on a hypertriton wavefunction and 3N scattering states, which are rigorous solutions of 3-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion-exchange together with heavier meson exchanges for the $\Lambda N \to N N$ transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free $\Lambda$ decay rate. Integrated as well as differential decay rates are given. The p- and n- induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.Comment: 27 pages, 20 figures, revtex, submitted to Phys. Rev.

Anisotropic charge dynamics in the quantum spin-liquid candidate κ\kappa-(BEDT-TTF)2_2Cu2_2(CN)3_3

We have in detail characterized the anisotropic charge response of the dimer Mott insulator $\kappa$-(BEDT-TTF)$_2$\-Cu$_2$(CN)$_3$ by dc conductivity, Hall effect and dielectric spectroscopy. At room temperature the Hall coefficient is positive and close to the value expected from stoichiometry; the temperature behavior follows the dc resistivity $\rho(T)$. Within the planes the dc conductivity is well described by variable-range hopping in two dimensions; this model, however, fails for the out-of-plane direction. An unusually broad in-plane dielectric relaxation is detected below about 60 K; it slows down much faster than the dc conductivity following an Arrhenius law. At around 17 K we can identify a pronounced dielectric anomaly concomitantly with anomalous features in the mean relaxation time and spectral broadening. The out-of-plane relaxation, on the other hand, shows a much weaker dielectric anomaly; it closely follows the temperature behavior of the respective dc resistivity. At lower temperatures, the dielectric constant becomes smaller both within and perpendicular to the planes; also the relaxation levels off. The observed behavior bears features of relaxor-like ferroelectricity. Because heterogeneities impede its long-range development, only a weak tunneling-like dynamics persists at low temperatures. We suggest that the random potential and domain structure gradually emerge due to the coupling to the anion network.Comment: 14 pages, 13 figure