1 Formation spectra of  -mesic nuclei by (  +,p) reaction at J-PARC and chiral symmetry for baryons Hideko Nagahiro (RCNP) Collaborators : Daisuke Jido (YITP) Satoru Hirenzaki (Nara WU) H.Nagahiro, D.Jido and S.Hirenzaki, NPA761(05)92 H.Nagahiro, D.Jido, S.Hirenzaki, PRC68(03) D.Jido, H.Nagahiro and S.Hirenzaki, PRC66(02) D.Jido, E.Kolomeitsev, H.Nagahiro, S.Hirenzaki, in preparation H.Nagahiro, D.Jido, S.Hirenzaki, in preparation International Nuclear Physics Conference “INPC2007” 4 June, 2007 Tokyo International Forum, Japan

Tokyo Japan, 4 June Introduction  -mesic nuclei  -mesic nuclei » works for  -mesic nuclei › (  +,p) * Liu, Haider, PRC34(1986)1845 [theo] * Chiang, Oset, and Liu, PRC44(1988)738 [theo] * Chrien et al., PRL60(1988)2595 [exp] › (d, 3 He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 [theo] * D. Jido, H.Nagahiro, S. Hirenzaki, PRC66(2002) [theo] * Exp. at GSI (Yamazaki, Hayano group) [exp] › ( ,p) * H.Nagahiro, D.Jido, S.Hirenzaki, NPA761(2005)92 [theo] ›  -light-nucleus system : [exp] etc… (ex. ( ,  Tohoku, etc …) » strong coupling to N*(1535) [J P = ½ - ] resonance › in-medium properties of N*(1535)   -mesic nuclei –Chiral doublet model … N* mass reduction in medium –Chiral unitary model … no change N* mass in medium formation of  -mesic nuclei induced by meson beam formation of  -mesic nuclei induced by meson beam »  and K beams are available at J-PARC  (  +,p) reaction › with the chiral doublet model & chiral unitary model › appropriate kinematics » comparison with the (  +,p) experiment at 1988

Tokyo Japan, 4 June Chiral models for N*(1535) in medium Chiral doublet model N* : Chiral partner of nucleon DeTar, Kunihiro PRD39(89)2805 Jido, Nemoto, Oka, Hosaka NPA671(00)471 Jido, Oka, Hosaka PTP106(01)873 Kim, Jido, Oka NPA640(98)77 mass difference of N* and nucleon mass C ~ 0.2 : strength of chiral restoration at the saturation density  0 reduction of mass difference in the nuclear medium N* : resonance dynamically generated in meson-baryon scattering 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 TVVV =+ + …  quasi bound state of K  No mass shifts of N* is expected in the nuclear medium coupled channel Bethe-Salpater eq. in medium no Pauli blocking for  in nuclear medium

Tokyo Japan, 4 June energy  /0/0 mm m N* -m N  -nucleus interaction ~ N* dominance model ~ + (cross term) Chiang, Oset, Liu PRC44(1991)738 Jido, Nagahiro, Hirenzaki, PRC66(2002)  self-energy optical potential associated with mass reduction m N* -m N r [fm] potential nature 48 MeV N* - hole  attractive medium effect repulsive level crossing Jido, Kolomeitsev, Nagahiro, Hirenzaki in preparation poster June 5: QT-111 by D. Jido

Tokyo Japan, 4 June Energy dependence of the optical potentials V(r) [MeV] doublet unitary  - m  = +100 MeV V(r) [MeV]  - m  = -100 MeV doublet unitary  [MeV] V(r) [MeV] doublet unitary  - m  = -70 MeV 2468 r [fm] Chiral unitary model Inoue, Oset, NPA710(02) 354, fig V(r) [MeV] doublet unitary  - m  = 0 MeV r [fm] V(r) [MeV] doublet unitary  - m  = -50 MeV 2468 r [fm]

Tokyo Japan, 4 June Missing mass spectroscopy : one nucleon pick-up (d, 3 He) : established by studies of pionic atom formation (d, 3 He) : established by studies of pionic atom formation –theory … S.Hirenzaki, H.Toki, T.Yamazaki, PRC44(91)2472, … –experiment … K.Itahashi et al., PRC62(00)025202, … ›  -mesic nuclei formation : D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202, H.N.,D.Jido,S.Hirenzaki, PRC68(03) ( ,p) : smaller distortion effect ( ,p) : smaller distortion effect –  -nucleus … Marco, Weise, PLB502(01)59 –  -atom … Hirenzaki, Oset, PLB527(02)69 ›  -mesic nuclei formation : H.N., D.Jido,S.Hirenzaki, NPA761(05)92. (  ,p) : could be possible at J-PARC ? (  ,p) : could be possible at J-PARC ? › secondary meson beam, , K, … emitted particle Incident particle target meson -hole nucleon

Tokyo Japan, 4 June energy range expected at J-PARC 12 C(  +,p) 11 C  reaction momentum transfer : forward proton angle (0 degree)  = m   = m  – 50 MeV  = m  – 100 MeV T  = 650 MeV (p  ~ 777 MeV/c) elementary cross section S.Prakhov et al., [Crystal Ball Collaboration] PRC72, (2005). angular distribution total ~ flat total cross section Green function method Morimatsu, Yazaki NPA435(85)727 NPA483(88)493

Tokyo Japan, 4 June (  +,p) spectra : 12 C target   = 650 MeV (p  = 777 MeV/c) :  = 0 deg. (Lab) Chiral doublet model [C=0.2] Chiral unitary model recoilless at  threshold - 50 MeV E ex – E 0 [MeV]  production threshold (s-state proton-hole) p n 12 C target 18 MeV bound region quasi-free quasi-free

Tokyo Japan, 4 June (  +,p) spectra : 12 C target   = 650 MeV (p  = 777 MeV/c) :  = 0 deg. (Lab) Chiral doublet model [C=0.2] Chiral unitary model recoilless at  threshold - 50 MeV E ex – E 0 [MeV] shallow b.s. quasi-free  unitary V(r) [MeV] at -100 MeV r [fm] 2468 V(r) V(r) [MeV] unitary r [fm] 2468 V(r) at threshold deep b.s V(r) [MeV] doublet r [fm] 2468 at threshold V(r) V(r) [MeV] doublet at -100 MeV r [fm] 2468 V(r)

Tokyo Japan, 4 June (  +,p) spectra : comparison of our calc. with the exp. data Chrien at al., PRL60(88)2595, Fig.1 Li C O Al Chrien et al., PRL60(1988)2595 Chrien et al., PRL60(1988)2595 » p  = 800 MeV/c » proton angle : 15 deg. (Lab.) » search for predicted narrow bound state ( ex.  ~ 10 MeV)  negative results (bound state was not observed) chiral unitary modelchiral doublet model E ex – E 0 [MeV] deg. 15 deg. bound region [MeV] p  [GeV/c] momentum transfer 0 deg. 15 deg.

Tokyo Japan, 4 June Chiral doublet model Chiral unitary model

Tokyo Japan, 4 June E ex – E 0 [MeV] Chrien at al., PRL60(88)2595, Fig.1 Li C O Al Chrien et al., PRL60(1988)2595 Chrien et al., PRL60(1988)2595 » p  = 800 MeV/c » proton angle : 15 deg. (Lab.) chiral unitary modelchiral doublet model E ex – E 0 [MeV] deg. 15 deg. The experimental data is consistent with both model The experimental data is consistent with both model  This experimental set-up is not sensitive to N* in-medium  This experimental set-up is not sensitive to N* in-medium (  +,p) spectra : comparison of our calc. with the exp. data proton angle should be 0 degree bound region [Also commented in Kohno et al, NPA519(90)755]

Tokyo Japan, 4 June Summary Formation of  -mesic nuclei Formation of  -mesic nuclei » In-medium properties of N*(1535) resonance › Chiral doublet model : deep bound state(s) –pocket-like potential, level crossing of  and N*-hole modes › Chiral unitary model : shallow bound state(s) (  +,p) reaction (  +,p) reaction » incident pion kinetic energy › T  = 820 MeV (p  ~ 950 MeV/c) : recoilless at  threshold › T  = 650 MeV (p  ~ 777 MeV/c) : recoilless at  threshold – 50 MeV Reconsideration of the experimental data at 1988 by Chrien at al. Reconsideration of the experimental data at 1988 by Chrien at al. » Is the 15°proton angle appropriate? › Not sensitive to the N* properties in-medium » We should discuss the whole shape itself in the case that the imaginary part might be large The proton angle ~ 0 deg. The proton angle ~ 0 deg. possible at J-PARC ? possible at J-PARC ? » realistic discussion with experimentalists [H.Fujioka, K.Itahashi] … refinements and concrete discussions for a real experiment … refinements and concrete discussions for a real experiment