1. 10 June 2015 Satoru Hirenzaki (Nara Womens University, Japan) Meson Properties at Finite Density from Meson Nucleus Systems * eta by d+d * Comments on phi data

2. 2 cf.) NJL model with KMT ’’’’   800 600 400 200 1000 Meson mass [MeV] Costa et al.,PLB560(03)171, Nagahiro-Takizawa-Hirenzaki, PRC74(06)045203 …… U A (1) breaking (KMT term [1,2] ) massless Jido et al., PRC85(12)032201(R) Nagahiro et al., PRC (2013) U A (1) anomaly effect U A (1) anomaly effect ChS manifest dynamically broken dyn. & explicitly broken [1] Kobayashi-Maskawa PTP44(70)1422 [2] G. ’t Hooft, PRD14(76)3432 Basic Motivation Symmetry Breaking Pattern and Meson Properties Schematic View of the PS meson mass spectrum

3. Formation of η-4He by d + d reaction at COSY with H. Nagahiro (Nara Women’s Univ.) N. Ikeno (Tottori Univ.) D. Jido (Tokyo Metropolitan Univ)

4. 4  -mesic nuclei Motivation and our aim »  -N system … strongly couples to the N*(1535) resonance   -mesic nuculei … doorway to in-medium N*(1535) » N*(1535) … a candidate of the chiral partner of nucleon  chiral symmetry for baryons ?  meson » » »  -N system Strong Coupling to N*(1535), Strong Coupling to N*(1535), » eta-Nucleus system Doorway to N*(1535)  NN* system -No I=3/2 baryon contamination -Large coupling constant -no suppression at threshold (s-wave coupling) properties of eta meson

5. 5  -mesic nuclei Many works for  mesic nuclei from 1980’s Theor. Theor. Liu, Haider, PRC34(1986)1845 Kohno, Tanabe, PLB231(1989)219; NPA519(1990)755 Garcia-Recio, Nieves, Inoue, Oset PLB550(02)47 C. Wilkin, T. Ueda, S. Wycech, …… Exp. Exp. Chrien et al., PRL60(1988)2595 TAPS@MAMI (  + 3 He   0 + p + X) COSY-GEM (p + Al  3 He + Mg-  ) WASA-at-COSY (d + d  3 He + p +  JPARC (Itahashi, Fujioka…),  Our works for eta-mesic nuclei R.S. Hayano, S. Hirenzaki, A. Gillitzer, Eur. Phys. J. (99) R.S. Hayano, S. Hirenzaki, A. Gillitzer, Eur. Phys. J. (99) D.Jido, H.Nagahiro and S.Hirenzaki, Phys.Rev.C66, 045202, 2002. D.Jido, H.Nagahiro and S.Hirenzaki, Phys.Rev.C66, 045202, 2002. H.Nagahiro, D.Jido, S.Hirenzaki, Phys.Rev.C68, 035205, 2003. H.Nagahiro, D.Jido, S.Hirenzaki, Phys.Rev.C68, 035205, 2003. H.Nagahiro, D.Jido and S.Hirenzaki, Nucl.Phys.A761,92, 2005. H.Nagahiro, D.Jido and S.Hirenzaki, Nucl.Phys.A761,92, 2005. D.Jido, E.E.Kolomeitsev, H.Nagahiro, S.Hirenzaki, Nucl.Phys.A811:158, 2008. D.Jido, E.E.Kolomeitsev, H.Nagahiro, S.Hirenzaki, Nucl.Phys.A811:158, 2008. H.Nagahiro, D.Jido, S.Hirenzaki, Phys.Rev.C80,025205, 2009. H.Nagahiro, D.Jido, S.Hirenzaki, Phys.Rev.C80,025205, 2009.

6. A Theoretical Calculation for Momentum transfer ------- Large Momentum transfer ------- Large p d = 1.025 GeV/c, p  = p  = 0 at threshold in C.M. Data of d d  4 He  above threshold Data of d d  4 He  above threshold Simple spectral structure is expected for light systems Simple spectral structure is expected for light systems It’s a few body system (2N+2N  4N + eta), but the momentum transfer is large. It’s a few body system (2N+2N  4N + eta), but the momentum transfer is large. NO SPECTATOR! All 4N participate to the formation reaction seriously for ‘the signal process’. Some remarks (discussions with P.Moskal, W. Krzemien, M. Skurzok) Results of experiments: Results of experiments: exclusive analysis for the final states, charge channels,,, exclusive analysis for the final states, charge channels,,,

7. Some remarks Transition (  -production) part Transition (  -production) part  High q transfer at each propagator Parameterize this part. A Theoretical Calculation for

8. d d   Green function method  total conversion escape threshold E tot  threshold  dd  4 He  ) data Schematic picture with  -  optical potential A Theoretical Calculation for

9. 9 Green’s function method Ref. O.Morimatsu and K. Yazaki, NPA435(1985)727-737  

10. 10 Scattering Amplitude d d F(q)F(q)F(q)F(q) F(q) ( f (r) : r-space representation)… Assumed to be Gaussian

11. 3 parameters in this model  -  optical potential  -  optical potential (used to calculate the eta Green’s function (used to calculate the eta Green’s function  production part dd  4 He   production part dd  4 He  A Theoretical Calculation for F should include the information on Deuterons and alpha particle structure and their overlap (fusion) Nucleon - nucleon interaction for eta meson production for high momentum transfer region. V0, W0 Potential Strength at nuclear center

12. Exp. Data of dd  4 He  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). A Theoretical Calculation for  threshold E tot  dd  4 He  ) data This part can be compared with the escape part of Green’s function calculation.  Some restrictions to the model parameters.

13. Numerical Results Arbitrary unit 0 1 2 3 4 5 6 7 8 010155 −5−5−5−5 − 10 − 15 − 20 E  − m  [MeV]  tot [nb] 0 5 10 15 20 25 (V 0,W 0 ) = (−100, −10) MeV p 0 = 500 MeV/c (Ideal case)

14. Numerical Results  tot [nb] 0 5 25 15 20 Arbitrary unit 0 2 3 4 5 6 10 (V 0,W 0 ) = (−100, −20) MeV p 0 = 500 MeV/c 010155 −5−5−5−5 − 10 − 15 − 20 E  − m  [MeV] ~~ ~~ (Larger imaginary part )

15. Numerical Results 010155 −5−5−5−5 − 10 − 15 − 20 E  − m  [MeV] 12 10 8 11 9 Arbitrary unit  tot [nb] 0 5 25 15 20 10 (V 0,W 0 ) = (−100, −40) MeV p 0 = 500 MeV/c ~~ ~~ 0 (Larger imaginary part )

16. (V0 = -100 MeV) (W0= -5, -10, -20, -40 MeV) (p0 =500 MeV/c)

17. (V0 = -100 MeV) (W0= -5, -10, -20 MeV) (p0 =1000 MeV/c)

18. (V0 = -100, -50, -30 MeV) (W0= -20 MeV) (p0 =500 MeV/c)

19. (V0 = -100, -50 MeV) (W0= -20 MeV) (p0 =1000 MeV/c)

20. (V0 = -100 MeV) (W0= -10 MeV) (p0 =1000, 500, 400 MeV/c)

21. (V0 = -100 MeV) (W0= -20 MeV) (p0 =1000, 500 MeV/c)

22. (V0 = -50 MeV) (W0= -5 MeV) (p0 =1000, 500 MeV/c) In these cases, eta production data above threshold can not be reproduced.

23. Summary for d+d reaction ★ Formation of  mesic nucleus d + d  ( 4 He-  )  X (several channels) reaction High momentum transfer (~1GeV/c)  production data above threshold exist Simple spectra are expected ★ A model calculation with Green’s function  It may provide an estimation and interpretation of the inclusive experimental data.  But for the comparison, backgrounds from non-(eta + alpha) processes must be removed (quasi-elastic pion production etc).

24. Summary for d+d reaction ★ Further studies = Better form for transition part = Exclusive treatment of the final particles * Evaluation of ImV for each channel * Implementation of the realistic meson self-energy * Independent treatment of the eta-alpha decay process could be fine (decay model different from formation part)

25. Vector mesons in nucleus = Transparency ratio and Invariant mass = with S. Tokunaga (Nara Women’s Univ.) J. Yamagata-Sekihara (Oshima National College of Maritime Technology) H. Nagahiro (Nara Women’s Univ.)

26. 26 Mass shift: 3.4% Mass shift: no mention Summary Table -- Results by independent groups

27. meson Isolated peak structure Long life time (selection of slow particle)

28. We consider here. DATA by KEK E325, LEPS/SPring8, JPARC E16 R. Muto et al., Phys. Rev. Lett. 98 (2007) 042501 T. Ishikawa et al., Phys. Lett. B 608 (2005) 215-222 T. Sawada, Doctor Thesis, Osaka University (2013) Thoretical works from Hatsuda and Lee, importance and sensitivity to S quark condensate.

29. * Determine the from in-medium * Importance of = How much is the strangeness component in nucleon (important for hadron structure studies.) = basic quantity for nuclear matter, which relate to various phenomena (KN sigma term => kaon condensattion in neutron star, etc ) = may complete SU(3) info. on condesates with SU(2) part info. by other data Motivation / Interests

30. * First of all, we need ‘Stable (consistent) interpretation of data’ * Then, we should check ‘How reliable is theoretical connection between in-medium phi property and condensate ? ’ * Mass shift is not mandatory. If, it is zero, it’s important to confirm how accurately 0.

31. 31 Mass shift: 3.4% Mass shift: no mention

32. 32 Goal for the first step Describe ‘Transparency ratio (LEPS/SPring8)’ and ‘Invariant Mass (KEK E325)’ in an unified manner. * Find the consistent interpretation of the observables. And deepen the understanding between observables and meson propertes.

33. 33 -T. Ishikawa et al., Phys. Lett. B 608 (2005) 215-222 -T. Sawada, Doctor Thesis, Osaka University (2013) Transparency ratio A : mass number : incident photon number : Flux loss of the incident photon : Flux loss of phi : path of the phi : phi momentum Formula of the transparency ratio

34. 3, Transparency Ratio – 計算結果 – 34 Calculated Results

35. Formula for Invariant Mass Unified treatment with Transparency → Calcualte Invariant mass dist. by the same model parameters as the Transparency 35 Decay phi number : Num of Incident particles : Branching Ratio of phi in vacuum, : Produced phi at (b, z0) : Number of phi at (b, z)

36. 36 An Example 入射粒子 φ の生成位置 (φ の飛距離 ) Production at origin Distance from production point density

37. 37 Phi meson decay number per unit length Phi meson decay number to e+e- channel

38. Distance from production point Target case

39. Distance from production point Target case density

40. Nuclear center Distance from production point Nuclear surface/ Outside Target case density

41. 41 Phi meson decay number per unit length : φ 中間子の生成位置 C : φ 中間子の質量変化の大きさを決めるパラメータ Phi meson decay number to e+e- channel Invariant mass distribution seen in e+e- decay channel phi production point Full width in vacuum phi mass in vacuum Parameter for mass shift

42. Input data γ-distortion: proton-distortion: 42 Numerical Results – Invariant Mass of e+e- pair

43. 43 proton-induced, target:, βγ=1.0 (KEK E325) Experimental energy resolution (~10.7MeV) is not taken into account.

44. 44 proton-induced, target:, βγ=1.0 (KEK E325) Experimental energy resolution (~10.7MeV) is not taken into account.

45. 45 proton-induced, target:, βγ=1.0 (KEK E325) Experimental energy resolution (~10.7MeV) is not taken into account.

46. 46 proton-induced, target:, βγ=1.0 (KEK E325) Experimental energy resolution (~10.7MeV) is not taken into account.

47. 47 proton-induced, target:, βγ=1.0 (KEK E325) Experimental energy resolution (~10.7MeV) is not taken into account.

48. 48, target:, βγ=1.0 γ-induced

49. 49 Larger initial distortion  Larger contribution of in-medium decay at forward directions. ( Meson is produced at early stage in Nucleus. ) Angular dependence of the mass shift contribution can be interesting (But large distortion of initial particles may break the target seriously before meson production.)

50. 50 proton-induced, target:, βγ=0.5 (J-PARC E16) Simulation By S. Yokkaichi (Resolution 5 MeV) (Slow phi in large Nucleus)

51. Summary for vector mesons In-medium vector (phi) meson interesting Data exist. But no consistent interpretation For φ meson An unified description of ‘Transparency Ratio’ and ‘Invariant mass’ Comparison with KEK E325 and LEPS/SPring8 data Some interesting features are observed in calculated results. We will try to implement the realistic meson self-energy. We will further try to understand the data consistently. 51