Properties of baryons from the Bonn-Gatchina partial wave analysis

Transcription

1 Properties of baryons from the Bonn-Gatchina partial wave analysis A. Sarantsev Petersburg Nuclear Physics Institute HISKP, Bonn (Bonn University) PNPI, Gatchina (Russia) 5-8 May 5, Osaka

2 Bonn-Gatchina partial wave analysis group: A. Anisovich, E. Klempt, V. Nikonov, A. Sarantsev, U. Thoma. The new solutions BG4- and BG4- are released

3 Energy dependent approach In many cases an unambiguous partial wave decomposition at fixed energies is impossible. Then the energy and angular parts should be analyed together: A(s,t) = ββ n An ββ (s)q (β)+ µ...µ n F µ...µ n ν...ν n Q (β ) ν...ν n. Correlations between angular part and energy part are under control.. Unitarity and analyticity can be introduced from the beginning. 3. Parameters can be fixed from a combined fit of many reactions. C. Zemach, Phys. Rev. 4, B97 (965); 4, B9 (965) S.U.Chung, Phys. Rev. D 57, 43 (998) 3 A. V. Anisovich, V. V. Anisovich, V. N. Markov, M. A. Matveev and A. V. Sarantsev, J. Phys. G G 8, 5 () 4 B. S. Zou and D. V. Bugg, Eur. Phys. J. A 6, 537 (3) 5 A. Anisovich, E. Klempt, A. Sarantsev and U. Thoma, Eur. Phys. J. A 4, (5) 6 A. V. Anisovich and A. V. Sarantsev, Eur. Phys. J. A 3, 47 (6) 7 A. V. Anisovich, V. V. Anisovich, E. Klempt, V. A. Nikonov and A. V. Sarantsev, Eur. Phys. J. A 34, 9 (7). 3

4 Resonance amplitudes for meson photoproduction γ p R R π p π π (k ) q3 R (L, S) (L π R, S π ) R u(k ) R q u(q ) General form of the angular dependent part of the amplitude: ū(q )Ñα...α n (R µn)f α...α n β...β n (q +q )Ñ(j)β...β n γ...γ m (R µr ) F γ...γ m ξ...ξ m (P)V (i)µ ξ...ξ m (R γn)u(k )ε µ F µ...µ L ν...ν L (p) = (m+ˆp)o µ...µ L L+( α...α L g α β L+ L L+ σ ) L α β g αi β i O β...β L ν...ν L i= σ αi α j = (γ α i γ αj γ αj γ αi ) 4

5 N/D based (D-matrix) analysis of the data π η K J m J K m δ JK D jm = D jk α Bα km (s) M m s + δ jm Mj s π η K ˆD = ˆκ(I ˆBˆκ) ( ) ˆκ = diag M s, M s,..., MN s,r,r... ˆB ij = α B ij α = α ds π g (R)i α ρ α (s,m α,m α )g (L)j α s s i 5

6 In the present fits we calculate the elements of theb ij α the channel thresholdm α = (m α +m α ): using one subtraction taken at B ij α(s) = B ij α(m α)+(s M α) ds π g (R)i α ρ α (s,m α,m α )g α (L)j (s s i)(s Mα). m a In this case the expression for elements of the ˆB matrix can be rewritten as: Bα(s) ij = g a (R)i b α +(s M α) m a ds π ρ α (s,m α,m α ) (s s i)(s Mα) g (L)j β = g a (R)i B α g (L)j β and D-matrix method equivalent to the K-matrix method with loop diagram with real part taken into account: A = ˆK(I ˆB ˆK) B αβ = δ αβ B α 6

7 Minimiation methods. The two body final statesπn,γn πn,ηn,kλ,kσ,ωn,k Λ:χ method. For n measured bins we minimie χ = n j (σ j (PWA) σ j (exp)) ( σ j (exp)) Present solutionχ = for33988 points.χ /N F =.6. Reactions with three or more final states are analyed with logarithm likelihood method.πn,γn ππn,πηn,ωp,k Λ. The minimiation function: f = N(data) j ln N(recMC) m σ j (PWA) σ m (PWA) This method allows us to take into account all correlations in many dimensional phase space. Above data events are taken in the fit. 7

8 Baryon data base DATA BG3-4 added in BG4-5 πn πn ampl. γp πn γn πn γn ηn γp ηp γp η p γp K + Λ γp K + Σ γp K Σ + π p ηn π p K Λ π p K Σ π + p K + Σ + π p π π n π p π + π n γp π π p γp π ηp γp π + π p γp ωp γp K (89)Λ SAID or Hoehler energy fixed dω,σ,t,p,e,g,h dω,σ,t,p dω,σ dω,σ dω,σ,p,t,c x,c,o x,o dω,σ,p,c x,c dω,σ,p dω dω,p,β dω,p (K Σ ) dω (K+ Σ ) dω,p,β dω (Crystal Ball) dω,σ,e,i c,i s dω,σ,i c,i s E (CB-ELSA, CLAS) dω (MAMI) dω (MAMI) T,P,H,E (CB-ELSA) dω,σ Σ,P,T,O x,o (CLAS) Σ,P,T,O x,o (CLAS) dω (HADES) dω,i c,i s (CLAS),E,G (CB-ELSA) dω,σ,ρ ij (CLAS) dω,σ,ρ ij,ρ ij,ρ ij 8

9 New MAMI Data onγn ηn reaction Fermi motion smearing σ tot [µb] CB-ELSA CB-ELSA σ[µb] MAMI.5 H, this work 8 σ n /σ p H, Jaegle et al E γ [GeV] M(γn) [MeV] σ p σ n.8..4 E γ [GeV] B. Krusche group B. Krusche group 9

10 Full event reconstruction Energy resolution of η: W =-4 MeV (W=5-85 MeV) [-.,-.9] [-.9,-.8] [-.8,-.7] [-.7,-.6] 5 σ[µb] 5 σ n /σ p σ p (3/)*σ n σ p, free W[GeV] H, this work H, Jaegle et al..6.8 W[GeV] /dω [µb/sr] [-.6,-] [-.,-.] [.,.3] [.6,.7] [-,-.4] [-.,.] [.3,.4] [.7,.8] [-.4,-.3] [.,.] [.4,] [.8,.9] [-.3,-.] [.,.] [,.6] [.9,.] data total func. S BW backgr. BW signal BW W[MeV]

11 σ, µb 5 Solution with interference betweens states σ n /σ p.5 /dω, µb/sr /dω, µb/sr σ p 6 8 W, MeV / σ n W, MeV cos θ η cos θ η

12 Solutions with thep (68) states 8 6 σ tot, µb / / - / / + / 3/ + / 3/ - / 5/ σ tot, µb / / - / / + / 3/ + / 3/ - / 5/ σ tot, µb / / - / / + / 3/ + / 3/ - / 5/ M(γn), MeV M(γn), MeV M(γn), MeV

13 The description of the new data as well as GRAAL data is notably worse Limit for the production ofp (68): A Br(ηn) <5 Gev 3 3

14 Helicity amplitudes fors states. The results is compared with Single-Quark-Transition model calculations V. D. Burkert, R. De Vita, M. Battaglieri, M. Ripani and V. Mokeev, Phys. Rev. C 67, 354 (3) A (γp) GeV A (γn) GeV N(535)/ N(65)/ N(535)/ N(65)/ T-matrix.4 ±.8.3 ± ±.6.9 ±.6 Bare states.96 ±.7.75 ±.7 -. ± ±.6 SQT.97 ±.7.53 ± ± ±.3 ) The coupling of bare N/D states can be fixed at SQT values. ) The mass of second bare states (65) bare = 4 48 MeV while the mass of Roper bare statep (44) bare = MeV. 3) TheηN coupling ofs (65) bare is almost (and can be fixed at ) as expected from SU(3) calculations. While ηn branching ratio calculated at pole is 3 ± 5%. 4

15 Parity doublets ofn and resonances at high mass region Parity doublets must not interact by pion emission and could have a small coupling toπn. J= J= 3 J= 5 J= 7 J= 9 N / +(88) ** N / (89) ** / +(9) **** / (9) ** N 3/ +(9) *** N 3/ (875) ** 3/ +(94) *** 3/ (99) ** N 5/ +(88) ** N 5/ (6) ** 5/ +(94) **** 5/ (93) *** N 7/ +(98) ** N 7/ (7) **** 7/ +(9) **** 7/ () * N 9/ +() **** N 9/ (5) **** 9/ +(3) ** 9/ (4) ** J= 5 J= 7 J= 9 N 5/ +(9) ** N 5/ (6) ** 5/ +(94) **** 5/ (93) *** N 7/ +() ** N 7/ (5) **** 7/ +(95) **** 7/ () * N 9/ +() **** N 9/ (5) **** 9/ +(3) ** 9/ (4) a ** 5

16 Data from CLAS and CBELSA/TAPS (E-preliminary) reveal ()7/ γp π p /dω, µb/sr 4 γp π + n /dω, µb/sr 4 χ total 7/ + 7/ 4 Data on γp π p and γp π + n reveal the existence of the one-star 7/ (). Its mass and width T 85 T 3 χ π p 4 are determined to M = 76 ± 4MeV Σ 9 Σ 93 E 57 E 9 E 8 E 7 4 χ χ χ χ π + n KΣ π π p π ηp Γ = ± 7MeV This value is compatible with a (L + N) predicting 95 MeV and not with parity doubling predicting 95 MeV. 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 M, MeV A. V. Anisovich, V. Burkert, E. Klempt, V. A. Nikonov, E. Pasyuk, A. V. Sarantsev, S. Strauch, and U. Thoma, ar- Xiv: [nucl-ex]. 6

17 Fit of the new polariation data onγp ηp. (CB ELSA, Preliminary) J. Müller, J. Hartmann, M. Grüner The fit is improved if a newd 5 state is introduced to the fit 7-8 E - - E E - H H 8-9 E -3 E 7-9 E H H 9- E 3-4 E 9- E H H - E 4-5 E -3 E P 7-75 P T 7-75 T T 3-43 P P T T 933- T P P T T - T G 7-8 G T T -97 T G 8-9 G T T 97-3 T G 9- G E T M(5/ - ), MeV cos θ η D 5 : M=±5 MeV,Γ = 6±5 MeV,A /A 3-7

18 Fit of the new polariation data on γp KΛ (CLAS Preliminary, courtesy of D. Ireland ) The best improvement is also fromd 5 state O Z O x W=7 W=74 W=76 W=78 W=7 W=74 W=76 W= W=8 W=8 W=84 W=86 W=8 W=8 W=84 W= W=88 W=899 W=98 W=94 W=88 W=899 W=98 W= W=96 W=98 W= W=8 W=96 W=98 W= W= W=4 W=6 W=8 W= W=4 W=6 W=8 W= W=9 W=4 W=6 W=8 W=9 W=4 W=6 W= D 5 : M 6 MeV,Γ 3 MeV,A /A

19 Photoproduction of vector mesons.γp K Λ Density matrices dω K dω dec = dω K W(cosΘ dec,φ dec ) γp ΛK (πk) W(cosΘ,Φ) = 3 ( 4π ( ρ )+ (3ρ )cos Θ Reρ sinθcosφ ρ sin ΘcosΦ). cosθ,φ direction of the relative momentum of pion and kaon 9

20 Capstick and Roberts: strongk Λ decays expected for N(895)/ andn(875)3/ N5/,N/ + /dω σ tot, µb K-exchange K-exchange / / - / / + / 5/ M(γp), MeV

21 Density matrix elementsγp K Λ (CLAS, Preliminary) ρ ρ ρ D 5 : M 8 MeV,Γ 7 MeV,A /A 3 -.8

22 The third shell 3N 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/ missing

23 Do we have a proof for the resonances in the region.9 GeV from theγp η p data? The contribution of the partial waves to theγp η p total cross. Left panel shows CLAS and right-hand panel the CB-ELSA data. 3

24 The description of the CLAS and CB-ELSA differential cross section

25 The description of the GRAAL beam asymmetry. With CLASS differential cross setion With CB-ELSA differential cross setion

26 The data onγp π π p andγp π ηp (For details of the analysis see the talk presented by V.Nikonov, and new data were shown by A. Thiel and will be presented by Ph. Mahlberg) 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 E γ =5-7 M (pπ ) (GeV ) ) (pπ ) (GeV M 4 3 E γ =8-3 4 M (pπ ) (GeV ) Theγp π + π p data should define the decay amplitudes of the resonances into ρ(77) N and practically saturate the unitarity condition in the region up to W=.8 GeV. We include in our data base the data on: )γp π + π p differential cross section (SAPHIR, CLAS) )γp π + π p,i c,i s (CLAS) 3) New HADES data onγp π + π n (See the talk presented by W. Prygoda). 6

27 I c andi s polariation data are very important for the partial wave analysis I s p I c p I s π I c π - 3/ + N(5)+π (S+D) ) (pπ ) (GeV M 3 E γ =3-65 N(5) / N(5)+π (P+F) region I (3) region I region II 3 M (pπ ) (GeV ) / N(5)+π (P+F) 5/ + N(5)+π (D+G) - 7/ + N(5)+π (D+G) Φ*, deg Φ*, deg Φ*, deg Φ*, deg 7

28 I c andi s forγp π + π p from CLAS (Preliminary) I c Courtesy of V. Crede, Florida State U I s I c cosθ (- -.8) 4-45 cosθ (.) 45-5 cosθ (- -.8) 45-5 cosθ (.) cosθ ( ) 4-45 cosθ (..4) 45-5 cosθ ( ) 45-5 cosθ (..4) cosθ ( ) 4-45 cosθ (.4.6) 45-5 cosθ ( ) 45-5 cosθ (.4.6) cosθ (-.4 -.) 4-45 cosθ (.6.8) 45-5 cosθ (-.4 -.) 45-5 cosθ (.6.8) cosθ (-. ) 4-45 cosθ (.8 ) 45-5 cosθ (-. ) 45-5 cosθ (.8 ) -9 9 φ(π + ) I s cosθ (- -.8) 4-45 cosθ (.) 45-5 cosθ (- -.8) 45-5 cosθ (.) cosθ ( ) 4-45 cosθ (..4) 45-5 cosθ ( ) 45-5 cosθ (..4) cosθ ( ) 4-45 cosθ (.4.6) 45-5 cosθ ( ) 45-5 cosθ (.4.6) cosθ (-.4 -.) 4-45 cosθ (.6.8) 45-5 cosθ (-.4 -.) 45-5 cosθ (.6.8) cosθ (-. ) 4-45 cosθ (.8 ) 45-5 cosθ (-. ) 45-5 cosθ (.8 ) -9 9 φ(π + ) I c cosθ (- -.8) 7-75 cosθ (.) 75-8 cosθ (- -.8) 75-8 cosθ (.) cosθ ( ) 7-75 cosθ (..4) 75-8 cosθ ( ) 75-8 cosθ (..4) cosθ ( ) 7-75 cosθ (.4.6) 75-8 cosθ ( ) 75-8 cosθ (.4.6) cosθ (-.4 -.) 7-75 cosθ (.6.8) 75-8 cosθ (-.4 -.) 75-8 cosθ (.6.8) cosθ (-. ) 7-75 cosθ (.8 ) 75-8 cosθ (-. ) 75-8 cosθ (.8 ) -9 9 φ(π + ) I s cosθ (- -.8) 7-75 cosθ (.) 75-8 cosθ (- -.8) 75-8 cosθ (.) cosθ ( ) 7-75 cosθ (..4) 75-8 cosθ ( ) 75-8 cosθ (..4) cosθ ( ) 7-75 cosθ (.4.6) 75-8 cosθ ( ) 75-8 cosθ (.4.6) cosθ (-.4 -.) 7-75 cosθ (.6.8) 75-8 cosθ (-.4 -.) 75-8 cosθ (.6.8) cosθ (-. ) 7-75 cosθ (.8 ) 75-8 cosθ (-. ) 75-8 cosθ (.8 ) -9 9 φ(π + ) 8

29 SUMMARY The number of new data sets are included in the fit and are successfully described. The fit of theπ π andπ + π final state should provide an important information about resonance properties and almost saturate the unitarity condition up to invariant masses.8 GeV The analysis of photoproduction of vector mesons likeωn andk (89)Λ provides an important constraint on the branching ratios and reveals signals from resonances above GeV. We have an indication for existence of the nucleon resonance withj P = 5/ in the mass region -3 MeV. There is a problem with description of theπ + π data in the region above GeV (and even below for some double polariation data). The new information about resonance properties will be obtained and hpefully new states will be discovered. 9

30 Boson projection operators In momentum representation: P µ µ...µ n ν ν...ν n = ( ) n O µ µ...µ n ν ν...ν n = n+ i= u (i) µ µ...µ n u (i) ν ν...ν n The projection operator can depends only on the total momentum and the metric tensor. For spin it is a unit operator. For spin the only possible combination is: O µ ν = g µν = g µν p µp ν p The propagator for the particle with spins > must be constructed from the tensors gµν : this is the only combination which satisfies: Then for spin state we obtain: p µ g µν =. O µ µ ν ν = (g µ ν g µ ν +g µ ν g µ ν ) 3 g µ µ g ν ν 3

31 Recurrent expression for the boson projector operator O µ...µ L ν...ν L = L 4 (L )(L 3) Normaliation condition: L i,j= g µ i ν j O µ...µ i µ i+...µ L ν...ν j νj+...ν L L i<j,k<m g µ i µ j g ν k ν m O µ...µ i µ i+...µ j µ j+...µ L O µ...µ L ν...ν L O ν...ν L α...α L = O µ...µ L α...α L ν...ν k ν k+...ν m ν m+...ν L 3

32 Orbital momentum operator The angular momentum operator is constructed from momenta of particlesk,k and metric tensorg µν. ForL = this operator is a constant:x = TheL = operator is a vectorx () µ, constructed from:k µ = (k µ k µ ) and P µ = (k µ +k µ ). Orthogonality: d 4 k 4π X() µ X () = d 4 k 4π X(n) µ...µ n X (n ) µ...µ n = ξp µ = Then: and: X () µ P µ = X (n) µ...µ n P µj = X () µ = k µ = k ν g νµ; g νµ = in c.m.sk = (, k) ( g νµ P ) νp ν p ; 3

33 Recurrent expression for the orbital momentum operatorsx (n) µ...µ n X (n) µ...µ n = n n n i= k µ i X (n ) µ...µ i µ i+...µ n k n n i,j= i<j Taking into account the traceless property ofx (n) we have: g µi µ j X (n ) µ...µ i µ i+...µ j µ j+...µ n X (n) µ...µ n X (n) µ...µ n = α(n)(k ) n α(n) = n i= i i = (n )!! n!. From the recursive procedure one can get the following expression for the operatorx (n) : [ ( ) X µ (n)...µ n = α(n) kµ kµ...kµ n k gµ µ kµ 3...kµ n + + k 4 (n )(n 3) n ( gµ µ gµ 3 µ 4 kµ 5 k µ4 + ) ] +. 33

34 Scattering of two spinless particles Denote relative momenta of particles before and after interaction as q and k, correspondingly. The structure of partial wave amplitude with orbital momentum L = J is determined by convolution of operatorsx (L) (k) andx (L) (q): A L = BW L (s)x (L) µ...µ L (k)o µ...µ L ν...ν L X (L) ν...ν L (q) = BW L (s)x (L) µ...µ L (k)x (L) µ...µ L (q) BW L (s) depends on the total energy squared only. The convolutionx (L) µ...µ L (k)x (L) µ...µ L (q) can be written in terms of Legendre polynomialsp L (): ( L X µ (L)...µ L (k)x µ (L)...µ L (q) = α(l) k q ) P L (), = (k q ) k q α(l) = L n= n n 34

35 πn interaction States withj = L / are called - states (/ +,3/,5/ +,...) and states with J = L+/ are called + states (/,3/ +,5/,...). Ñ + µ...µ n = X (n) µ...µ n Ñ µ...µ n = iγ ν γ 5 X (n+) νµ...µ n A = ū(k )N ± µ...µ L F µ...µ L ν...ν L N ± ν...ν L u(q )BW ± L (s) c.m.s.ω [G(s,t)+H(s,t)i( σ n)]ω G(s,t) = L H(s,t) = L [ (L+)F + L (s) LF L (s)] P L (), [ F + L (s)+f L (s)] P L(). F + L = ( ) L+ ( k q ) L χi χ f α(l) L+ BW+ L (s), F L = ( ) L ( k q ) L α(l) χi χ f L BW L (s). L l χ i = m i +k i α(l) = = (L )!! l L! l=. 35

36 γn interaction Photon has quantum numbersj PC =, proton/ +. Then in S-wave two states can be formed is/ and3/. Then P-wave/ +,3/ + and/ +,3/ +,5/ +. In general case:/,/ + described by two amplitudes and higher states by three amplitudes. V (+)µ α...α n = γ µ iγ 5 X (n) α...α n, V (+)µ α...α n = γ ν iγ 5 X (n+) µνα...α n, V ( )µ α...α n = γ ξ γ µ X (n+) ξα...α n, V ( )µ α...α n = X (n+) µα...α n, V (3+)µ α...α n = γ ν iγ 5 X (n+) να...α n g µα n, V (3 )µ α...α n = X (n ) α...α n g α µ. Gauge invariance:ε µ q µ = whereq -photon momentum. wherec ± do not depend on angles. ε µ V (±)µ α...α n = C ± ε µ V (3±)µ α...α n 36

37 Resonance amplitudes for meson photoproduction γ p R R π p π π (k ) q3 R (L, S) (L π R, S π ) R u(k ) R q u(q ) General form of the angular dependent part of the amplitude: ū(q )Ñα...α n (R µn)f α...α n β...β n (q +q )Ñ(j)β...β n γ...γ m (R µr ) F γ...γ m ξ...ξ m (P)V (i)µ ξ...ξ m (R γn)u(k )ε µ F µ...µ L ν...ν L (p) = (m+ˆp)o µ...µ L L+( α...α L g α β L+ L L+ σ ) L α β g αi β i O β...β L ν...ν L i= σ αi α j = (γ α i γ αj γ αj γ αi ) 37