Few-Body Hypernuclei. - dependence on NN and 3N force - separation energies based on chiral interactions - CSB of four-body hypernuclei

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1 Mitglied der Helmholtz-Gemeinschaft Few-Body Hypernuclei Andreas ogga, Forschungszentrum Jülich Perspectives of high resolution hypernuclear spectroscopy at Jefferson Lab, ewport ews, VA Motivation umerical technique Light Hypernuclei - dependence on and 3 force - separation energies based on chiral interactions - CSB of four-body hypernuclei Conclusions & Outlook

2 Hypernuclear interactions Why is understanding hypernuclear interactions interesting? phenomenologically hyperon contribution to the EOS, neutron stars, supernovae as probe to nuclear structure conceptually -Σ conversion process experimental access to explicit chiral symmetry breaking (S1987a) Σ π π π K Σ π suppressed by isospin symmetry (CSB) 2

3 Hypernuclear interactions 35 Y data, no Y bound state, large uncertainties no partial wave analysis possible Y interaction models (Jülich 89/0, ijmegen 89/97a-f, ESC, ) describe all data more than perfectly, but are not phase equivalent 1 3 SC97a SC97b SC97c SC97d SC97e SC97f SC Jülich How to further constrain the Y interactions? 3

4 Hypernuclei interactions are generally weaker than the interaction naively: core nucleus + hyperons separation energies are almost independent from (+3) interaction no Pauli blocking of in nuclei good to study nuclear structure even light hypernuclei exist in several spin states size of Y interactions? non-trivial constraints on the Y interaction even from lightest ones 3 1 H 2 + H 0 + He 0 + (from Panda@FAIR web page) H 1 + He 1 +

5 umerical technique non-rel. Schrödinger equation decomposition in five Yakubovsky components solution of the Yakubovsky equations ( ) improved convergence in terms of partial waves we carefully checked convergence with respect to partial waves, stability with respect to mesh points,... (see ogga et. al., PRL 88, (2002)) 5

6 Known results I: independendence of force separation energies E = E(core) E(hypernucleus) are not strongly dependent on the interaction Bonn B ijm ijm 93 + TM for Y interaction: SC97e (A, Kamada, Glöckle, 2002) Y interaction can be discussed independently of an and 3 force model 6

7 7 Known results II: -Σ conversion is important strong -Σ conversion process Σ π π π K Σ π suppressed by isospin symmetry strong conversion process mass difference comparable to typical momenta no π-exchange - interaction test: use t in Yakubovsky equations (here for a chiral interaction) is weaker than interaction Σs need to be explicitly included in any realistic calculation w/ Σ w/o Σ E E effective interactions are not useful to study Y forces

8 Known results III: model dependence in MeV in MeV in fm SC97d % SC97e % SC97f % SC % Jülich % Expt ?? - none of these interaction models predicts the hypernuclei correctly no strict relation of the scattering lengths to any separation energy With this in mind: qualitative study of predications based on LO and LO interactions w/o SU(3) breaking first attempt to estimate 2LO/3BF contribution by variation of λ qualitative study of CSB of H He mostly from (A, Kamada, Glöckle, 2002) 8

9 Chiral & Y interactions reminder: BB force 3B force B force 5 /Y short range parameters 26 /Y short range parameters (from Epelbaum, 2008) additional constraints required (only 35 data, but 26 parameters at LO) SU(3) broken by physical mπ,mk,mη no SU(3) breaking in contact terms (although expected) 23 contact terms no SU(3) breaking in Fπ,FK,Fη minimize P-waves and 1 P1-3 P1 mixing realizations for λ = MeV one possible realization at LO more constraints required only 13 parameters determined by data (J. Haidenbauer et al., 2013 & previous talk) 9

10 10 Chiral interactions at LO, LO 1 3 LO LO LO Jülich 0 LO Jülich (Polinder et al., PA 779, 2 (2006), Haidenbauer et al., PA 915, 2 (2013) see Johann Haidenbauer s talk) hypertriton binding energy provides constraint on spin dependence of the Y interaction better description of the energy dependence in LO significantly increased scattering lengths in LO compared to LO

11 How important are 3B forces? BB force 3B force B force? (from Epelbaum, 2008) we explicitly include the Σ (otherwise the 3BF should be LO) the missing 3BF are either short-ranged or induced by decouplet baryons (Σ*, Δ) Important tool to estimate 3BF in absence of explicit calculations: cutoff variations allow one to get lower bounds on their contribution 11

12 Hypertriton separation energies separation energies: E = E(core) E(hypernucleus) singlet scattering length for one cutoff chosen so that hypertriton binding energy is OK cutoff variation is lower bound for magnitude of higher order contributions correlation with χ 2 of Y interaction? long range 3BFs need to be explicitly estimated 12

13 Separation energies for H LO/LO results: LO uncertainty in 0 + is underestimated by cutoff variation LO results in line with model results, implies underbinding long range 3BFs need to be explicitly estimated but: for this version of LO, results are inconsistent with experiment note: this LO does not allow for SU(3) breaking in contact part of Y ad-hoc p-waves 13

14 Separation energies of H LO/LO cutoff dependence does not indicate 3BF contribution long range 3BF needs to be studied results cutoff dependence for small? related to non-optimal description of data? LO/LO: splitting stabilizes but: LO results are inconsistent with experiment 1

15 15 CSB at LO & for model interactions Contributions to the difference E H E He 0 + state 1 + state force contribution due to small deviation of Coulomb Y force contribution: SC89 CSB is strong LO CSB is zero, only Coulomb acts (Σ component) kinetic energy contribution is driven by Σ component

16 16 CSB and Σ probability Σ probabilities in H 0 + state 1 + state spin/isospin structure of hypernuclei drives Σ components kinetic energy contribution is given linearly by differences of Σ components / m m +

17 Conclusions & Outlook Y interactions are interesting and not well understood -Σ conversion, explicit chiral symmetry breaking well known: Y models fail LO of chiral interactions: still freedom to adjust Y forces but: further estimates of three-baryon interactions (in progress) hypernuclei are an essential source of information on Y it is not trivial to describe the simplest systems consistently experiments for very light hypernuclei are important The data needs to be accurate (better data for the hypertriton?) We need to be sure that these data are reliable. CSB for four-body hypernuclei is a puzzle obviously related to -Σ conversion Can we engineer chiral interactions with different conversion strength? experiments for very light hypernuclei are important Is today s data reliable? extension of complete calculations to larger systems (access more data) (see also Roland Wirth s talk) 17