η-mesic nucleus by d + d reaction ー how to deduce η-Nucleus int. ー 東北大ELPH拠点研究会、2016年12月1日（木）、2日（金） 「マルチフレーバーで探るエキゾチックハドロンとハドロン多体系の物理」 12月2日（金） 11:15-- [Session 5] eta and etaprime in medium (II) η-mesic nucleus by d + d reaction ー how to deduce η-Nucleus int. ー Satoru Hirenzaki Nara Women’s University Collaborate with Natsumi Ikeno (Tottori University) Hideko Nagahiro (Nara Women’s University) Daisuke Jido (Tokyo Metropolitan Univ.) H. Nagahiro, D. Jido, S. Hirenzaki, PRC(09) Kolomeitsev, Jido, Nagahiro, Hirenzaki, NPA(08) H.Nagahiro., D.Jido and S.Hirenzaki, NPA761(05)92 H.Nagahiro., D.Jido, S.Hirenzaki, PRC68(03)035205 D.Jido, H.Nagahiro. and S.Hirenzaki, PRC66(02)045202

Introduction of h-mesic nuclei properties of eta meson h meson hNN* system -No I=3/2 baryon contamination -Large coupling constant -no suppression at threshold (s-wave coupling) h-N system Strong Coupling to N*(1535), eta-Nucleus system Doorway to N*(1535) Motivation and our aim h-N system … strongly couples to the N*(1535) resonance h-mesic nuculei … doorway to in-medium N*(1535) N*(1535) … a candidate of the chiral partner of nucleon chiral symmetry for baryons

h-Nucleus Interaction: general remark ~ N* dominance model ~ optical potential (Chiang, Oset, Liu PRC44(1991)738) (D.Jido, H.N., S.Hirenzaki, PRC66(2002)045202) to reproduce the partial width at tree level. potential nature In free space attractive N & N* properties in medium evaluated by two kinds of Chiral Models General feature medium effect Repulsive ?? mN & mN* change ?? ?

Chiral models for N and N* and h-nucleus interaction Chiral doublet model DeTar, Kunihiro, PRD39 (89)2805 Jido, Nemoto, Oka, Hosaka NPA671(00)471 Jido, Oka, Hosaka, PTP106(01)873 Jido, Hatsuda, Kunihiro, PRL84(00)3252 etc Lagrangian Physical fields N* : chiral partner of nucleon Mass difference * reduction of mass difference * C~0.2 :the strength of the Chiral restoration at the nuclear saturation density Chiral unitary model Kaiser, Siegel, Weise, PLB362(95)23 Waas, Weise, NPA625(97)287 Garcia-Recio, Nieves, Inoue, Oset, PLB550(02)47 Inoue, Oset, NPA710(02) 354 A coupled channel Bethe-Salpeter eq. * No mass shift of N* is expected in the nuclear medium. * In this study, we directly take the eta-self-energy in the ref.NPA710(02)354 * the N* is introduced as a resonance generated dynamically from meson-baryon scattering.

h -Nucleus optical potential associated with mass reduction

Formation ofη-4He by d + d reaction at COSY Today’s main topics 　　　　　　　Formation ofη-4He 　　　　by d + d reaction at COSY

Isospin dependence  only expected at decay process

A Simple Theoretical Model for (COSY Proposal) (P.Moskal, arXiv:nucl-ex/09093979) Some remarks Momentum transfer ------- Large pd = 1.025 GeV/c, pa = ph= 0 at threshold in C.M. Data of d d  4He h above threshold Simple spectral structure is expected for light systems System consists of 2 Nucleon + 2 Nucleon  4 Nucleon + 1 meson Exp. was performed

High q transfer at each propagator A Simple Theoretical Model for Some remarks Transition (h-production) part h High q transfer at each propagator Parameterize this part. Fix by h production data

with h-a optical potential A Simple Theoretical Model for Schematic picture d h Green function method a d with h-a optical potential Correspond to ‘η Production EXP.’ s total s s(dd4Heh) data escape conversion threshold Etot threshold Etot Correspond to the ‘Decay Product Observation’

F(q) ( f(r): r-space representation)… Assumed to be Gaussian h a F(q) Scattering Amplitude F(q) ( f(r): r-space representation)… Assumed to be Gaussian

A Theoretical Model for 3 parameters in this model h-a optical potential h production part dd  4Heh Exp. Data of dd  4Heh Fig. taken from NFQCD10@YITP, 2010 slide by S. Schadmand R.Frascaria et al., Rhys.Rev.C50 (1994) 573, N. Wills et al., Phys. Lett. B 406 (1997) 14, A.Wronska et al., Eur. Phys. J. A 26, 421-428 (2005).

(V0,W0) = (−100, −10) MeV p0 = 500 MeV/c (Ideal case) 8 7 6 5 Numerical Results (Ideal case) 8 stot [nb] 25 20 7 15 10 5 6 5 (V0,W0) = (−100, −10) MeV p0 = 500 MeV/c Arbitrary unit 4 3 2 1 −20 −15 −10 −5 5 10 15 Eh − mh [MeV]

How to know new info. on eta-Nucleus pot. ? Theory – 3 parameters, Absolute size of σ -- difficult. EXP – Above threshold -- η production cross section Below threshold – Upper limit of ‘Peak heght’ on 　　　　 　　　　　‘Smooth spectrum (background)’

How to know new info. on eta-Nucleus pot. ? Theory – 3 parameters, Absolute size of σ -- difficult. EXP – Above threshold -- η production cross section Below threshold – Upper limit of ‘Peak heght’ on 　　　　 　　　　　‘Smooth spectrum (background)’ Procedure Data above threshold  size of cross section Info. on eta-Nucleus pot. from data

How to know new info. on eta-Nucleus pot. ? Theory – 3 parameters, Absolute size of σ -- difficult. EXP – Above threshold -- η production cross section Below threshold – Upper limit of ‘Peak heght’ on 　　　　 　　　　　‘Smooth spectrum (background)’ Procedure Data above threshold  size of cross section Info. on eta-Nucleus pot. from data (Implicit assumption) Structure of spectra around eta threshold is dominated by the eta-processes.

Numerical Results again. --- p0 dependence We fix p0=500MeV/c.

Let’s remember Total, Conversion, Escape parts.

Comparison: Escape part vs. η production data 　　　( This is a good case.)

＊Results for various combinations of V0 and W0 paranmeters ＊Results of Total spectra

-40 -20 -5 Total Spectra

＊Results for various combinations of V0 and W0 paranmeters ＊Results of Total spectra ＊Results of Escape parts with η Production Data

Scaled escape part with data

＊Results for various combinations of V0 and W0 paranmeters ＊Results of Total spectra ＊Results of Escape parts with η Production Data 　　Not so sensitive to V0 and W0 values. It seems difficult to determine V0 and W0.

＊Results for various combinations of V0 and W0 paranmeters ＊Results of Total spectra ＊Results of Escape parts with η Production Data 　　Not so sensitive to V0 and W0 values. It seems difficult to determine V0 and W0. ＊Total spectra again with two modifications (1) Scaled by η production data (2) Flat contributions are removed

Scaled Total spectra, Flat contributions are removed.

＊Results for various combinations of V0 and W0 paranmeters ＊Results of Total spectra ＊Results of Escape parts with η Production Data 　　Not so sensitive to V0 and W0 values. It seems difficult to determine V0 and W0. ＊Total spectra again with two modifications (1) Scaled by η production data (2) Flat contributions are removed ＊Conversion part of the spectra with the modifications before.  Corresponding to the EXP. upper limit below threshold.

Scaled conversion part, Flat contributions are removed.

Back to the experimental upper limits

Back to the experimental upper limits Our results are Inclusive for decay process Upper limit estimated to = 36 + 9 = 45 nb

Back to Numerical results Back to the experimental upper limits Our results are Inclusive for decay process Upper limit estimated to = 36 + 9 = 45 nb Assume Isospin n+pi0 channel × (2+1) / 1 = Inclusive、 Upperlimit = 108 nb p+pi- channel × (2+1) / 2 = Inclusive、 Upperlimit = 13.5 nb　（Smallest limit） Back to Numerical results

Important numbers here are 13.5、 45、 and 108 nb

Summary for d+d reaction Formation of h mesic nucleus d + d  (4He-h)  N + p + 3He reaction High momentum transfer (~1GeV/c) h production data above threshold Simple spectra are expected A simple model with Green’s function Provide estimation and interpretation of data.

Summary for d+d reaction Formation of h mesic nucleus d + d  (4He-h)  N + p + 3He reaction High momentum transfer (~1GeV/c) h production data above threshold Simple spectra are expected A simple model with Green’s function Provide estimation and interpretation of data. Combined analysis ( data above/below threshold and theoretical model) may provide strong limitation to eta-Nucleus interaction.