International workshop Strangeness Nuclear Physics 2017 March, 12th-14th, 2017, Osaka Electro-Communication University, Japan. quark mean field theory

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1 International workshop Strangeness Nuclear Physics 2017 March, 12th-14th, 2017, Osaka Electro-Communication University, Japan The strangeness quark mean field theory Jinniu Hu School of Physics, Nankai University J.H, A. Li, H. Shen, and H. Toki, Prog. Theor. Exp. Phys (2014) 013D02 J.H, A. Li, H. Toki, and W. Zuo, Phys. Rev. C 89 (2014) X. Xing, J.H., and H. Shen, Phys. Rev. C 94 (2016) X. Xing, J.H., and H. Shen, in preparation 11/20/13 14/03/2017 Jinniu Hu 1

2 Outline! Introduction! Strangeness quark mean field theory! Numerical results and discussions! Summary and Perspectives

3 Strangeness nuclear physics Hadrons Compact star Baryon-baryon force n Hypernuclei n p p n n Λ p n A.Gal, E. V. Hungerford, and D. J. Millener, Rev. Mod. Phys. 88(2016) /03/2017 Jinniu Hu

4 Theoretical methods ab initio methods H. Nemura, Y. Akaishi, and Y. Suzuki, Phys. Rev. Lett. 89(2002) E. Hiyama and T. Yamada, Prog. Part. Nucl. Phys. 63(2009)339 D. Lonardoni, S. Gandolfi, and F. Pederiva, Phys. Rev. C 87(2013)041303(R) R. Wirth, et al. Phys. Rev. Lett. 113(2014) Shell model D. J. Millener, Nucl. Phys. A 881(2012)298 Skyrme Hartree-Fock model M. Rayet, Ann. Phys. (NY) 102(1976)226 X. R. Zhou, et al. Phys. Rev. C 76(2007) H.-J. Schulze and T. Rijken, Phys. Rev. C 88(2013) Relativistic mean-field model R. Brockmann and W. Weise, Phys. Lett. B 69(1977)167 H. Shen, F. Yang, and H. Toki, Prog. Theor. Phys. 115(2006)325 R. L. Xu, C. Wu, and Z. Z. Ren, J. Phys. G 39(2012) T. T. Sun, et al., Phys. Rev. C 94(2016) /03/2017 Jinniu Hu

5 Relativistic many-body theories from quark level baryons are not point particles! baryon properties change in medium! quark-gluon plasma!... Hadron model Self-consistently σ,ω,ρ many-body method

6 Quark meson coupling (QMC) model K. Tsushima, et al. Nucl. Phys. A 630(1998)691 Friedberg-Lee model e) Fractions of leptons and baryons in NS nction of total baryon density, for both (upper fm 2 and (lower panel) k s = 1100 MeV/fm 2 J. S. Liang and H. Shen, Phys. Rev. C88 (2013) Quark mean field (QMF) model ppear at ρ = 0.46 fm 3,followedby 0 6 fm 3.Thesetwovaluesdonotchange hoose the SU(3) breaking potential or The fractions of hyperons increase with 1.25 fm 3,thefractionsof and are e fractions of protons and neutrons., ear until very high density, up to 2.0 fm 3. ron sequences are essentially different lculations using the quark counting rule 13], where would be the first hyperon r density of, asisalsothecaseforthe 28]. pressure of β-equilibrated matter as a nsity in Fig. 5.Thesolidcurverepresents e hyperon, and the dot-dashed curve is erons. The EoS becomes softer after the geness freedom. s are calculated by using the EoSs with obtained from the EQMF theory. The tions are plotted in Fig. 6. Itisfound ass of the NSs, including hyperons, is le it is around 1.88M without hyperons. H. Shen, H. Toki, Nucl. Phys. A 707 (2002) 469 J.H, A. Li, H. Shen, and H. Toki, Prog. Theor. Exp. Phys. 2014(2014) 013D02 J.H, A. Li, H. Toki, and 1.88M W. Zuo, in the present Phys. QMF Rev. model, C one 89(2014) would not expect that 14/03/2017 Jinniu Hu studies [54 56] based on developed realistic baryon-baryon interactions [38]. Since the NS maximum mass is determined by the highdensity region of EoS, a stiffer EoS generates a heavier NS. It is necessary to introduce the extra repulsive mechanism in the QMF scheme, as theoretical efforts are done in the RMF framework in Refs. [3,9 12]. Also, in a recent work of the QMC model [23], besides the usual σ, ω, ρ fields, a nonlinear ω ρ term was introduced (with a new coupling parameter v )inthelagrangiantocorrectthestiffbehavior of the symmetry energy at large densities. For example, the slope parameter L of the symmetry energy was lowered from MeV to MeV for v = 0.1. As a result, they got a softer nuclear EoS at high densities (which hinders the onset of hyperons) and a harder EoS with hyperons. Strangeness system with quark model With the help of the reduction of the attractiveness of potential U,a2M NS was finally possible in the model. Similar extensions can be done in the QMF model. However, since the maximum mass of the pure NSs is as heavy as Properties of hypernuclei and neutron star with QMF model FIG. 6. (Color online) Gravitational masses of NSs are shown as» Chiral symmetry» Gluon exchange Miss!

7 Outline! Introduction! Strangeness quark mean field theory! Numerical results and discussions! Summary and Perspectives

8 Quark level Constituent quark in Dirac equation [ i r + m i + U(r)]q i (r) =" i q i (r) where, the effective quark mass is m i = m i + g i and effective single particle energy is " i = " i g! i g i 3 Confinement potential U(r) = 1 2 (1 + 0 )(ar 2 + V 0 ) Center-of-mass corrections hb 3X i=1 X. Xing, J.H., and H. Shen, Phys. Rev. C 94 (2016) (i){ 1 3X 3 (i) ~p j (1 + 0 (i))[u(r i ) U( i )]} Bi j=1

9 Quark level Pionic self-energy correction Gluon correction Color-electric Color-magnetic V δmb π = k B ( E B ) E g = 1 8π i,j ( E B ) M g = 1 8π BB j w k V BB j 8 d 3 r i d 3 r j r i r j a=1 i,j 8 a=1 B J 0a i ( r i )Jj 0a ( r j ) B, d 3 r i d 3 r j r i r j B J a i ( r i) J a j ( r j) B. Quark color current density J µa i (x) =g c ψq (x)γ µ λ a i ψ q(x) Baryon mass M B = E 0 B ϵ c.m. + δm π B +( E B ) E g +( E B ) M g

10 Baryon level Strangeness QMF Lagrangian L QMF [ = ψ iγ µ µ MN g ω ωγ 0 g ρ ρτ 3 γ 0 e (1 τ ] 3) Aγ 0 ψ 2 [ + ψ H iγ µ µ MH gh ω ωγ0 + f ] ω H σ 0i i ω ψ H 2M H 1 2 ( σ)2 1 2 m2 σ σ2 1 3 g 2σ g 3σ ( ω) m2 ω ω c 3ω ( ρ) m2 ρ ρ ( A)2, Equations of motion for mesons 14/03/2017 Jinniu Hu Dirac equations for baryons [ σ m 2 σσ g 2 σ 2 g 3 σ 3 = M N σ ψψ + M H σ ψ H ψ H, ω m 2 ω ω c 3ω 3 = g ω ψγ 0 ψ g H ω ψ H γ 0 ψ H + ρ m 2 ρ ρ = g ρ ψτ 3 γ 0 ψ, A = e ψ (1 τ 3) γ 0 ψ. 2 iγ µ µ MN g ωωγ 0 g ρ ρτ 3 γ 0 e (1 τ ] 3) Aγ 0 ψ =0, 2 [ iγ µ µ MH gh ω ωγ0 + f ] ω H σ 0i i ω ψ H =0. 2M H f H ω 2M H i ψ H σ 0i ψ H,

11 Outline! Introduction! Strangeness quark mean field theory! Numerical results and discussions! Summary and Perspectives

12 SQMF parameters The strength of quark confinement potential MeV. m u (MeV) V u (MeV) a u (fm 3 ) m s (MeV) V s (MeV) a s (fm 3 ) set A set B set C and the The thirdcoupling for u =350MeVnamedQMF-NK3S. constants between meson and baryons Model m u g u σ g ω g Λ ω g Ξ ω g ρ g 2 g 3 c 3 (MeV) (fm 1 ) QMF-NK1S g ω g ω QMF-NK2S g ω g ω QMF-NK3S g ω g ω /03/2017 Jinniu Hu U = 30 MeV U = 12 MeV

13 Baryon masses in nuclear medium RMF

14 The properties of nuclei Binding energy and charge radii Model E/A (MeV) R c (fm) 40 Ca 48 Ca 90 Zr 208 Pb 40 Ca 48 Ca 90 Zr 208 Pb QMF-NK Without pion and gluon corrections QMF-NK QMF-NK QMF[18] Expt = = Charge density distribution

15 The properties of nuclear matter Nuclear saturation properties Model ρ 0 E/A K 0 J M N /M N L 0 K 0 sym K asy Q 0 K τ (fm 3 )(MeV)(MeV)(MeV) (MeV)(MeV)(MeV)(MeV)(MeV) QMF-NK QMF-NK QMF-NK symmetric nuclear matter pure neutron matter

16 The properties of hypernuclei The Λ energy levels of hypernuclei

17 The properties of hypernuclei SU(3) The Ξ 0 energy levels of hypernuclei

18 Ξ 0 Ξ The properties of hypernuclei The scalar and vector potentials of Λ and Ξ 0 hypernuclei

19 The properties of hypernuclei The binding energies of Λ hypernuclei Exp. Data:A. Gal, E. V. Hungerford and D. J. Millener, Rev. Mod. Phys. 88(2016)035004

20 The properties of neutron star The equations of state of neutron star matter

21 The properties of neutron star The particle fractions

22 The properties of neutron star The mass of neutron star

23 Outline! Introduction! Strangeness quark mean field theory! Numerical results and discussions! Summary and Perspectives

24 Summary and Perspective The quark mean field model is extended to strangeness nuclear physics within the pionic and gluonic corrections. The binding energies of Λ hypernuclei can be reproduced very well in present framework. The ones of Ξ 0 hypernuclei are also predicted. The massive neutron stars are obtained with Λ and hyperon, whose masses are around 2.1M. The double Λ and Ξ - hypernuclei will be studied. 14/03/2017 Jinniu Hu