1 / 33

Hideko Nagahiro Research Center for Nuclear Physics (RCNP), Osaka University Makoto Takizawa

PANIC05 Particles and Nuclei International Conference Santa Fe, NM - October 24, 2005. h ’ (958)-mesic nuclei formation. and U A (1) anomaly at finite density. H.Nagahiro, S.Hirenzaki, Phys.Rev.Lett.94 (2005) 232503. Hideko Nagahiro

morley
Télécharger la présentation

Hideko Nagahiro Research Center for Nuclear Physics (RCNP), Osaka University Makoto Takizawa

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. PANIC05 Particles and Nuclei International Conference Santa Fe, NM - October 24, 2005 h’(958)-mesic nuclei formation and UA(1) anomaly at finite density H.Nagahiro, S.Hirenzaki, Phys.Rev.Lett.94 (2005) 232503 Hideko Nagahiro Research Center for Nuclear Physics (RCNP), Osaka University Makoto Takizawa Showa Pharmaceutical University Satoru Hirenzaki Nara Women’s University

  2. Introduction • Interests of meson bound systems : mesic nuclei • important information on in-medium hadron physics and QCD symmetries • our previous work : h-mesic nuclei with chiral models : (d,3He), (g,p) reactions • h’(958) meson • close connections with UA(1) anomaly • heavy h’ mass due to the existence of anomaly term • many theoretical works • in vacuum / at finite temperature / at finite density • R. D. Pisarski, R. Wilczek, PRD29(84)338 • T. Kunihiro, T. Hatsuda, PLB206(88)385 / T. Kunihiro, PLB219(89)363 • V. Bernard, R.L.Jaffe and U.-G.Meissner, NPB308(1988)753 • Y. Kohyama, K.Kubodera and N.Takizawa, PLB208(1988)753 • K. Fukushima, K.Onishi, K.Ohta, PRC63(01)045203 • P. Costa et al.,PLB560(03)171, PRC70(04)025204, etc; etc… - partial restoration of chiral sym. in medium • D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202, • H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205, • H.N., D.Jido,S.Hirenzaki, NPA761(05)92

  3. Kunihiro, Hatsuda, PLB206(88)385, Fig.3 d u s u s d Anomaly effect in vacuum One can reproduce the heavy h’ mass Our Motivation & present work • apoor experimental information on the UA(1) anomaly effect at finite density • proposal for the formation reaction of the h’-mesic nuclei • UA(1) anomaly effect in medium from the viewpoint of “mesic nuclei” • the h’ properties, especially mass shift, at finite density • new information on the properties of UA(1) anomaly ? • Nambu-Jona-Lasinio model with the KMT interaction • unified treatment of the h and h’ meson explicit breaking the UA(1) sym. Kobayashi, Maskawa Prog.Theor.Phys.44, 1422 (70) G. ’t Hooft, Phys.Rev.D14,3432 (76)

  4. Gap equations for quarks = + + flavor mixing terms condensate in finite T/r Bethe-Salpeter equation Fermi distribution function + = SU(2) sym. matter partial restoration in medium [MeV] [MeV] SU(3) … = + meson quark-anti-quark scattering meson properties (mass) T. Kunihiro, PLB219(89)363 P. Costa et al.,PLB560(03)171 etc… Masses in finite T/r with NJL

  5. parameters (in vacuum) P. Rehberg, et al., PRC53(96)410. L = 602.3 [MeV] gS L2 = 3.67 gDL5 = -12.36 mu,d = 5.5 [MeV] ms = 140.7 [MeV] h’ Mu,d = 367.6 [MeV] Ms = 549.5 [MeV] 〈uu〉1/3 = -241.9 [MeV] 〈ss〉1/3 = -257.7 [MeV] mh’ = 958 [MeV] mh = 514 [MeV] mp = 135 [MeV] h p Dmh’ ~ -150 MeV @ r0 Dmh ~ +20 MeV @ r0 SU(2) symmetric matter • we consider the SU(2) sym. matter as the sym. nuclear matter. anomaly term effect h and h’ mass shifts @ r0 We can see the large medium effect even at normal nuclear density.

  6. gD : constant h’ h’ Dmh’ ~ -250 MeV @ r0 Dmh ~ -100 MeV @ r0 h h p p anomaly effect in the finite density • We simulate an extreme case. gD = gD(r) ?? gD = gD(r=0) exp(-(r/r0)2) Dmh’ ~ -150 MeV @ r0 Dmh ~ +20 MeV @ r0

  7. gD = gD(r=0) e-(r/r0) 2 gD : constant Vh(r) Vh(r) Vh’(r) Vh’(r) h : repulsive h’ : attractive h : attractive h’ : attractive h- & h’-Nucleus optical potential ~ potential description Real Part V0 • evaluated by possible h, h’ mass shift at r0

  8. (only one resonance included) ’ fix a coupling g h’ • in analogy with D-hole model for the p-nucleus system N g N*(1535) ’ Imaginary Part for h W0 = - 40 MeV • D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202, • H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205, h- & h’-Nucleus optical potential ~ potential description Real Part V0 • evaluated by possible h, h’ mass shift at r0 Imaginary Part W0 for h’ • estimated from nucl-th/0303044 (A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth)analysis of gp h’p data ~ phenomenological estimation

  9. look carefully !! Peaks!! In-medium dispersion relation medium effects (d,3He) reactions … p atom formation (96, 98, 01) (g,p) reactions … smaller distortion Candidate reactions Missing mass spectroscopy

  10. Data:SAPHIR collaboration, PLB444(98)555-562 Chiang, Yang, PRC68(03)045202 (g,p) reaction : Parameters • (g,p) reaction @ Eg=2.7 GeV • target … 12C • Forward (q ~ 0 deg.) • Elementary cross section for gp  h’p • w-mesic nuclei • mh ~ 547 MeV mw ~ 783 MeV mh’ ~ 958 MeV • plan of experiment for the formation of w-mesic nuclei @ SPring-8, 2005 • two different predictions for optical potentials • 【attractive】 V= - (156 + 29 i) r/r0 MeV [Klingl, Waas, Weise NPA650(99)299] • 【repulsive】 V= - ( - 42.8 + 19.5i) r/r0 MeV [Lutz, Wolf, Friman NPA706(02)431] • elementary cross section ~ 150 nb/sr • event # [h] ~ [w] ~ [h’]@ test experiment at SPring-8 [N.Muramatsu, private communication] • h-mesic nuclei • elementary cross section ~ 150 nb/sr

  11. quasi-free quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ no medium effect We only observe the quasi-free h’ peak

  12. quasi-free quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ no medium effect quasi-free V0= - (- 42.8 + 19.5i) [MeV] (Lutz) w

  13. quasi-free quasi-free V0= - (156+29i) [MeV] (Weise) quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ no medium effect w

  14. quasi-free quasi-free V0= - (156+29i) [MeV] (Weise) quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ gD = -12.36/L5 W0h’ = -5 MeV w

  15. quasi-free quasi-free V0= - (156+29i) [MeV] (Weise) quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ gD = -12.36/L5 mass reduction due to the medium effect throughanomaly term W0h’ = -20 MeV w

  16. quasi-free quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ gD = -12.36/L5 quasi-free Quasi-free w overlap with bound h’ V0= - (- 42.8 + 19.5i) [MeV] (Lutz) w

  17. quasi-free h and h’ mass reductions quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ density dependent gD quasi-free V0= - (- 42.8 + 19.5i) [MeV] (Lutz)

  18. quasi-free quasi-free V0= - (156+29i) [MeV] (Weise) quasi-free h’ h Numerical results : 12C(g,p)11Bh,w,h’ density dependent gD w

  19. Summary • UA(1) anomaly effect in finite density through the view point of “mesic nuclei” • possibility of observation of anomaly effects in-medium • h and h’ mesic nuclei with NJL model • response to the environment change • (g,p) reaction for the mesic nuclei formation • Reasonably large cross sections predicted • S/N ~ 1/10 … N.Muramatsu, private communication • the experiment for the formation of w-mesic nuclei @ SPring-8  Coming soon (information on h & h’ also expected) • (d,3He) experiment for h mesic nuclei formation @ GSI  Coming soon • Future • What is the density dependence of gD ? • Other treatment ? • relation with other models for h & h’ • chiral doublet model & chiral unitary approach for the h-mesic nuclei

  20. simple quark matter • Mixed phase • Quark droplet (confine) … chiral sym. restored • Quark gas … constituent quark

  21. Omega potentials • Attractive potential • one loop approximation with an effective Lagrangian based on the SU(3) chiral symmetry incorporating vector mesons. • Repulsive potential • in a relativistic and unitary approach for meson-baryon amplitudes. • Repulsive due to a subthreshold effect of the wN(1520).

  22. at finite Temperature at finite density P. Costa et al., PLB560(03)171, Fig.2 T.Kunihiro, PLB219(89)363, Figs.2, 3 : const : const T0=100 MeV Case I Case II pseudo-scalar meson masses with KMT term

  23. gD : constant h’ h’ h’ Dmh’ ~ -250 MeV @ r0 Dmh ~ -100 MeV @ r0 h h h p p p anomaly effect in the finite density • We simulate extreme cases. ex.) w/o KMT term gD = gD(r=0) exp(-(r/r0)2) no change anomaly term effect Dmh’ ~ -150 MeV @ r0 Dmh ~ +20 MeV @ r0

  24. gD : constant gD = 0 (w/o KMT term) gD = gD(r=0) e-(r/r0) 2 Vh(r) Vh(r) Vh(r) Vh’(r) h’ h’ h’ Vh’(r) h Vh’(r) h h h : repulsive h’ : attractive h : repulsive h’ : [no effect] h : attractive h’ : attractive p p p Optical potentials : 11B

  25. Ms Mu

  26. SU(2) symmetric matter • we consider the SU(2) sym. matter as the sym. nuclear matter. baryon density constituent quark mass (result of Gap eq.) chemical potential

  27. h-production threshold (s-wave) h-production threshold 18 MeV eta binding region quasi-free region For s-state contribution, the eta-production threshold is shifted 18MeV corresponding to the difference of the separation energy. -20 0 20 40 60 Eex-E0 [MeV]

  28. P. Costa et al., PLB560(03)171, Fig.2

  29. associated with mass reduction h-nucleus optical potential

  30. Elementary Cross Section PLB72(1977)144 R. W. Clifft et al. PRD9(1974)1917 H.Brody, et al.

  31. 0.02 ~ 0.04 mb/sr Reaction Parameters • (g,p) reaction @ Eg = 2.7 GeV (around SPring-8 energy) • Target 12C • Forward(q~0 deg.) • Elementary cross section Data:SAPHIR collaboration PLB444(98)555-562 Fig: Chiang, Yang, PRC68(03)045202

  32. formation of mesic-nuclei • momentum transfer • (g,p) reaction • missing mass spectroscopy • small distortion effect • nearly(?) recoilless condition (g,p) reaction (d,3He) reaction h’ h’ SPring-8 energy ~ Eg=2.7 GeV • Green function method • [O.Morimatsu, K.Yazaki, NPA435, 727(85) • NPA483,493(88)] • to calculate the formation cross section • of the quasi-stable h, h’-nucleus system w-nucleus (Marco, Weise, PLB502(01)59) p-atom (Hirenzaki, Oset, PLB527(02)69) h/w/s-nucleus (Nagahiro, Jido, Hirenzaki, NPA in press)

  33. These two reactions have different sensitivity to the system. Distortion factor [Eikonal approx.] distortion Factor reduction of the flux due to absorption

More Related