Maximum Mass of Neutron Stars with Hadron-Quark Transient Core □Introduction □Universal 3-body force □Approach by 3-Window Model □Some results In collaboration with T. Hatsuda and K. Masuda T. Takatsuka ( RIKEN; Prof. Emeritus Iwate Univ.) Mini-Symposium on Hadrons and hadron Interaction in QCD 2015 YITP,

Introduction ○Recent observation of 2-solar mass NSs * is providing a challenging problem how to reconcile the conflict between observations and theory. ・ Massive NSs stiff EOS ! ・ Dense matter theory (including phase transition ) Soft EOS ! #This contradiction is serious when we include the Y-mixing in NS cores ---- inndeed, “Hyperon Crisis” Fig. ○There are two viewpoints (frameworks)of approach : ① pure hadron(H) matter with hadron interactions (assuming that the point-like picture of hadrons is valid) ② hadron(H)+deconfined quark(Q) ( explicitly taking account of quark degrees of freedom) ○ As to the framework ①, Universal 3-body force ○ ② 3-window model for H-Q trans. * Demorist et al., Nature 467 (2010). Antoniadis et al., Science 340 (2013).

TNI3 NO Y TNI2 Y-mixing with Y × × (1) Strong Softening of the EOS ● ●

R.B. Wiringa, V. Fiks and A. Fabrocini, PR C38 (1988) A. Akmal, V.R. Pandharipande and D.G. Ravenhall, PR C58 (1998) Y Y But with Y ?

Efects of Universal 3-body force repulsion ① It is natural to consider that the 3-body force should be operative not only among NNN but also NNY, YYN and YYY. make an extended use of the 3-body force of Illinoi-Group type also to {N+Y}-matter. Then it is found that strong softening is remarkably moderated. This is, however, a phenomenological way of approach. ② What is the origin? We make a step forward to microscopic description as Univ.3-body force = Short range part + Medium- long range part 3-body repulsion from String-junction model (SJM) : Flavor- independent ! 2π-exchange via Isobar ⊿ (1232) excitation(Fujita-Miyazawa type) : extended to {N+Y} system

Dramatic softening of EOS Necessity of “Extra Repulsion” As a review T.Takatsuka, Prog.Theor.Phys.Suppl.No.156 (2004) Universal 3body force Y-mixing EOS TNI3 (NO Y) P TNI3u (Y) Mass TNI3(NO Y) TNI3u(Y) TNI3(Y)

Extended 2πΔ-Type 3-body Force ; not universal B* ; T.Kasahara,Y.Akaishi and H.Tanaka,PTP Suppl.No.56(1974)96

EOS of Neutron Star Matter Y-mixing (MeV)

(a) 2B come in short distance (b) Deformation (resistance) (c) Fusion into 6-quark state (by R. Tamagaki) Repulsion from SJM-----flavor independent Prog. Theor. Phys. 119 (2008) 965. ○ Energy barrier ( ～ 2GeV) corresponds to repulsive core of BB interactions

Mass v.s. Central Density T.Takatsuka,S.Nishizaki and R.Tamagaki, AIP Conference Proceedings 1011 (2008) 209.

② hadron(H)+deconfined quark(Q ) ○Hadrons are not a point-like particle but are composed of quarks ( gluons) and tend to loose their identity as the matter density increases deconfinement effects ○Quark matter gets to have strong correlations and eventually quarks are confined Into hadrons as the density decreases. ○H-Q transition region is very uncertain due to the confine-deconfine effects ○Our way of approach is to sandwitch the very uncertain HQ –EOS in between the H- and Q- EOSs relatively “well-known” window model. ○Here our aim is, though phenomenological, to seek whether Q-matter is existent or Q-degrees of freedom is revealed in NS cores in the light of massive NS observations,just by using the fact that HQ-EOS shoud meet the H-EOS somewhere in low density side and the Q-EOS at high density side.

“known” unknown “known” H HQ Q (G-matrix) (NJL) (interpolation) P(x) uncertain 3-Window Model Deconfinement and confinement are concerned

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□ Approach by 3-window model □ Some results

“H-Q crossover model” ・ K. Masuda, T. Hatsuda and T. Takatsuka, ApJ. 794 (2013) 12; PTEP 073D01 (2013).

Summary (1) Hadron-Quark transition in NS cores generates a stiff EOS compatible with massive NSs(2-solar-mass NSs), as far as q-degrees of freedom sets in at rather low density(e.g. due to percolation) and the Q-EOS is stiff(e.g. due to vector interractions) (2) So possible candidates to resolve a so-called “ two-solar- mass problem”: ○ pure hadronic scheme Universal 3-body force ○ hadron+quark scheme NSs with HQ transition core