3. New Cascade Physics Program Yongseok Oh (Univ. of Georgia) With K. Nakayama (UGA) & H. Haberzettl (GWU) Cascade Physics Working group: B. Nefkens et al.

4. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 3 Contents 1.Motivation 2.Experiments 3.Theories 4.Photoproduction process 5.Outlook

5. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 4 1. Motivation Characters of the X hyperons  strangeness = -2, baryon number = 1, and isospin = 1/2  Narrow widths: G(X * )/G(N * or D * ) ~ 1/10 for pionic decays  G is proportioanl to (# of light quarks) 2 Riska, EPJA 17 (2003)  Insignificant sea quark contributions to hyperons DecayG exp Ratio exp (# of light quark) 2 DNpDNp 120129 S*  S p 4044 X*  X p 1011 Decuplet  octet + p expected to have larger effects for excited states from J. Price

6. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 5 Why X ? What do we know about X baryons?  If flavor SU(3) symmetry is exact for the classification of all particles, then we have N(X) = N(N * ) + N(D * )  Currently, only a dozen of X have been identified so far. (cf. more than 20 N * s & more than 20 D * s)  Only X(1318) and X(1530) have four-star status. (cf. the rating is based on the clearness of the peak.)  Even the quantum numbers of most X resonances are still to be identified: practically, no meaningful information for the X resonances. Particle Data Group (2006)

7. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 6 Advantages Easy identification  Small decay widths  Identifiable in a missing mass plot, e.g., missing mass m(K + K + ) in  + p  K + + K + + X, invariant mass of decay products such as X  p L  Background is less complicated. (  + p  K + + K + + X *  K + + K + + p + X gs )  Isospin ½ (cf. nucleonic resonances have N * & D * ; I=1/2 and 3/2)  No flavor singlet state (unlike L hyperons) What can we learn from it?  Baryon structure from X spectroscopy  Properties of S=-1 resonances  Exotic particles (penta-quarks & tetra-quarks)  New particles (perhaps S=-4 dibaryon?)

8. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 7 Exotic X(1860) or  (1860) Isospin-3/2 state: therefore, penta-quark exotic Report from NA49 in pp collision PRL 92 (2004)  but never be confirmed by other experiments with higher statistics, e.g. WA89 in S - -nucleus collisions, PRC 70 (2004) (no signal of X(1860) with the 40-year accumulation of Xp spectra) NA49 WA89

9. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 8 2. Experiments Difficulties in searching for X * Mostly processes through K  p reactions or the S-hyperon induced reactions were used. (initial state has S=-1)  No current activity in X physics with hadron beams They can only produced via indirect processes from the nucleon. (initial state has S=0)  In the case of photon-nucleon reaction, we have at least three-body final state.  The current CLAS data indicate that the production cross section is less than 20 nb at low energies. (cf. KL or KS photoproduction have cross sections of order of a few mb).  Other technical difficulties Questions  What is the third lowest state following X(1320) and X(1530)?  Can we confirm the existence of X(1620)?

10. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 9 Earlier experiments WA89 results with S - beam (hep-ex/0406077) Comments by PDG (2006) 153016901860(?)

11. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 10 Recent activity CLAS at JLab: initiated new Cascade physics program photoproduction processes:  p  K K X More data with higher statistics are under analyses. PRC 71 (2005) CLAS preprint (2006) g6b g6a

12. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 11 3. Theories Review on the works before 1975 Samlos, Goldberg, and Meadows, Rev. Mod. Phys. 46 (1974) 49 What is the first excited state following X(1320) and X(1530)? What is X(1690)? Even the parity of the ground state X was not directly measured. Model predictions for the X spectrum are needed. Most model builders have not considered X spectrum or the structure of X resonances seriously, except the lowest X ’ s of octet and decuplet.

13. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 12 Quark model (One-gluon-exchange model) Chao, Isgur, Karl, PRD 23 (1981) Non-relativistic quark model Chao, Isgur, Karl, PRD 23 (1981)  First order perturbation calculation in anharmonic terms (linear, Coulomb) and in hyperfine interactions. from S. Capstick X(1690) has J P =1/2 + ? The first negative parity state appears at ~1800 MeV. Decay widths are not fully calculated by limiting the final state. (but indicates narrow widths) Relativistic quark model ?

14. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 13 One-boson-exchange model Glozman, Riska, Phys. Rep. 268 (1996) Exchange of octet pseudoscalar mesons.  First order perturbation calculation around harmonic oscillator spectrum. Negative parity state seems to have lower mass: but no clear separation between +ve and – ve parity states Strong decay widths are not calculated.

15. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 14 Comparison of OGE and OBE The two models show very different X hyperon spectrum. The predictions on the candidate for X(1690) are different.

16. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 15 Improved OBE model Semi-relativistic OBE model Glozman et al., PRD 58 (1998) OBE + OGE Valcarce, Garcilazo, Vijande, PRC 72 (2005) Glozman et al.Valcarce et al. MNMN

17. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 16 1/N c (constituent quark model) Expand the mass operator by 1/N c expansion Basically O(3) X SU(6) quark model Mass formula (e.g. 70-plet: L=1, p=-1)  Fit the coefficients to the known particle masses and then predict. from J.L. Goity Where is X(1690)? Schat, Scoccola, Goity, PRL 88 (2002) and other groups

18. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 17 QCD sum rules Mass splitting between 1/2 + and1/2 - baryons.  Jido & Oka, hep-ph/9611322 (unpublished)  Interpolating field (with a parameter t)  X(1/2+) = 1320 MeV and X(1/2-) = 1630 MeV.  So, X(1690) would be X(1/2 - ). Sum rules for 1/2 +, 1/2 -, and 3/2 -.  F.X. Lee & X. Liu, PRD 66 (2002)  Three-parameter calculation (similar interpolating field)  X(1/2+) = 1320 MeV, X(1/2-) = 1550 MeV, X(3/2-) = 1840 MeV (exp. 1820 MeV)  X(1820) is well reproduced, but where is X(1690)?

19. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 18 Other hadron models No rigorous calculation for X spectrum was done in other hadron models in the market. NNJL model, Skyrme model, bag models(?), … This is a good place to test and improve hadron models. Various model calculations are highly desirable.

20. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 19 Lattice calculation F.X. Lee et al., Nucl. Phys. B (PS) 119 (2003) Quenched approx. with Bayesian statistics Level cross-over in the physical region? Results for 1/2+ and 1/2- states Higher-spin states?

21. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 20 Lattice calculation Bern-Graz-Regensburg Coll., PRD 74 (2006) Quenched approx. (variational method) The first excited state seems to have negative parity. Higher-spin states? X octet with J = 1/2

22. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 21 S=-4 dibaryon? A new dibaryon (possibly at JLab & J-PARC) Feasibility of an 1 S 0 di-Cascade bound state? A simple estimate G.A. Miller, nucl-th/0607006  Both NN and XX are in the same 27-plet representation of SU(3).  N and X iso-doublets occupy analogous positions.  Use 4-point interactions (meson-exchange is ignored)  Invariant under NN  XX  Maybe good for 1 S 0

23. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 22 di-Cascade NR Schroedinger equation with a potential whose parameters are fixed by n-n/p-p or n-p system.  Square well potential, non-local separable potential, delta-shell potential.  Obtained results for XX system  Scattering length: 8~11 fm  Binding energy: 0.5 ~ 7.5 MeV Deuteron binding energy ~ 2.2 MeV With Nijmegen potential (6 versions of it)  Binding energy: 0.1 ~ 16 MeV Suggests the existence of a XX bound state. Needs other model predictions. Possible reactions:  D (JLab) or KD (J-PARC)

24. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 23 4. Photoproduction CLAS at JLab succeeded to produce X by photon- induced reactions.  So far, only a few inclusive X photoproduction were reported. Tagged Photon Spectrometer Collab., NPB 282 (1987) No theoretical work on X photoproduction  Except one for pentaquark X photoproduction Liu, Ko, PRC 69 (2004) Our strategy  Investigate the production mechanism using the currently available information only.  Then consider other possible (and important) mechanisms.  Final-state interactions & coupled channel?  Ideal, but practically impossible at this stage.  Use the tree-level approximation as the first attempt to understand the production mechanism. Nakayama, Oh, Haberzettl PRC 74 (2006) 035205

25. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 24 Forbidden or suppressed mechanisms In kaon — anti-kaon production, meson production processes, especially f meson production, are important. In X photoproduction,  such processes are suppressed since the produced meson should be exotic having strangeness S=+2 in order to decay into two kaons.  By the same reason, t-channel meson-exchange for KN  KX is also suppressed as the exchange meson should have S=+2. E: exotic meson with S=+2

26. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 25 Considered diagrams Consider K and K * exchange only.  Axial-vector K 1 mesons: lack of information & heavy mass  Scalar k or K 0 mesons: not allowed since k  K  coupling is forbidden by angular momentum and parity conservation. Consider  N ’ = N and D  Y, Y ’ = low-lying L and S hyperons  X ’ = X(1320) and X(1530) + exchanged diagrams q 1 q 2

27. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 26 Strategy Problems  There are many hyperon resonances of S=-1, which can contribute to the production process.  We start with a very simple model for the production mechanism by choosing only a few intermediate hyperon states.

28. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 27 Intermediate hyperons Particle Data Group Decay widths and couplings are in a very wide range. No information for the other couplings.

29. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 28 Strategy Problems  There are many hyperon resonances of S=-1, which can contribute to the production process.  We start with a very simple model for the production mechanism by choosing only a few intermediate hyperon states. Lots of unknown coupling constants and ambiguities.  We make use of the experimental (PDG) or empirical data (like Nijmegen potential) if available.  Or we use model predictions for the unknowns: SU(3) relations, quark model, ChPT, Skyrme model, chiral quark model etc.  The details are in nucl-th/0605169. Preliminary CLAS data (of Weygand and Guo)  The total cross sections data ( hep-ex/0601011 ) is used to determine the cutoff parameter of the form factors.

30. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 29 Model (A) First, consider only the low mass hyperons: L(1116), L(1405), L(1520), S(1190), S(1385)  Their couplings are rather well-known. The cross sections for the two non-identical kaon productions are larger than those for two identical kaon productions: isospin factors The dominant contribution to  p  K + K + X - comes from the spin-1/2 hyperon resonances. spin-1/2 baryons spin-3/2 baryons

31. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 30 Invariant mass distributions Invariant mass distributions of K + X - and K + K +.  No structure for K + K + distribution as expected: absence of S=+2 exotic mesons in this calculation.  No structure for K + X -  distribution since we are considering the low-lying hyperons only whose masses are below 1.6 GeV, while the minimum value for m(K + X - ) is > 1.8 GeV pv couplingps coupling

32. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 31 Higher-mass resonances As the K + X -  mass distribution covers the energy larger than 1.8 GeV, it is natural to expect important role from the higher-mass hyperon resonances around 1.8 GeV and above. The properties of higher-mass hyperons are poorly known. We first consider the hyperons of spin-1/2 and 3/2 only. What we know are  The broad range of the NYK couplings: from  (Y  NK) of PDG  The photoproduction amplitudes at the hyperon on-shell point have  So 1/2  and 3/2 + hyperon resonances around M = 1.8 GeV are expected to be important.

33. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 32 Intermediate hyperons Particle Data Group Decay widths and couplings are in a very wide range. No information for the other couplings.

34. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 33 Model (B) Assumptions.  In order to reduce the number of unknown couplings, we consider two hyperon resonances only, L(1800)1/2  and L(1890)3/2 + in addition to the low mass hyperons.  Neglect their magnetic moments and radiative transitions.  Then the only unknown is the product of the coupling constants, g NLK g XLK.  We take g NLK g XLK = 2 for simplicity.  Form factors are readjusted to fit the total cross section data.

35. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 34 Results (I) Total cross sections Nearly the same results as before.  total cross section alone cannot distinguish the contributions from the low- mass and the high-mass resonances.  Other quantities should be measured. Spin -1/2 Spin -3/2

36. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 35 Results (II) Invariant mass distributions of K + X  and K + K +.  No structure for K + K + distribution as before.  Two bump structure for K + X -  distribution is seen.  L(1800) bump cannot be seen.: below threshold  The first bump at lower mass is due to L(1890).  The second bump is not from a resonance at higher mass. » The position depends on the energy. » So-called kinematic reflections of the three-body final states.

37. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 36 Model (C) What happens if we have (unknown) hyperon resonance at a mass around 2 GeV which couples strongly enough to the nucleon and X? In fact, the preliminary CLAS data do not show a sharp peak in K + X  channel. Some well-established L and S resonances of spin-5/2 and 7/2 at around 2 GeV. Consider a fictitious spin-3/2 + hyperon at around 2 GeV, so we consider three high-mass resonances in addition to the low-lying resonances. L(1800)1/2 , L(1890)3/2 +, and L(2050)3/2 + (fictitious particle) Adjust the parameters so that we have similar total cross sections.

38. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 37 Results (IV) But we have very different K + X  invariant mass distribution.  The bump structure disappears.  The valley between the two peaks is now filled up by the additional resonance.  This shows that the higher-mass resonance at around 2 GeV should be examined.

39. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 38 5. Outlook CLAS at JLab initiated Cascade Physics Program.  Opens the door to many avenues of research for X hyperons. More data are coming!  Does X(1620) exist?  Should confirm other X resonances in PDG. Role of L and S resonances in X photoproduction.  Offers a chance to study those hyperons.  Higher mass and high spin resonances: under progress Theoretical models for X spectrum  Only a few model gives the X spectrum.  Where is the low-lying X resonances?  Possible di-baryon?  Etc …

40. UGA Quarks, Nuclei and Universe, Nov. 2006 Yongseok Oh 39 Cascade Physics Working Group Members B. Nefkens, D.S. Carman, S. Capstick, J.L. Goity, L. Guo, H. Haberzettl, N. Marthur, K. Nakayama, Y. Oh, J. Price, D.G. Richards, S. Stepanyan, D.P. Weygand, and more.

41. 60 회 생신 축하합니다.