H.Nagahiro, S.Hirenzaki, Phys.Rev.Lett.94 (2005) H.Nagahiro, M.Takizawa, S.Hirenzaki, Phys.Rev.C74 (2006) D. Jido, H. Nagahiro, S. Hirenzaki, D. Jido, H. Nagahiro, S. Hirenzaki, Phys.Rev.C 85, (R) (2012) H. Nagahiro, S. Hirenzaki, E. Oset, A. Ramos, H. Nagahiro, S. Hirenzaki, E. Oset, A. Ramos, Phys. Lett. B 709 (2012) (Exp.) K. Itahashi et al., submitted to Prog. Theor. Phys.; (Exp.) K. Itahashi et al., submitted to Prog. Theor. Phys.; Letter of Intent for GSI-SIS (2011) Satoru Hirenzaki, Hideko Nagahiro, Daisuke Jido Nara Women’s University, YITP, Kyoto University Nara Women’s University, YITP, Kyoto University Formation of η’(958) mesic nuclei

ETA07 in Peniscola, 11 May 2007 『 Meson Mass Reduction 』, What do you mean ?? 1, Mass reduction will be equivalent to attractive V in Eq. of Motion..

ETA07 in Peniscola, 11 May 2007 『 Meson Mass Reduction 』, What do you mean ?? 1, Mass reduction will be equivalent to attractive V in Eq. of Motion.. 2, But “ Attractive  Mass reduction ’’ is wrong. Ex.) Coulomb case. Origin of the attraction is important. Origin of the attraction is important. Invariant mass data ONLY at small kinetic energy 

ETA07 in Peniscola, 11 May 2007 『 Meson Mass Reduction 』, What do you mean ?? 1, Mass reduction will be equivalent to attractive V in Eq. of Motion.. 2, But “ Attractive  Mass reduction ’’ is wrong. Ex.) Coulomb case. Origin of the attraction is important. Origin of the attraction is important. Invariant mass data ONLY at small kinetic energy 3, Thus, “exclusive” and/or “systematic” are important ! ==> Bound state spectroscopies ==> Bound state spectroscopies (Quantum number selection rules, No vacuum background) (Quantum number selection rules, No vacuum background) 

ETA07 in Peniscola, 11 May 2007 『 η(958) Bound State 』, What do you like ?? 4, For Bound State observation as peaks, however, ReV>ImV ReV>ImV is important. 3, Thus, “exclusive” and/or “systematic” are important ! ==> Bound state spectroscopies ==> Bound state spectroscopies (Quantum number selection rules, No vacuum background) (Quantum number selection rules, No vacuum background)

ETA07 in Peniscola, 11 May 2007 『 η(958) Bound State 』, What do you like ?? 4, For Bound State observation as peaks, however, ReV>ImV ReV>ImV is important. 3, Thus, “exclusive” and/or “systematic” are important ! ==> Bound state spectroscopies ==> Bound state spectroscopies (Quantum number selection rules, No vacuum background) (Quantum number selection rules, No vacuum background) 5, And “clear (dominant) origin” is important to deduce something.

ETA07 in Peniscola, 11 May 2007 『 η(958) Bound State 』, What do you like ?? 4, For Bound State observation as peaks, however, ReV>ImV ReV>ImV is important. 3, Thus, “exclusive” and/or “systematic” are important ! ==> Bound state spectroscopies ==> Bound state spectroscopies (Quantum number selection rules, No vacuum background) (Quantum number selection rules, No vacuum background) 5, And “clear (dominant) origin” is important to deduce something. 6, η(958) seems interesting, in these senses.

ETA07 in Peniscola, 11 May 2007  ’ (958) meson … close connections with U A (1) anomaly  ’ (958) meson … close connections with U A (1) anomaly » some theoretical works › the effects of the U A (1) anomaly on  ’ properties › at finite temperature/density –T. Kunihiro, PLB219(89)363 –R.D.Pisarski, R.Wilczek, PRD29(84)338 –Y. Kohyama, K.Kubodera and M.Takizawa, PLB208(1988)165 –K.Fukushima, K.Onishi, K.Ohta, PRC63(01) –P. Costa et al.,PLB560(03)171, hep-ph/ etc… › the possible character changes of  ’ at  ≠0 » a poor experimental information on the U A (1) anomaly at finite density  ’ (958) meson 『 Specialties 』  ’ (958) meson 『 Specialties 』

ETA07 in Peniscola, 11 May 2007 Higgs mechanism Higgs mechanism U A (1) Anomaly EffectU A (1) Anomaly Effect : J p = 0 - Spontaneous Chiral Spontaneous Chiral Symmetry Breaking Symmetry Breaking Kunihiro, Hatsuda, PLB206(88)385, Fig.3 Anomaly effect in vacuum Mass of  ’ (958) meson Vogl,Weise, Prog.Part.Nuc.Phys.270, 195 (91)

ETA07 in Peniscola, 11 May 2007 First Point: Origin of Mass; ‘Chiral’+’Anomaly’ 10 NGBosons ’’’’ U A (1) D. Jido, H. Nagahiro, S. Hirenzaki, D. Jido, H. Nagahiro, S. Hirenzaki, Phys.Rev.C 85, (R) (2012) D. Jido, 『 η’meson under partial restoration of chiral symmetry in nuclear medium 』 POSTER.

ETA07 in Peniscola, 11 May 2007 『 η(958) Bound State 』, What do you like ?? 4, For Bound State observation as peaks, however, ReV>ImV ReV>ImV is important. 3, Thus, “exclusive” and/or “systematic” are important ! ==> Bound state spectroscopies ==> Bound state spectroscopies (Quantum number selection rules, No vacuum background) (Quantum number selection rules, No vacuum background) 5, And “clear (dominant) origin” is important to deduce something. 6, η(958) seems interesting, in these senses.

ETA07 in Peniscola, 11 May 2007 Strength of optical potential; ReV vs. ImV 12 Chance to have ReV  ImV Same Order!! ………. But, We love ReV  ImV !!! D. Jido, H. Nagahiro, S. Hirenzaki, Phys.Rev.C 85, (R) (2012) D. Jido, POSTER. 『 η’meson under partial restoration of chiral symmetry in nuclear medium 』 Only Real Part for η(958)N elastic channel from U A (1) Anomaly Effect

ETA07 in Peniscola, 11 May 2007  ’N interaction : Chiral Unitary model : Oset-Ramos, PLB704(11)334  ’ N  vector-baryon (VB) P B V B P P B V B V V B V B V B P 13  | a  ’ N | = 0.03 fm  1 N   1 N : singlet component – contribution to ELASTIC channel Borasoy, PRD61(00) Kawarabayashi-Ohta, PTP66(81)1789 1111 N N 1111    … free parameter  | a  ’ N | = 0.1 fm  ’ N   ’ N,  N,  N,  (PB) Weinberg-Tomozawa +  -  ’ mixing  | a  ’ N | = 0.01 fm cf. | a  ’ N | ~ 0.1 – 0.8 fm [Moscal:PLB’00] ’’’’ N

ETA07 in Peniscola, 11 May 2007 Strong Attraction but Weak absorption in Nucleus, Is really possible ? ＝＝＞ 1, Experimental information ? 2, Theoretical evaluation ? H. Nagahiro, S. Hirenzaki, E. Oset, A. Ramos H. Nagahiro, S. Hirenzaki, E. Oset, A. Ramos ”eta-prime nucleus optical potential and possible eta-prime bound states" ”eta-prime nucleus optical potential and possible eta-prime bound states" Phys. Lett. B 709 (2012) 87-92; arXiv: (hep-ph). Phys. Lett. B 709 (2012) 87-92; arXiv: (hep-ph).

ETA07 in Peniscola, 11 May 2007 Reported DATA 1. CBELSA/TAPS (transparency) 1. CBELSA/TAPS (transparency) by M. Nanova et al., Phys. Lett. B (2012), Prog. Part. Nucl. Phys. (2012) by M. Nanova et al., Phys. Lett. B (2012), Prog. Part. Nucl. Phys. (2012)    GeV/c) ~ 15 – 25 MeV (No string p-dependence)    GeV/c) ~ 15 – 25 MeV (No string p-dependence) (Reasonally smaller than theoretically expected  m  ’ ) (Reasonally smaller than theoretically expected  m  ’ ) 2 (1) COSY (final state interaction) 2 (1) COSY (final state interaction) by P. Moskal et al., Phys. Lett. B 482 (2000) 356. by P. Moskal et al., Phys. Lett. B 482 (2000) 356. ABS(a  ’p )~ 0.1 fm (V(   ) ~ 10 MeV), sign is not known ABS(a  ’p )~ 0.1 fm (V(   ) ~ 10 MeV), sign is not known 2 (2) COSY (final state interaction) 2 (2) COSY (final state interaction) by P. Moskal et al., Phys. Lett. B 474 (2000) 416. by P. Moskal et al., Phys. Lett. B 474 (2000) 416. ABS( RE (a  ’p ) ) ＜ 0.8 fm, sign is not known ABS( RE (a  ’p ) ) ＜ 0.8 fm, sign is not known 3. RHIC: PHENIX/STAR (Low energy pion) 3. RHIC: PHENIX/STAR (Low energy pion) by T. Csorgo et al., Phys. Rev. Lett. 105 (2010) by T. Csorgo et al., Phys. Rev. Lett. 105 (2010)  m  ’ ~ 200 MeV (Roughly Consistent to NJL, but at different T)  m  ’ ~ 200 MeV (Roughly Consistent to NJL, but at different T) 15

ETA07 in Peniscola, 11 May 2007 Calculated V  ’ 16 opt Inputs for V opt ’’’’ N ’’’’ N ’’’’ N  N '''' N  N small t t 1111 B B 1111   ’ mainly contibutes to elastic channel, not to inelastic channel ~ the anomaly effect [D.Jido, H.N., S.Hirenzaki, PRC85(12)]  Only free parameter in this model. [10 –2 MeV –1 threshold Attractive sign is assumed. (No exp. Info. on sign) Nagahiro, Hirenzaki, Oset, Ramos, PLB709(2012)87  –0.193 | a  ’ N | [fm] 0.1 t’N’Nt’N’Nt’N’Nt’N’N –1.26 – 0.25i t’NNt’NNt’NNt’NN – i – –3.85 – 0.31i – i – –6.43 – 0.43i – i – –12.9 – 1.01i – i [Oset-Ramos:PLB704(11)]

ETA07 in Peniscola, 11 May 2007 Our calculation for V  ’N 17 opt optical potential V opt : Lowest order in desnity ’’’’ N ’’’’ t optical potential V opt : Second oder in density ’’’’ ’’’’ t t  ’  ’’’’ X  ’’’’

ETA07 in Peniscola, 11 May 2007 Numerical result : potential depth 18 in unit of MeV V opt total (–8.6–1.7i)(–0.1–0.1i)0.1(–8.7–1.8i) (–26.3–2.1i)(–0.6–0.9i)0.3(–26.8–3.0i) (–43.8–3.0i)(–1.3–2.5i)0.5(–44.1–5.5i) (–87.7–6.9i)(–4.1–10.4i)1(–91.8–17.2i) ~ COSY  ~ MeV ~ TAPS transparency ratio ’’’’ ’’’’ (’)(’)(’)(’) + = (’)(’)(’)(’)

ETA07 in Peniscola, 11 May 2007  ’ (958) mesic nuclei formation by (p,d) reaction momentum transfer elementary cross section pn  d  ’ target : 12 C proton kinetic energy T p =2.5GeV d p target ’’’’ n-hole forward reaction :  d = 0 deg. K. Itahashi et al., Letter of Intent for GSI (2011) H. Fujioka, Talk, Friday q [GeV/c] proton kinetic energy T p [GeV] m’m’m’m’ m  ’ – 50 MeV m  ’ – 100 MeV   no experimental information ~ 0.2  T p = 2.5 GeV J.Klaja et al., PRC81(10) (COSY) Assumption1 : Same ratio as  production ~ Assumption2 : Flat distribution in CM ~ 30  b/sr Lab.~10 CELSIUS/WASA, PRL70(97)2642

ETA07 in Peniscola, 11 May 2007 –150–100–500 –5 –10 –15 –20 20  ’ (958) mesic nuclei formation by (p,d) reaction optical potentials V0V0V0V0 W0W0W0W0 in unit of MeV cf.) NJL with KMT  m  ’ ~ –150  0 cf.) coupled-channel |a  ’ N |= fm case cf.)   ’ ~  0 CBELSA/TAPS M. Nanova et al., PLB Various combination within the range of V 0 = 0 ~ –150 MeV, W 0 = –5 ~ –20 MeV 

ETA07 in Peniscola, 11 May Numerical results : ‒ (150, 20) MeV : 12 C(p,d) 11 C  ’ d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] (0p 3/2 ) ‒ 1 s’s’s’s’ p’p’p’p’ d’d’d’d’ f’f’f’f’ total (BE,  )= (-93,34) MeV (-56,28) (-21,21) quasi-free contributions ( V 0, W 0 )= ‒ (150,20) MeV V 0 ~ NJL  ~ 40 MeV (> TAPS) threshold enhancement owing to the attractive potential Green’s function method [Morimatsu-Yazaki, NPA435(85)727]

ETA07 in Peniscola, 11 May Numerical results : ‒ (150, 20) MeV : 12 C(p,d) 11 C  ’ d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] (0p 3/2 ) ‒ 1 s’s’s’s’ p’p’p’p’ total ( V 0, W 0 )= ‒ (150,20) MeV V 0 ~ NJL  ~ 40 MeV (> TAPS) total with ( V 0, W 0 )= ‒ (0,20) MeV (0p 3/2 ) ‒ 1 d’d’d’d’ f’f’f’f’

ETA07 in Peniscola, 11 May Numerical results : ‒ (150, 20) MeV : 12 C(p,d) 11 C  ’ d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] (0p 3/2 ) ‒ 1 s’s’s’s’ p’p’p’p’ d’d’d’d’ f’f’f’f’ total ( V 0, W 0 )= ‒ (150,20) MeV V 0 ~ NJL  ~ 40 MeV (> TAPS)

ETA07 in Peniscola, 11 May Numerical results : ‒ (150, 15) MeV : 12 C(p,d) 11 C  ’ d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] ( V 0, W 0 )= ‒ (150,15) MeV V 0 ~ NJL  ~ 30 MeV (> TAPS) (0p 3/2 ) ‒ 1 s’s’s’s’ p’p’p’p’ d’d’d’d’ f’f’f’f’ total ~

ETA07 in Peniscola, 11 May Numerical results : ‒ (150, 10) MeV : 12 C(p,d) 11 C  ’ d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] ( V 0, W 0 )= ‒ (150,10) MeV V 0 ~ NJL  ~ 20 MeV (~ TAPS) (0p 3/2 ) ‒ 1 s’s’s’s’ p’p’p’p’ d’d’d’d’ f’f’f’f’ total

ETA07 in Peniscola, 11 May Numerical results : ‒ (150, 5) MeV : 12 C(p,d) 11 C  ’ d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] ( V 0, W 0 )= ‒ (150,5) MeV V 0 ~ NJL  ~ 10 MeV (< TAPS) (0p 3/2 ) ‒ 1 s’s’s’s’ p’p’p’p’ d’d’d’d’ f’f’f’f’ total

ETA07 in Peniscola, 11 May –(150,20) –(150,15) –(150,10) –(150,5) –(100,20) –(100,15) –(100,10) –(100,5) –(50,20) –(50,15) –(50,10) –(50,5)

ETA07 in Peniscola, 11 May 2007 Decomposition: Coversion(1body, 2body), Escape parts d2d2d2d2 d  dE [nb/sr MeV] –150 –100 –50 E ex – E 0 [MeV] |a  ’ N | = 1fm : coupled-channel (V 0,W 0 ) = – (92, 17) MeV  ’ escape part  ’ N  mB (conversion)  ’ NN  NN (absorption) Vopt obtained in Nagahiro, Hirenzaki, Oset, Ramos, PLB709(2012)87

ETA07 in Peniscola, 11 May 2007 Clear origin of mass is important.  ’ (958) seems Special.  ’ (958) seems Special. » Clear Origin of Mass Reduction by change with help of U A (1) change with help of U A (1) » Re V ~  m >> ImV, thanks to U A (1) Narrow Peak expected for  ’ Mesic Nuclei Formation, Missing mass spectra. Narrow Peak expected for  ’ Mesic Nuclei Formation, Missing mass spectra. Consistency with the scattering length data ? Consistency with the scattering length data ? 29 Summary

ETA07 in Peniscola, 11 May 2007