Chiral dynamics of Σ\Sigma-hyperons in the nuclear medium

Using SU(3) chiral perturbation theory we calculate the density-dependent complex mean field $U_\Sigma(k_f)+ i W_\Sigma(k_f)$ of a $\Sigma$-hyperon in isospin-symmetric nuclear matter. The leading long-range $\Sigma N$-interaction arises from one-kaon exchange and from two-pion exchange with a $\Sigma$- or a $\Lambda$-hyperon in the intermediate state. We find from the $\Sigma N\to \Lambda N$ conversion process at nuclear matter saturation density $\rho_0 = 0.16$fm$^{-3}$ an imaginary single-particle potential of $W_\Sigma(k_{f0}) =-21.5$ MeV, in fair agreement with existing empirical determinations. The genuine long-range contributions from iterated (second order) one-pion exchange with an intermediate $\Sigma$- or $\Lambda$-hyperon sum up to a moderately repulsive real single-particle potential of $U_\Sigma(k_{f0})= 59$ MeV. Recently measured $(\pi^-,K^+$) inclusive spectra related to $\Sigma^-$-formation in heavy nuclei give evidence for a $\Sigma$-nucleus repulsion of similar size. Our results suggest that the net effect of the short-range $\Sigma N$-interaction on the $\Sigma$-nuclear mean field could be small.Comment: 7 pages, 2 figures, published in: Phys. Rev. C 71, 068201 (2005

Few-body calculations of η\eta-nuclear quasibound states

We report on precise hyperspherical-basis calculations of $\eta NN$ and $\eta NNN$ quasibound states, using energy dependent $\eta N$ interaction potentials derived from coupled-channel models of the $S_{11}$ $N^{\ast}(1535)$ nucleon resonance. The $\eta N$ attraction generated in these models is too weak to generate a two-body bound state. No $\eta NN$ bound-state solution was found in our calculations in models where Re $a_{\eta N}\lesssim 1$ fm, with $a_{\eta N}$ the $\eta N$ scattering length, covering thereby the majority of $N^{\ast}(1535)$ resonance models. A near-threshold $\eta NNN$ bound-state solution, with $\eta$ separation energy of less than 1 MeV and width of about 15 MeV, was obtained in the 2005 Green-Wycech model where Re $a_{\eta N}\approx 1$ fm. The role of handling self consistently the subthreshold $\eta N$ interaction is carefully studied.Comment: a second footnote added in v2, matching published versio

Onset of η\eta-nuclear binding in a pionless EFT approach

$\eta NNN$ and $\eta NNNN$ bound states are explored in stochastic variational method (SVM) calculations within a pionless effective field theory (EFT) approach at leading order. The theoretical input consists of regulated $NN$ and $NNN$ contact terms, and a regulated energy dependent $\eta N$ contact term derived from coupled-channel models of the $N^{\ast}(1535)$ nucleon resonance plus a regulated $\eta NN$ contact term. A self consistency procedure is applied to deal with the energy dependence of the $\eta N$ subthreshold input, resulting in a weak dependence of the calculated $\eta$-nuclear binding energies on the EFT regulator. It is found, in terms of the $\eta N$ scattering length $a_{\eta N}$, that the onset of binding \eta\,^3He requires a minimal value of Re$\,a_{\eta N}$ close to 1 fm, yielding then a few MeV $\eta$ binding in \eta\,^4He. The onset of binding \eta\,^4He requires a lower value of Re$\,a_{\eta N}$, but exceeding 0.7 fm.Comment: v4 consists of the published Physics Letters B version [31] plus Erratum ([30], Appendix A here); main results and conclusions remain intac

Faddeev calculation of a K−ppK^- p p quasi-bound state

We report on the first genuinely three-body ${\bar K}NN - \pi \Sigma N$ coupled-channel Faddeev calculation in search for quasi-bound states in the $K^- p p$ system. The main absorptivity in the $K^- p$ subsystem is accounted for by fitting to $K^- p$ data near threshold. Our calculation yields one such quasi-bound state, with $I=1/2$, $J^{\pi}=0^-$, bound in the range $B \sim 55-70$ MeV, with a width of $\Gamma \sim 95-110$ MeV. These results differ substantially from previous estimates, and are at odds with the $K^- p p \to \Lambda p$ signal observed by the FINUDA collaboration.Comment: Minor editorial revision; version accepted for publication in Phys. Rev. Let

Preference-Informed Fairness

We study notions of fairness in decision-making systems when individuals have diverse preferences over the possible outcomes of the decisions. Our starting point is the seminal work of Dwork et al. which introduced a notion of individual fairness (IF): given a task-specific similarity metric, every pair of individuals who are similarly qualified according to the metric should receive similar outcomes. We show that when individuals have diverse preferences over outcomes, requiring IF may unintentionally lead to less-preferred outcomes for the very individuals that IF aims to protect. A natural alternative to IF is the classic notion of fair division, envy-freeness (EF): no individual should prefer another individual's outcome over their own. Although EF allows for solutions where all individuals receive a highly-preferred outcome, EF may also be overly-restrictive. For instance, if many individuals agree on the best outcome, then if any individual receives this outcome, they all must receive it, regardless of each individual's underlying qualifications for the outcome. We introduce and study a new notion of preference-informed individual fairness (PIIF) that is a relaxation of both individual fairness and envy-freeness. At a high-level, PIIF requires that outcomes satisfy IF-style constraints, but allows for deviations provided they are in line with individuals' preferences. We show that PIIF can permit outcomes that are more favorable to individuals than any IF solution, while providing considerably more flexibility to the decision-maker than EF. In addition, we show how to efficiently optimize any convex objective over the outcomes subject to PIIF for a rich class of individual preferences. Finally, we demonstrate the broad applicability of the PIIF framework by extending our definitions and algorithms to the multiple-task targeted advertising setting introduced by Dwork and Ilvento

On the Stability of Λ(1405)\Lambda(1405) Matter

A hypothesis of absolutely stable strange hadronic matter composed of $\Lambda(1405)$ baryons, here denoted $\Lambda^*$, is tested within many-body calculations performed using the Relativistic Mean-Field approach. In our calculations, we employed the $\Lambda^*\Lambda^*$ interaction compatible with the $\Lambda^*\Lambda^*$ binding energy $B_{\Lambda^*\Lambda^*}=40$~MeV given by the phenomenological energy-independent $\bar{K}N$ interaction model by Yamazaki and Akaishi (YA). We found that the binding energy per $\Lambda^*$, as well as the central density in $\Lambda^*$ many-body systems saturates for mass number $A\geq120$, leaving $\Lambda^*$ aggregates highly unstable against strong interaction decay. Moreover, we confronted the YA interaction model with kaonic atom data and found that it fails to reproduce the $K^-$ single-nucleon absorption fractions at rest from bubble chamber experiments.Comment: Proceedings of the HYP2018 conference, Norfolk/Portsmouth, USA, June 24 - 29, 2018, submitted to AIP Conference Proceeding