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Formation spectra of h -mesic nuclei by ( p + ,p) reaction at J-PARC

『 ストレンジネスとエキゾティクス・理論の課題 』 3 Mar. 2007 @ 鳥羽 , 三重. Formation spectra of h -mesic nuclei by ( p + ,p) reaction at J-PARC. 永廣 秀子 ( 阪大 RCNP). H.Nagahiro, D.Jido and S.Hirenzaki, NPA761(05)92 H.Nagahiro, D.Jido and S.Hirenzaki, PRC68(03)035205

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Formation spectra of h -mesic nuclei by ( p + ,p) reaction at J-PARC

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  1. 『ストレンジネスとエキゾティクス・理論の課題』3 Mar. 2007 @ 鳥羽, 三重 Formation spectra of h-mesic nuclei by (p+,p) reactionat J-PARC 永廣 秀子 (阪大RCNP) H.Nagahiro, D.Jido and S.Hirenzaki, NPA761(05)92 H.Nagahiro, D.Jido and S.Hirenzaki, PRC68(03)035205 D.Jido, H.Nagahiro and S.Hirenzaki, PRC66(02)045202 E.Kolomeitsev, D.Jido, H.Nagahiro, S.Hirenzaki, in preparation H.Nagahiro, D.Jido, S.Hirenzaki, in preparation Collaborators : 慈道 大介 (京大基研) 比連崎 悟 (奈良女)

  2. negative result Introduction • h 中間子原子核 • works for h-mesic nuclei • (p+,p) * Liu, Haider, PRC34(1986)1845 [theo]* Chrien et al., PRL60(1988)2595 [exp] * Chiang, Oset, and Liu, PRC44(1988)738 [theo]* Kohno et al., NPA519(1990)755 [theo] • (d,3He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 [theo] * Jido, Nagahiro, Hirenzaki, PRC66(2002)045202 [theo] * Exp. at GSI (Yamazaki, Hayano group) 2005-6 [exp] • (g,p) * Nagahiro, Jido, Hirenzaki, NPA761(2005)92 [theo] • h-light-nucleus system : TAPS @ MAMI(2004) [exp] • etc… (ex. (g,h) @ Tohoku, etc …) • strong coupling to N*(1535) [JP= ½-] resonance • 有限密度中における N*(1535) の性質 h 中間子原子核 • カイラル二重項模型 … N* mass reduction in medium • カイラルユニタリー模型 … no change N* mass in medium • formation of h-mesic nuclei induced by meson beam • p and K beams are available at J-PARC (p+,p) reaction • カイラル模型を用いたスペクトラム • 運動学的な考察 • “(p+,p) experiment at 1988” の再考 • “negative result” の意味するところ。

  3. mass Kaiser, Siegel, Weise PLB362(95)23 Waas, Weise NPA625(97)287 Garcia-Recio, Nieves, Inoue, Oset PLB550(02)47 Inoue, Oset NPA710(02)354 Chiral unitary model  quasi bound state of KS … T V V V = + + no Pauli blocking for S in nuclear medium coupled channel Bethe-Salpater eq. in medium No mass shift of N* is expected in the nuclear medium 核媒質中の N*(1535) に対するカイラル模型 DeTar, Kunihiro PRD39(89)2805 Jido, Nemoto, Oka, Hosaka NPA671(00)471 Jido, Oka, Hosaka PTP106(01)873 Kim, Jido, Oka NPA640(98)77 Chiral doublet model N* : Chiral partner of nucleon mass difference of N* and nucleon C ~ 0.2 : strength of chiral restoration at the saturation density r0 reduction of mass difference in the nuclear medium N* :resonance dynamicallygeneratedin meson-baryon scattering

  4. N* - N N* - N medium effect associated with mass reduction repulsive energy w mN*-mN mh mN*-mN 1 2 3 4 5 6 7 r [fm] Kolomeitsev, Jido, Nagahiro, Hirenzaki in preparation r/r0 h-nucleus interaction ~ N* dominance model ~ h self-energy optical potential + (cross term) potential nature Chiang, Oset, Liu PRC44(1991)738 Jido, Nagahiro, Hirenzaki, PRC66(2002)045202 48 MeV attractive h level crossing

  5. bound region Energy dependence of the h self-energy Chiral unitary model Inoue, Oset, NPA710(02) 354, fig.6

  6. doublet bound region doublet unitary unitary w - mh = +100 MeV w - mh = -100 MeV 150 150 150 150 150 150 150 150 150 150 doublet 100 100 100 100 100 100 100 100 100 100 doublet 50 50 50 50 50 50 50 50 50 50 doublet 0 0 0 0 0 0 0 0 0 0 -50 -50 -50 -50 -50 -50 -50 -50 -50 -50 -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 -150 -150 -150 -150 -150 -150 -150 -150 -150 -150 V(r) [MeV] V(r) [MeV] V(r) [MeV] V(r) [MeV] V(r) [MeV] unitary unitary unitary w - mh = -50 MeV w - mh = -70 MeV w - mh = 0 MeV 6 8 4 2 2 2 4 4 6 6 8 8 r [fm] r [fm] r [fm] Energy dependence of the optical potentials 50 -100 -50 0 100 w [MeV] Chiral unitary model Inoue, Oset, NPA710(02) 354, fig.6

  7. Missing mass spectroscopy : one nucleon pick-up • (d,3He) : 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, … • h-mesic nuclei formation : D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202, H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205. • (g,p) : smaller distortion effect • w-nucleus … Marco, Weise, PLB502(01)59 • p-atom … Hirenzaki, Oset, PLB527(02)69 • h-mesic nuclei formation : H.N., D.Jido,S.Hirenzaki, NPA761(05)92. • (p+,p) : could be possible at J-PARC ? • secondary meson beam, p, K, … nucleon -hole Incident particle emitted particle target meson

  8. J-PARC で可能になると期待されるエネルギー領域 S.Prakhov et al., [Crystal Ball Collaboration] PRC72,015203 (2005). として見積もり total Tp = 650 MeV (pp ~ 777 MeV/c) Tp = 820 MeV (pp ~ 950 MeV/c) 12C(p+,p)11Bh reaction elementary cross section momentum transfer : forward angle (0 degree) w = mh – 100 MeV w = mh – 50 MeV total cross section w = mh ~ flat angular distribution

  9. * Morimatsu, Yazaki NPA435(85)727 NPA483(88)493 h productionthreshold quasi-free bound region pion proton 150 -100 -50 0 50 100 150 Eex – E0 [MeV] h productionthreshold (s-state proton-hole) (p+,p) spectra : 12C target by Green function method* recoilless at h threshold Tp = 820 MeV (pp = 950 MeV/c) : q = 0 deg. Chiral doublet model [C=0.0] (t-r approx.) Chiral doublet model [C=0.2] Chiral unitary model 20 15 10 5 0 -100 -50 0 50 100 150 -100 -50 0 50 100 -100 -50 0 50 100 150 Eex – E0 [MeV] Eex – E0 [MeV] Eex – E0 [MeV]

  10. V(r) V(r) unitary doublet V(r) [MeV] w - mh = -100 MeV 2 2 2 2 4 4 4 4 6 6 6 6 8 8 8 8 r [fm] r [fm] r [fm] r [fm] 150 150 100 100 shallow b.s. 50 50 0 0 deep b.s. -50 -50 -100 -100 -150 -150 V(r) doublet V(r) unitary V(r) [MeV] at threshold (p+,p) spectra : 12C target : Green function method recoilless at h threshold Tp = 820 MeV (pp = 950 MeV/c) : q = 0 deg. (Lab) Chiral doublet model [C=0.0] (t-r approx.) Chiral doublet model [C=0.2] Chiral unitary model 20 quasi-free h 15 10 5 0 -100 -50 0 50 100 150 -100 -50 0 50 100 150 -100 -50 0 50 100 150 Eex – E0 [MeV] Eex – E0 [MeV] Eex – E0 [MeV] * Total spectrum shape : 顕著な違い * 束縛状態の存在 - 浅い束縛状態 : CUM - 深い束縛状態 : CDM * ピーク構造は見えない。 - 幅が広い

  11. Tp = 650 MeV (pp = 777 MeV/c) 80 Chiral doublet model [C=0.2] recoilless position 60 20 20 40 15 15 20 10 10 0 Chiral unitary model 5 5 60 0 0 -100 -50 0 50 100 150 -100 -100 -50 -50 0 0 50 50 100 100 150 150 40 Eex – E0 [MeV] Eex – E0 [MeV] Eex – E0 [MeV] 20 0 (p+,p) spectra : 12C target : 入射 p+ エネルギー依存性 Tp = 820 MeV (pp = 950 MeV/c) Chiral doublet model [C=0.2] Chiral unitary model

  12. momentum transfer 500 hole 15 deg. 400 h [MeV] 300 200 0 deg. 100 0.4 0.6 0.8 1 1.2 1.4 pp [GeV/c] 0 Chrien at al., PRL60(88)2595, Fig.1 Liu, Haider, PRC34(86)1845, Fig.7 Li C O quasi free h Al (B.E, G/2) = (2.65, 4.77) [MeV] (p+,p) spectra : past experiment in 1988 • Chrien et al., PRL60(1988)2595 • pp = 800 MeV/c • proton angle : 15 deg. (Lab.) • search for predicted narrow bound state ( ex. G ~ 10 MeV)  negative results (bound state was not observed) b.s. + quasi-free bound state

  13. momentum transfer 500 15 deg. 400 [MeV] 300 200 0 deg. 100 0.4 0.6 0.8 1 1.2 1.4 pp [GeV/c] 0 Liu, Haider, PRC34(86)1845 quasi free h 100 80 60 40 20 0 -20 -40 -60 Eex – E0 [MeV] (p+,p) spectra : past experiment in 1988 • quasi-free の取り扱い • virtual h absorption (due to Imaginary potential) • The peak structure is hidden in quasi-free contribution • Difference of nucleon separation energy in 16O • 1p1/2  1p3/2  1s1/2~ 6 MeV ~ 23 MeV [Also commented in Kohno et al, NPA519(90)755] green function method (V0,W0) = -(34,23) [MeV] green function method (V0,W0) = -(34,15) [MeV] Liu, Haider, PRC34(86)1845, Fig.7 50 bound region 40 b.s. + quasi-free 30 20 bound state 10 0 (B.E, G/2) = (2.65, 4.77) [MeV]

  14. Chrien at al., PRL60(88)2595, Fig.1 bound region bound region bound region bound region Li C O Al -100 -100 -50 -50 0 0 50 50 100 100 -100 -100 -50 -50 0 0 50 50 100 100 Eex – E0 [MeV] Eex – E0 [MeV] Eex – E0 [MeV] Eex – E0 [MeV] (p+,p) spectra : comparison of our calc. with the exp. data • Chrien et al., PRL60(1988)2595 • pp = 800 MeV/c • proton angle : 15 deg. (Lab.) chiral doublet model chiral unitary model 80 0 deg. 0 deg. 40 0 30 15 deg. 15 deg. 20 10 0

  15. Chiral doublet model Chiral unitary model

  16. Chrien at al., PRL60(88)2595, Fig.1 bound region bound region bound region bound region Li C O Al -100 -50 0 50 100 -100 -50 0 50 100 Eex – E0 [MeV] Eex – E0 [MeV] (p+,p) spectra : comparison of our calc. with the exp. data • Chrien et al., PRL60(1988)2595 • pp = 800 MeV/c • proton angle : 15 deg. (Lab.) • どちらの模型も実験データとは矛盾しない。 [Also commented in Kohno et al, NPA519(90)755] proton angle ~ 0 degree chiral doublet model chiral unitary model 80 0 deg. 0 deg. 40 0 30 30 15 deg. 15 deg. 20 20 10 10 0 0

  17. Summary • formation of h-mesic nuclei • In-medium properties of N*(1535) resonance • Chiral doublet model : deep bound state • pocket-like potential, level crossing of h and N*-hole modes • Chiral unitary model : shallow bound state • (p+,p) reaction • incident pion kinetic energy • Tp = 820 MeV (pp ~ 950 MeV/c) : recoilless at h threshold • Tp = 650 MeV (pp ~ 777 MeV/c) : recoilless at h threshold – 50 MeV • possible at J-PARC ? • (p+,p) 実験結果(Chrien at al., 1988)の再考 • 15°proton angle は妥当か? • It is hard to observe the peak structures of the bound states, even if it exist. • We should discuss the whole shape itself in the case that the imaginary part might be large like h-mesic nuclei • The proton angle ~ 0 deg.

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