Baryon Spectroscopy: what do we learn, what do we need?

Transcription

1 Baryon Spectroscopy: what do we learn, what do we need? E. Klempt Helmholtz-Institut für Strahlen und Kernphysik Universität Bonn Nußallee 14-16, D Bonn, GERMANY Sixth International Workshop on Pion-Nucleon Partial-Wave Analysis and the Interpretation of Baryon Resonances 3-7 May, 11, Washington, DC, U.S.A.

2 1. Introduction Topics:. Are three-quark baryons, pentaquarks (qqqq q), hybrids, and dynamically generated resonances realized independently in Nature (even though mixing)? 3. Can quark spin and orbital angular momenta be defined for baryon resonances? 4. Can missing resonances be uncovered in inelastic reactions? 5. Can missing resonances be explained by a quark-diquark structure? 6. Are missing resonances clustered in few SU(6) multiplets? 7. Is chiral symmetry restored in highly excited baryons? 8. Summary

3 1. Introduction: Strong QCD, the physics of strongly interacting hadrons. Lattice QCD Do we understand QCD once LQCD predicts all observables? confinement non-perturbative QCD 1 Q chiral perturbation theory Q Λ QCD Q perturbative QCD asymptotic freedom Q Λ QCD QCD observables as a function of Q.

4 Aim: to understand the dynamics of strongly interacting hadrons at the level of quarks and gluons and their interactions. Naming scheme: ++ (4) requires knowledge of quantum numbers by heart ++ (4)H 3,11 requires knowledge that H is even and corresponds to L = 4. Refers to π + p scattering. Not straightforward to calculate Nω partial wave (which is L = 6). ++ (4)(11/) + is self explanatory / + (4) is compact, self explanatory; close to mesons: a (13) 11/ +(4) used here!

5 . Are three-quark baryons, pentaquarks, hybrids, and dynamically generated resonances realized independently in Nature? Fock expansion ψ(q) > = α 1 qqq(q) > + α qqqq q(q) > + α 3 qqqg(q) > + α 4 b 1 m (Q) > baryons pentaquarks hybrids dyn. gen. res.

6 Two examples: There is no super-numerocity neither for baryons nor for mesons ] [GeV M 6 π (36) [a] M - 1/ (16) 3/ - (17) - N 1/ (165) - N 3/ (17) - N 5/ (1675) 4 π (7) π (18) 1 π (13) (13) - N 1/ (15) - N 3/ (1535) π (14) n There are no mesons or baryons beyond the quark model. 1 1 There are fiercely defended candidates for glueballs (f (15)), hybrids (π 1 (16)), and dynamically generated resonances (a (98), f (98)). Quantum number exotics and heavy-light tetraquarks may exist

7 3. Can quark spin S and orbital angular momenta L be defined quantities for baryon resonances? A simple mass formula with two parameters using L and S M = a (L + N + 3/) b α D a: Regge slope, b: fraction of good diquarks (i.e. in spin and isospin) reproduces the baryon masses with surprising accuracy: (δm/m) FK =.5% (p); (δm/m) CI = 5.6% (9p) (δm/m) BnA = 5.1% (7p); (δm/m) BnB = 5.4% (7p) (δm/m) KM = 9.1% (p). FK: AdS/QCD (Forkel, Klempt) Bn: Quark model (Löring et al.) CI: Quark model (Capstick, Isgur) KM: Skyrme model (Karliner, Mattis) Is the baryon a non-relativistic system? What is the mass of quark plus string?

8 4. Can missing resonances be found in inelastic reactions? Re T Re T a) a) Im T Im T b) b) M(πN), GeV M(πN), GeV The elastic πn amplitude for the I(J P ) = 1 ( 1 ) and ) waves have 1 ( 3 little sensitivity for resonances above the first excitation shell! Need inelastic reactions!

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10 N(144)P ± 3 -(83 ± 1) BG Arndt:6 4 Hohler: ± 5 -(1 ± 35) Cutkosky:198rh N(171)P 11 5 ± 4 -(8 ± 4) BG1-1 7 ± 3 -(19 ± 5) BG1-15 Hohler:1993xq Cutkosky:198rh N(17)P 13 ± 5 -(85 ± ) BG1-1 8 ± 6 -(85 ± ) BG Arndt:6 15 Hohler: ± -(16 ± 3) Cutkosky:198 (13)P ±.5 -(47 ± 1) BG Arndt: Hohler: ± 5-47 Cutkosky:198 (16)P ± 3 -(17 ± 15) BG Arndt:6 17 ± 4 -(15 ± 3) Cutkosky:198 (191)P ± 8 -(1 ± 15) BG1 38 Hohler:1993 ± 4 -(9 ± 3) Cutkosky:198 (19)P 33 1 ± 6 ( ± 6) BG1 4 ± 4 -(15 ± 3) Cutkosky:198

11 5. Can missing resonances be explained by a quark-diquark structure? There are ambiguous solutions which lead to different interpretations wave: N1/ +(187) and (?) N 1/ +(1) + -wave: N3/ +(19) and (?) N 3/ +(1975) + -wave: N5/ +(1975) or N 5/ +(9) + -wave: N7/ +(198) or N 7/ +(7) There are four positive-parity resonances within 1 MeV, forming a spin quartet of resonances with L =, S = 3/. spin flavor spatial S = 3/ I = 1/ L = symm. mixed mixed If (qq) diquark in S-wave, then L = wave function symmetric. Diquark models ruled out!

12 6. Are missing resonances clustered in few SU(6) multipl.? χ tot χ KΛ M, MeV M, MeV M, MeV M, MeV M, MeV N 1/ (188) N 3/ (189) N 3/ (13) N 5/ (75) N 7/ (185) No 9 in γp: N 9/ (5) from πn Re T Im T M(πN), GeV

13 N 1/ (188) N 3/ (189) L = 1, S = 1/ doublet N 3/ (13) N 5/ (75) N 7/ (185) N 9/ (5) L = 3, S = 3/ quartet N 1/ (188), N 3/ (189) have no close-by N 5/ (xxx) companion. This is not a triplet plus doublet, it is an isolated doublet. Remainder: [a] M 1 1/ - (16) (13) 3/ - (17) N 1/ - (165) N - 1/ (15) N 3/ - (17) N - 3/ (1535) N 5/ - (1675) N 3/ (13), N 5/ (75), N 7/ (185), N 9/ (5) is a quartet, a doublet may be unresolved or unresolvable.

14 Recap: SU(6) decomposition: = 56 S 7 M 7 M + A 56 = = The spin-doublet N 1/ (188), N 3/ (189) must be accompanied with a spin triplet of states. Indeed, there are 1/ (19), 3/ (194), 5/ (193). These resonance are radial excitations belonging to the third shell. The spin quartet N 3/ (13), N 5/ (75), N 7/ (185), N 9/ (5) likely hides or absorbs the spin doublet. The spectrum adds a doublet: 7/ () and a 5/ (3) from GWU. The resonances above all belong to the third excitation shell.

15 3 rd J P = (56, 1 3 ) S = 3/; L = 1; N=1 1/ (19) 3/ (194) 5/ (193) S = 1/; L = 1; N=1 N 1/ (188) N 3/ (187) (7, 3 3 ) S = 1/; L = 3; N= 5/ (3) 7/ () S = 3/; L = 3; N= N 3/ (17) N5/ (7) N 7/ (19) N 9/ (5) S = 1/; L = 3; N= (56, 3 3 ), (, 3 3 ), (7, 3 ), (7, 1 3 ), (7, 1 3 ), (, 1 3 ) : Many states predicted, no candidates known All observed resonances in the third shell fit into two multiplets. Theses are (nearly) full. Six multiplets are empty. accidental? max and min moments of inertia? else?

16 7. Is chiral symmetry restored in highly Choosing the alternative solution: excited baryons? (Glozman and others) + -wave: N1/ +(187) and (?) N 1/ +(1) + -wave: N3/ +(19) and (?) N 3/ +(1975) + -wave: N5/ +(1975) or N 5/ +(9) + -wave: N7/ +(198) or N 7/ +(7) N 1/ +(171) N 1/ (165) N 5/ +(168) N 5/ (1675) N 3/ +(19) N 3/ (1875) N 7/ +(7) N 7/ (19) N 3/ +(17) N 3/ (17) N 1/ +(188) N 1/ (1895) N 5/ +(9) N 5/ (75) N 9/ +() N 9/ (5) The new resonances yield new parity doublets!

17 8. Summary Baryon spectroscopy may reveal fundamental aspects of strong QCD. Highly sensitive data have been taken and are being taken boosting the data base for excited baryon analyses. Methods have been developed suited to raise the treasure hidden in the data. We may expect a breakthrough in baryon spectroscopy in the forthcoming years.