What do we learn from the inclusion of photoproduction data into the multichannel excited baryon analysis?

Transcription

1 What do we learn from the inclusion of photoproduction data into the multichannel excited baryon analysis? Eberhard Klempt Helmholtz-Institut für Strahlen und Kernphysik Universität Bonn Nußallee 4-6, D-535 Bonn, GERMANY SFB/TR6 Baryon resonances: why? What is the point in doing baryon spectroscopy? Why baryons and not mesons (only)? What can we still learn? Baryon resonances: data and partial wave analysis The data base The BnGa approach Pion elastic scattering versus pion photoproduction Complete experiments Baryon resonances: test of models Parity doublets: is chiral symmetry restored? Test of quark models: diquarks Three-quark nature from γp π π p Missing resonances The third shell Dynamically generated resonances Conclusions

2 Baryon resonances: why? Baryons on the lattice MeV 3 R.Edwards et al., arxiv:4.55 [hep ph] (3) 338 N(938) m = 4 MeV π 3 a Lattice and quark models predict even-odd staggering (exp: parity doublets) b Lattice and quark models predict more states than observed (diquark models) c Quark models predict three-body dynamics d Missing resonances e The third shell

3 Baryon resonances: data base and partial wave analysis The Bonn Gatchina approach The helicity-dependent amplitude for photoproduction of the final state b in one partial wave is calculated as P-vector: a h b = P h a (I iρk) ab where K is called K matrix, ρ the phase space, and where P h a = α A h αg α a M α s + F a. and A h α is photo-coupling of the K-matrix pole α and F a is a non-resonant transition. In the BnGa analysis, the K-matrix has up to 9 channels and up to 4 poles. Resonances and background contributions are combined in a K matrix K ab = α g α a g α b M α s + f ab. The background terms f ab can be arbitrary functions of s. We use f ab = constant{mostly}; f ab = (a + b s) (s s ) {(I)J P = ( ) } The angular momentum barrier q L is suppressed by Blatt and Weisskopf form factors. 3

4 Meson exchange in the t-channel is represented by a Reggeon exchange amplitude: A = g(t) + ξexp( iπα(t)) sin(πα(t)) ( ν ν ) α(t). we use g(t) = c exp( bt) as vertex function and form factor. α(t) describes the trajectory, ν = (s u), ν is a normalization factor, and ξ the signature of the trajectory. (Pomeron, f and π have a positive, ρ, ω and a exchanges have a negative signature.) The Reggeon propagators are written as R(+, ν, t) = e i π α(t) sin( π α(t)) ( ) ν π α(t), R(, ν, t) = ie i α(t) ν cos( π α(t)) ( ν ν ) α(t). where + and - indicate the signature of the Regge-trajectories. To eliminate the poles at t < additional Γ-functions are introduced in (). In the case of Pomeron trajectory: ( ) ( ) ( ) π π α(t) sin α(t) sin α(t) Γ. For ρ and ω exchanges the negative poles start from a = and therefore ( ) ( ) ( π π α(t) cos α(t) cos α(t) Γ + ). For pion production, e.g., we use ρ and ρ exchanges with trajectories: ρ α(t) = t ρ α(t) = t 4

5 The data base We use data on photoproduction, RE and IM of the πn elastic scattering amplitude, and inelastic reactions: dσ dω Σ E G T P H C x C z O x O z CLAS, CBELSA, old γp π p x x x x x x x x x γp π π p γp π n x x x x x x x ( γp π π p) γp ηp x x x x x x x γp π + π p γp K + Λ x x x x x x x x ( γp π + π p) γp K + Σ x x x x x x x x γp π ηp γp K Σ + x x x ( γp π ηp) γp ωp x x x x SDMEs (γp) event based likelihood γp K + Λ x SDMEs ( γp) fit to distributions S S 3 P P 3 π p ηn dσ/dω P 3 P 33 D 3 D 33 π + p K + Σ + dσ/dω P β D 5 F 5 F 35 F 37 π p K Λ(Σ ) dσ/dω P β F 7 G 7 G 9 H 9 π p π π p event based likelihood The fit minimizes the total log likelihood defined by ln L tot = ( wi χ i w i ln L i ) Ni wi N i 5

6 γp π π p dσ/d M(pπ), µb/.35 GeV 9 < E γ < < E γ < < E γ < < E γ < 3 3 < E γ < 4 4 < E γ < 5 5 < E γ < 6 6 < E γ < 7 7 < E γ < 8 8 < E γ < 9 9 < E γ < < E γ < < E γ < < E γ < 3 3 < E γ < 4 4 < E γ < M(pπ), GeV 6

7 .5 I s p I c p I s π I c π / + 3/ +π (S) 3/ + 3/ +π (D) / 3/ +π (P) 3/ 3/ +π (F) / 3/ +π (P) 5/ 3/ +π (F) / + 3/ +π (D) 7/ + 3/ +π (D) -.5 total γp π π p total no 3/ + φ*, deg φ*, deg φ*, deg φ*, deg 7

8 .5 I s cosθ (- -.8) 8-85 cosθ ( ) 8-85 cosθ ( ) 8-85 cosθ (-.4 -.) 8-85 cosθ (-. ) I c cosθ (.) -9 9 cosθ (..4) -9 9 cosθ (.4.6) -9 9 cosθ (.6.8) -9 9 cosθ (.8 ) -9 9 φ(π + ) cosθ (- -.8) 8-85 cosθ ( ) 8-85 cosθ ( ) 8-85 cosθ (-.4 -.) 8-85 cosθ (-. ) cosθ (.) cosθ (..4) cosθ (.4.6) cosθ (.6.8) cosθ (.8 ) -9 9 φ(π + ) γp π + π p : I s, I c 8

9 Complete experiments A reconstruction of the CGLN amplitude requires the precise measurement of at least eight carefully chosen experiments. It returns four invariant amplitudes and phases for each bin in energy and angle, up to one unknown phase. A fit to the angular dependence of the reconstructed amplitudes returns the multipoles. The fit needs to be truncated at a maximum angular momentum. The many experiments determine small amplitudes and their phases due to interference with large amplitudes. A fit to the data with multipoles exploits the analyticity of the angular distributions. Undefined is one phase per energy bin. The fit needs to be truncated at a maximum angular momentum. The number of required experiments, two or more, depends on the mass range and accuracy of the data magnitude[mfm] E magnitude[mfm].8 E magnitude[mfm].5 M magnitude[mfm] M magnitude[mfm] E E- magnitude[mfm] magnitude[mfm] M magnitude[mfm] M E phase[deg] E phase[deg] M phase[deg] M phase[deg] E phase[deg] phase[deg] 5 E M phase[deg] M phase[deg] Decomposition of γp K + Λ amplitude with S, P, and D multipoles. Dashed line: BnGa 4. It is used to define the free phase and the multipoles with L 3. A.V. Anisovich et al., EPJ A5, 9 (4). 9

10 A complete experiment should identify all decay modes of contributing resonances. Channel N(895)/ N(7)/ + N(88)/ + N(875)3/ N(9)3/ + N π 4% 5% 5-% 6% 4% % N η 4% % -3% 7% % % KΛ 8% 5% 5-5% % 7% 5% KΣ 9% 5%?% % % 3% Branching ratios unconstrained in K matrix: π 9% 33% 5-4% 5% % 3% π 3% 33% N σ % % -4% % 45% % N ω 5% 3% 8±5% % % % N(44)π 4% % % N(5)π % % N ρ(77) 5% % 5-5% 9% 6% 6% N ρ(77) 9% 8% 6% 3% Total/Γ Preliminary results; CLAS data on γp π + π p were included only recently

11 Baryon resonances: test of models a Is chiral symmetry restored in high-mass hadrons? Strong interactions respect chiral symmetry. The chirality of quarks is conserved in one-gluon exchange. However, confinement leads to an inversion of the three-momenta of quarks and the chirality of quarks is changed: the chiral invariance is spontaneously broken by strong fields carrying a topological charge or winding number. Mass of ground-state baryons is due to spontaneous breaking of chiral symmetry. Thus, N / (535) is much heavier than its chiral partner, N / + (94), the pion mass is lower than the mass of the σ = f (5), and the mass of the ρ(77) meson is lower than the a (8) mass. At high excitation energies, details of the chiral potential could be irrelevant. Chiral symmetry could be restored. Then: hadrons should be organized as mass-degenerate parity doublets. L. Y. Glozman, Phys. Rept. 444, (7).

12 Parity doublets in mesons Mesons are observed in parity doublets (or even chiral quartets), except those on the leading Regge trajectory. RPP, Summary nn RPP, ss Bugg 4, 3* - 4* Bugg 4, * - * RPP, Omitted from Summary RPP, Further States ] M [GeV / + (4) 5/ + (95) f 6 a 6 (5) (45) / + 7/ + (3) (95) ω 3 ρ 3 f 4 a 4 (67) (69) ρ 5 (35) (5) () f (7) a (3) ω (78) ρ (77) J Two alternative scenarios:. Masses of mesons follow the formula M = a (L + N) note : h.o. : M = a (L + N) E. Klempt, Phys. Rev. C 66, 58 ().. Chiral symmetry is restored But: why no parity partners on leading Regge trajectory? For pp f 4 (5) in formation, L = 3 is needed, for pp η 4 (xxx), L = 4: could be suppressed. L. Y. Glozman and A. Sarantsev, Phys. Rev. D 8, 375 () M GeV

13 Parity doublets in baryons: is chiral symmetry restored? Chiral multiplets for J = /, 3/, 5/ (first three lines) and for J = /,, 7/ (last four lines) for nucleon and resonances. Limited predictive power! N / + (7) N / (65) / + (75) / (6) ** **** **** N 3/ + (7) N 3/ (7) 3/ + (6) 3/ (7) **** *** *** **** no chiral partners N 5/ + (68) N 5/ (675) **** **** N / + (88) N / (895) / + (9) / (9) ** * **** ** N 3/ + (9) N 3/ (875) 3/ + (9) 3/ (94) ** ** *** ** no chiral partners 5/ + (95) 5/ (93) **** *** N 7/ + (99) N 7/ (9) 7/ + (95) 7/ () ** **** **** * N 9/ + () N 9/ (5) 9/ + (3) 9/ (4) **** **** ** ** For γp 7/ + (95), E + 4, M + 4 are needed, for γp 7/ (xxx), E 3, E 3 : favored! Is there a 7/ (xxx) degenerate in mass with 7/ + (95)? 3

14 Data from CLAS and CBELSA/TAPS reveal ()7/ γp π p dσ/dω, µb/sr T -.5 γp π + n dσ/dω, µb/sr 4 3 T 4 χ total 4 χ π p χ π + n Data on γp π p and γp π + n reveal the existence of the one-star 7/ (). Its mass and width are determined to M = 76 ± 4 MeV Γ = ± 7 MeV Σ 9 Σ 93 5 χ KΣ 5 This value is compatible with a (L + N) predicting 95 MeV and not with parity doubling predicting 95 MeV E 57 E 9 E 8 E 7 χ π π p 5 χ 5 π ηp Both data (CLAS and CBELSA/TAP) are required to achieve this result! Chiral symmetry is not restored in high-mass hadrons cos θ cos θ 9 3 M( 7/ ), MeV A. V. Anisovich, V. Burkert, E. Klempt, V. A. Nikonov, E. Pasyuk, A. V. Sarantsev, S. Strauch, and U. Thoma, arxiv: [nucl-ex]. 4

15 b Test of quark models: diquarks ] M [GeV / + 7/ + (3) f (7) a (3) ω (78) ρ (77) 3 / + (95) ω 3 ρ 3 7 (4) 5/ + f 4 a 4 (67) (69) ρ 5 (35) (5) () (95) f 6 a 6 (5) (45) 5 J M (GeV ) 3/ +(3) N= / (6) 3/ (7) / +(75) 3/ +(6) / +(9) 3/ +(9) 5/ +(95) 7/ +(95) / (9) 3/ (94) 5/ (93) 5/ (3) 7/ () 3/ + 5/ + 5/ + 7/ +(39) 9/ +(3) / +(4) 3/ 5/ (35) 7/ 9/ (4) / / 7/ + 9/ + 9/ + / + 3/ + 5/ +(95) / 3/ (75) N= 7/ 9/ L+N N(88)/ + N(9)3/ + ** *** N()5/ + N(99)7/ + ** ** S = 3/ symmetric N mixed symmetry L = must have mixed symmetry qq not a diquark in S-wave A.V. Anisovich, E. Klempt, V.A. Nikonov, A.V. Sarantsev, U. Thoma, Phys. Lett. B 7, 67 (). 5

16 c Three-quark nature from γp π π p W, MeV σ tot, µb CBELSA 4 CBELSA/TAPS CBELSA/TAPS GRAAL MAMI (this fit) MAMI (Kashevarov) MAMI (Zehr) E γ, MeV ) (pπ ) (GeV M 3 3 M E γ =5-7 (pπ ) (GeV ) ) (pπ ) (GeV M M E γ =8- (pπ ) (GeV ) L L L (9)/ + (9)3/ + (95)5/ + (95)7/ + S = { [ ϕ s ( ρ) ϕ d ( ] [ λ) + ϕ d ( ρ) ϕ s ( ] }(L=) λ) excited excited + excited L L N(88)/ + N(9)3/ + N()5/ + N(99)7/ + M S = { [ ϕ s ( ρ) ϕ d ( ] λ) M A = [ ϕ d ( ρ) ϕ s ( ] }(L=) λ) [ ϕ p ( ρ) ϕ p ( (L=) λ)]. Ground state A. Thiel et al. [CBELSA/TAPS Collaboration], Phys. Rev. Lett. 4, no. 9, 983 (5). 6

17 Nπ π N(44)π N(5)π N(535)π L N(68)π L Nσ N(535)/ 5±5.5±.5 ± ±4 N(5)3/ 6± 8±5 < < N(65)/ 5±4 ±6 6± ±8 N(7)3/ 5±6 74±6 7±4 <4 < - 8±6 N(675)5/ 4± 3± ± - (6)/ 8±3 6± 6± x (7)3/ ±4 3±7 < 3± < - x N(7)3/ + ±4 68±7 < 3± < - 8±6 N(68)5/ + 6±4 7±5 - < - - 4±5 (9)/ + ±3 5±6 6±3-5±3 - x (9)3/ + 8±4 76±8 < 4 < 5 < - x (95)5/ + 3± 33± - - < ±5 x (95)7/ + 46± 5± x N(88)/ + 6±3 3± - - 8±4-5±5 N(9)3/ + 3± 5±4 < 5±8 7±3-4±3 N()5/ + 8±4 56±8 - ± - 6±9 ±5 N(99)7/ +.5±.5 48± < < < - - N(99)7/ + ± 6±6 < < < - - N(895)/.5±.5 7±4 8± ±5 N(875)3/ 4± ±9 5±3 < < - 45±5 (9)/ 7± 5± ± 6±4 - - x (94)3/ ± 58± 7±7 4±3 8±6 - x 7

18 Branching ratios Nπ, π N(44)π, N(5)π, N(535)π, N(68)π, Nσ Quartet of ( 95)J + 6% 8% Quartet of N( 95)J + 47% 7% In quark models, the four N s have a component in their wave function in which both oscillators are excited and a high frequency to decay into orbitally excited states. The four s have no component in their wave function in which both oscillators are excited and a low frequency to decay into orbitally excited states. Two oscillators are required to describe the wave function of N s. Reminder: = 56 S 7 M 7 M A. 56 = 4 8, 7 = 4 8 8, =

19 d Missing resonances MeV 9 MeV 7 MeV Number of expected states:. shell. shell 3. shell J P / 3/ 5/ / + 3/ + 5/ + 7/ + / 9/ Mass range N : 7; 9; 8; 5; - 3 5: 3; 5; 4; ; (D, L + N ) J P = / + J P = 3/ + J P = 5/ + J P = 7/ + (7, + (7, + (7, + (7, + (56, + (56, + (, + ) S=3/; L= (88) S=3/; L= (9) S=3/; L= (5) S=3/; L= (99) ) S=/; L= () S=/; L= (86) ) S=3/; L= (96) ) S=/; L= (7) ) S=/; L= (7) S=/; L= (68) ) S=/; L= (44) No SU(6) assignment, only for counting! ) S=/; L= S=/; L= We fit all five states but claim two only! 9

20 f The third shell 3 N s and 5 s expected in a large number of multiplets: (7, 3 ); (56, 3 ); (, 3 ); (7, ); (7, ); (7, ); (56, ); (, ) (56, ) : (9)/ (94)3/ (93)5/ N(895)/ N(875)3/ (7, 3 ): (3)5/ ()7/ N(5)3/ N(8)5/? N(9)7/ N(5)9/ N(6)5/ Show total cross section for K Λ with contributions. Capstick and Roberts: strong K Λ decays expected for N(895)/ and N(875)3/ N5/, N/ + missing

21 dσ/dω

22 ρ

23 ρ

24 ρ

25 3.5 σ tot, µb 3 K-exchange K-exchange / / -.5 / / + / 5/ M(γp), MeV 5

26 Dynamically generated resonances Are dynamically generated resonances atop of q q or qqq? Very tempting due to large N c argument: ϱ-meson: M const; Γ N, belongs to q q sector, c f (98) is a K K molecule and M, Γ increase with N c Roper resonance not fitting to quark models: dynamically generated. However: [a] M - / (6) - 3/ (7) N - / (65) - N 3/ (7) N - 5/ (675). The quark model predicts five negativeparity N resonances. N(535)/ can be generated dynamically from Nη ΣK interactions (3) - N / (5) N 3/ - (535) Can all excited mesons and baryons be generated dynamically? Oset: f (7) generated from ρρ but a (3) not from ρω (M. Lutz) 6

27 Why is this important? Meson-meson interactions: Meson resonances can be interpreted as q q q qq q q qg gg m m mesons tetraquarks hybrids glueballs molecules Meson-baryon interactions: Baryon resonances can be interpreted as qqq qqqq q qqqg b m baryons pentaquarks hybrids molecules Are all these Fock components realized individually, and then mix? Conjecture: there are no independent realizations of the Fock components. 7

28 Conclusions Presently here is a continuous increase of high-precision photoproduction data There are several groups analyzing the data Complete experiments should include multichannel analyses of all important channels Multichannel analyses give important new information: [a] The * and ** resonances of Höhler and Cutkosky are mostly confirmed [b] The mass of ()7/ is incompatible with chiral symmetry restoration [c] The four N s: (N(88)/ +, N(9)3/ +, N()5/ +, N(99)7/ + ) are incompatible with a (qq) S wave q structure of N s [d] Cascade decays of high-mass nucleon resonances show their three-body nature [e] It seems feasible to clarify the second excitation shell of N s and s [f] The relation between dynamically generated resonances and quark model states needs to be understood better 8

29 Pion elastic scattering versus pion photoproduction Pion elastic scattering: 3 (+) measurements yield two real amplitudes plus one phase dσ dω = f + + f P + A + R = P dσ dω = f + f (R + ia) dσ dω = f + f exp[ i(θ cm θ p )]. f +, f transversity amplitudes, P target asymmetry, R, A spin rotation parameters. Pion photoproduction: 8 (+8) measurements yield four real amplitudes plus three phases dσ dω = H + H + H 3 + H 4 P dσ dω = I(H H3 + H H4 ) Σ dσ dω = R(H H4 H H3 ) E dσ dω = H + H H 3 + H 4 plus T, G, H, F, C x, C z, O x, O z, T x, T z, L x, L z. Pion photoproduction is experimentally more demanding but constrains the complex amplitudes much better! 9