The missing resonance problem. E. Santopinto INFN KL2016, 1-3 february 2016

Transcription

1 The missing resonance problem E. Santopinto INFN KL2016, 1-3 february 2016

2 N* SPECTRUM Missing resonance problem What are collective modes? What is the structure of the states? m = 396 MeV π" Dudek et al. Experiment

3 hypercentral ConsNtuent Quark Model CIPANP St. Petersburg, June 3rd 2012 Annalisa D'Angelo - Review of QCD, Hadron spectroscopy and exotics sessions 11

4 Non-strange baryons. Complete spectrum Interac(ng qd Model FerreO, S., Vassallo,Phys. Rev.. C83, (2011) E.S.,Phys. Rev. C 72, (R) (2005). 0 missing resonances Caps(ck & Isgur s Model Caps(ck and Isgur, Phys. Rev. D34, missing resonances U(7) Algebraic Model Hypercentral CQM Bijker, Iachello and Leviatan, Annals Phys. 236, missing resonances Giannini, Santopinto, Vassallo, Eur. Phys. J.A12:447 9 missing resonances

5 The InteracNng Quark Diquark Model

6 Missing resonance problem! States predicted by quark models with no corresponding experimental counterparts! QMs predict eccessive number of states! Possible explanations: 1) Some baryon states may be very weakly coupled to single-pion channels. Look for two-pion, three-pion, eta decay channels 2) Consider models based on smaller number of effective degrees of freedom (like quark-diquark model): number of missing states decreases notably

7 Evidences of diquark correlanons Regge behavior of hadrons Baryons arranged in rotational Regge trajectories (J=α+α M2) with the same slope of the mesonic ones. I I = ½ rule in weak nonleptonic decays Neubert and Stech, Phys. Lett. B 231 (1989) 477; Phys. Rev. D 44 (1991) 775 Regularities in parton distribution functions and in spindependent structure functions Close and Thomas, Phys. Lett. B 212 (1988) 227 Regularities in Λ(1116) and Λ(1520) fragmentation functions Jaffe, Phys. Rept. 409 (2005) 1 [Nucl. Phys. Proc. Suppl. 142 (2005) 343] Wilczek, hep-ph/ Any interaction that binds π and ρ mesons in the rainbow-ladder approximation of the DSE will produce diquarks Cahill, Roberts and Praschifka, Phys. Rev. D 36 (1987) 2804 Indications of diquark confinement Bender, Roberts and Von Smekal, Phys. Lett. B 380 (1996) 7 7

8 Interac(ng qd model E. Santopinto, PRC72, (2005) I part:construc(on of the states Diquark Two correlated quarks in S wave:symm. Baryon in 1 c color representazion à diquark in bar- 3 c (A) Diquark WF: Ψ D spin- flavor part symm. à 15 (A) repr. not present SU(6) sf representa(ons for baryons Problem of missing resonances

9 Scalar & axial- vector diquarks 21 SU(6) sf representa(on Decomposed in SU(2) s x SU(3) f [bar- 3,0] & [6,1] representa(ons. Nota(on: [flavor,spin] Good & bad diquarks According to OGE- calcula(ons, [bar- 3,0] is energe(cally favored [Wilczek, Jaffe] [bar 3,0]: good (scalar) diquark [6,1]: bad (axial- vector) diquark

10 the Interac(ng qd model E. Santopinto, PRC72, (2005) Hamiltonian H = + ( 1) 2 p 2m τ + βr + [ BδS r 2Ae [( s s ) l+ 1 αr ,1 + Cδ ] + + ( t 12 0 t 3 ) + ( s 12 s 3 )( t 12 t 3 )] Non- rel. Kine(c energy + Coulomb + linear confining terms Splikng between scalar & axial- vector diquarks Exchange poten(al

11 Baryon L 2I,2J Status Mass J p M cal (MeV) (MeV) N(939)P 11 **** 939 1/ N(1440)P 11 **** / N(1520)D 13 **** / N(1535)S 11 **** / N(1650)S 11 **** / N(1675)D 15 **** / N(1680)F 15 **** / N(1700)D 13 *** / N(1710)P 11 *** / N(1720)P 13 **** / N(1860)F 15 ** / N(1875)D 13 *** / N(1880)P 11 ** / N(1895)S 11 ** / N(1900)P 13 *** / N(1990)F 17 ** / N(2000)F 15 ** / N(2040)P 13 * / N(2060)D 15 ** / N(2100)P 11 ** / N(2120)D 13 ** /2 2069

12 Rel. Interac(ng qd model J. Ferrek, E. Santopinto & A. Vassallo, PRC83, (2011) Rela(vis(c extension of the previous model (point- form formalism). Numerical solu(on with varia(onal program Parameters filed to nonstrange baryon spectrum

13 Extension to strange baryons 13 Mass formula M = E 0 + q 2 + m q 2 + m M dir + M ex + M cont Exchange potennal is generalized to Gürsey- RadicaN inspired! interacnon M ex = ( 1) L+1 e σ r [A s s1 s!! 2 + A I t1 t!! 2 + A F λ1! λ 2 ] λ s are SU(3) Gell- Mann matrices Results updated to most recent exp. data. Global fit to strange & nonstrange baryons SANTOPINTO AND FERRETTI, PRC92, (2015)

14 Parameters

15 N spectrum and N(1900)P 13 3 missing states SANTOPINTO AND FERRETTI, PRC92, (2015) 15

16 Σ, Σ *, Ξ, Ξ * and Ω spectrum *** and **** PDG states below 2 GeV SANTOPINTO AND FERRETTI, PRC92, (2015) 16

17 Λ and Λ * spectrum Λ * (1405) *** and **** PDG states below 2 GeV SANTOPINTO AND FERRETTI, PRC92, (2015) 17

18 N spectrum and N(1900)P 13 3 missing states SANTOPINTO AND FERRETTI, PRC92, (2015) 18

19 Δ spectrum No missing states below 2 GeV Delta(1930) 3/2- well described, on the contrary it is a problem in 3quark models since it corresponds to higher shells 19

20 Σ and Σ * spectrum 1 missing state 20

21 Ξ, Ξ * and Ω spectrum 5 missing states 21

22 Λ and Λ * spectrum 13 missing states SANTOPINTO AND FERRETTI, PRC92, (2015) 22

23 A long standing problem of three quarks QMs in the strange sector is that of Λ (1405), since its experimental mass is not reproduced with a reasonable accuracy within this kind of models. Here, the mass of this resonance is well reproduced in terms of a quark-diquark picture of baryons. Λ(1116) Λ(1116) and Λ (1520) are described as bound states of a scalar diquark [n, n] andaquarks, wherethequark- diquark system is in S or P -wave, respectively. This is in accordance with the observations of Refs. [29, 30] on Λ s fragmentation functions, that the two resonances can be described as [n, n] s systems. See Table VII.

24 Strong decays of Baryons and Missing resonances Elena Santopinto Hugo García Tecocoatzi Jacopo Ferretti Roelof Bijker Università di Genova, Instituto de Ciencias Nucleares UNAM, INFN sezione di

25 different CQMs for bayons Kin. Energy SU(6) inv SU(6) viol date Isgur-Karl non rel h.o. + shift OGE Capstick-Isgur rel string + coul-like OGE 1986 U(7) B.I.L. rel M^2 vibr+l Guersey-R 1994 Hyp. O(6) non rel/rel hyp.coul+linear OGE 1995 Glozman Riska non rel/relplessas h.o./linear GBE 1996 Bonn rel linear 3-body instanton 2001

26 2 Quarks models of baryons and mesons E ective Models U(7) Model The Hypercentral Model Strong Decays 3 Results U(7) Model results The Hypercentral Model results

27 U(7) Model Ann. Phys. 284, 89 (2000) In the U(7) algebraic model the baryon spectrum is computed through algebraic methods, introduced in the 60 s by Gell-Mann, Ne eman and Okubo (flavor and spin part). In the U(7) model, such methods are also used to describe the spatial part. The full algebraic structure is obtained by combining the symmetry of the spatial part, U(7), with that of the internal spin-flavor-color part SU sf (6) SU c (3) U(7) SU sf (6) SU c (3). The baryon mass formula is written as the sum of three terms ˆM 2 = M ˆM 2 space + ˆM 2 sf, where ˆM space 2 is a function of the spatial degrees of freedom and ˆM 2 depends on the internal ones. The sf energy spectrum, corresponding to the spatial degrees of freedom, is given by: ˆM 2 space = ˆM 2 vib + ˆM 2 rot. Since the space-spin-flavor wave function is symmetric under permutation group S 3 of the three identical constituents, the permutation symmetry of the spatial wave function has to be the same as that of the spin-flavor part. Thus, the spatial part of the mass operator ˆM 2 space has to be invariant under the S 3 permutation symmetry. The mass formula ˆM 2 = M Ÿ 1 v 1 + Ÿ 2 v 2 + L + M 2 GR,

28 N ú Spectra in U(7) Model Ann. Phys. 284, 89 (2000) Mass spectrum of nonstrange baryon resonances in the oblate top model. The masses are given in MeV. Baryon L 2I,2J Status Mass State (v 1, v 2 ) M calc N(939)P 11 **** /2 [56, 0 + ] (0,0) 939 N(1440)P 11 **** /2 [56, 0 + ] (1,0) 1444 N(1520)D 13 **** /2 [70, 1 ] (0,0) 1563 N(1535)S 11 **** /2 [70, 1 ] (0,0) 1563 N(1650)S 11 **** /2 [70, 1 ] (0,0) 1683 N(1675)D 15 **** /2 [70, 1 ] (0,0) 1683 N(1680)F 15 **** /2 [56, 2 + ] (0,0) 1737 N(1700)D 13 *** /2 [70, 1 ] (0,0) 1683 N(1710)P 11 *** /2 [70, 0 + ] (0,1) 1683 missing 2 81/2 [20, 1 + ] (0,0) 1713 missing 2 83/2 [20, 1 + ] (0,0) 1713 N(1720)P 13 **** /2 [56, 2 + ] (0,0) 1737 misssin 2 83/2 [70, 2 ] (0,0) 1874 misssin 2 85/2 [70, 2 ] (0,0) 1874 misssin 2 85/2 [70, 2 + ] (0,0) 1874 N(1860)F 15 ** /2 [70, 2 + ] (0,0) 1975 N(1875)D 13 *** /2 [70, 2 ] (0,0) 1975 N(1880)P 13 ** /2 [70, 2 + ] (0,0) 1975 N(1895)S 11 ** /2 [70, 2 ] (0,0) 1975 N(1900)P 13 *** /2 [70, 2 + ] (0,0) 1874 misssin [70 1 ] (1,0) 1909

29 The Hypercentral Model (hqm) PL. B364, 231 (1995) In the hqm, the Jacobi coordinates fl = 1 Ô 2 ( r 1 r 2 ) and = 1 Ô 6 ( r 1 + r 2 2 r 3 ),whichconstitutetheusual choice in QM calculations, are substituted with the hyperspherical coordinates. These are the angles fl =( fl, fl ) and =(, ),thehyperradius,x, andthehyperangle,, definedas apple x = fl 2 + 2, = arctan fl. the hqm has the assumption that the quark interaction only depends on the hyperradius : V 3q ( fl, ) =V (x) With the form where and are free parameters. Thus,  space,isfactorizedas V (x) = x + x  space =  3q ( fl, ) = (x)y [ ]l fll ( fl,, ), where the hyperradial wave function,  (x), islabeledbythegrandangularquantumnumber and the number of nodes. Thedynamicsiscontainedin (x), whichisasolutionofthehyperradialequation [ d2 dx x d dx ( +4) x 2 ] (x) = 2m [E V 3q (x)]  (x). The complete hcqm hamiltonian is then H hcqm = 3m + p fl 2 2m + p 2 2m x + x + H hyp. where p and p are the momenta conjugated to the Jacobi coordinates and.

30 The baryon spectra in the hqm P. L. B364, 231 (1995) Mass spectrum of N and resonances within the hqm, compared with the existing experimental data. Baryon L 2I,2J Status Mass (MeV) State M hqm (MeV) N(939)P 11 **** /2 [56, ] 938 N(1440)P 11 **** /2 [56, ] 1550 N(1520)D 13 **** /2 [70, 1 1 ] 1525 N(1535)S 11 **** /2 [70, 1 1 ] 1507 N(1650)S 11 **** /2 [70, 1 2 ] 1574 N(1675)D 15 **** /2 [70, 1 1 ] 1579 N(1680)F 15 **** /2 [56, ] 1798 N(1700)D 13 *** /2 [70, 1 2 ] 1606 N(1710)P 11 *** /2 [70, ] 1808 N(1720)P 13 **** /2 [56, ] 1797 missing 4 83/2 [70, ] 1835 missing 2 81/2 [20, ] 1836 missing 2 83/2 [20, ] 1836 N(1860)F 15 ** /2 [70, ] 1844 N(1875)D 13 *** /2 [70, 1 1 ] 1899 N(1880)P 11 ** /2 [70, ] 1839 N(1895)S 11 ** /2 [70, 1 1 ] 1887 N(1900)P 13 *** /2 [70, ] 1853 missing 4 81/2 [70, 1 2 ] N(1990)F 17 ** /2 [70, ] 1840 N(2000)F INFN sezione 4 ** di Genova KL2016, 8 [70 JLAB, ] february

31 Strong Decays of baryons, 3P 0 mechanism arxiv: The 3 P 0 pair-creation model of hadron vertices; the q q pair (45) is created in a 3 P 0 flavor-color singlet. A is the initial state baryon, B and C are the final baryon and meson states, respectively. The 3 P 0 operator T = 3 q s i,j 2# $ (0) d p i d p j ( p i + p j )C ij F ij V (p i p j ) ij Y 1 ( p i p j ) b 0 i ( p i )d j ( p j ) γ 0 γ eff 0 = m n m i γ 0,

32 Γ A BC = Φ A BC (q 0 ) l BCq 0 lj T A 2 Φ A BC (q 0 )=2πq 0 E b (q 0 )E c (q 0 ) M a, (21) depending on q 0 and on the energies of the two intermediate-state hadrons, E b = Mb 2 + q2 0 and E c = M 2 c + q0 2. The third possibility is to use an effective phase space factor [3, 15], Φ A BC (q 0 )=2πq 0 Mb Mc M a, (22) where Mb and M c are the effective baryon and meson masses, respectively, evaluated by means of a spinindependent interaction (see Table I). According to Ref. [15], this is valid in the weak-binding limit, where ρ and π are degenerate and m π =5.1m π. In the case of heavy baryons and mesons, whose internal dynamics is almost non-relativistic and the hyperfine interactions are relatively small, the three types of phase space factors provide almost the same results.

33 U(7) Model Results, arxiv: * and 4* states TABLE III: Strong decay widths of three- and four-star nucleon resonances (in MeV), calculated with the U(7) Model of II A and Refs. [39, 40], in combination with the relativistic phase space factor (RPSF) of Eq. (21) and the values of the m parameters of Table II (second column), or the effective phase space factor(epsf)of Eq. (22)and the values of the m parameters of Table II (third column). The experimental values are taken from Ref. [1]. Decay channels labeled by are be threshold. The symbols (S) and(d) standfors- andd-wave decays, respectively. Resonance Status M [MeV] Nπ Nη ΣK ΛK π Nρ Nω N(1440)P 11 **** Exp /2 [56, ] RPSF 2 8 1/2 [56, ] EPSF N(1520)D 13 **** Exp /2 [70, 1 1 ] RPSF 2 8 3/2 [70, 1 1 ] EPSF N(1535)S 11 **** < 2 Exp /2 [70, 1 1 ] RPSF 2 8 1/2 [70, 1 1 ] EPSF N(1650)S 11 **** Exp /2 [70, 1 1 ] RPSF 4 8 1/2 [70, 1 1 ] EPSF N(1675)D 15 **** < Exp /2 [70, 1 1 ] RPSF 4 8 5/2 [70, 1 1 ] EPSF N(1680)F 15 **** Exp /2 [56, ] RPSF 2 8 5/2 [56, ] EPSF N(1700)D 13 *** < (S) Exp. < 50 (D) 4 8 3/2 [70, 1 1 ] RPSF 4 8 3/2 [70, 1 1 ] EPSF N(1710)P 11 *** Exp /2 [70, ] RPSF 2 8 1/2 [70, ] EPSF N(1720)P 13 **** Exp /2 [56, ] RPSF 2 8 3/2 [56, ] EPSF N(1875)D 13 *** (S) Exp (D) Exp /2 [70, 2 1 ] RPSF 4 8 3/2 [70, 2 1 ] EPSF N(1900)P 13 *** Exp /2 [70, ] RPSF 2 8 3/2 [70, ] EPSF

34 U(7) Model Results, arxiv: TABLE IV: As Table III, but for resonances. The symbols (S), (P ), (D) and(f )standfors-, P -, D- andf -wave decays, respectively. Resonance Status M [MeV] Nπ ΣK π η Σ K Nρ (1232)P 33 **** Exp /2 [56, ] RPSF /2 [56, ] EPSF (1600)P 33 *** < 88 Exp /2 [56, ] RPSF /2 [56, ] EPSF (1620)S 31 **** Exp /2 [70, 1 1 ] RPSF /2 [70, 1 1 ] EPSF (1700)D 33 **** (S) Exp (D) /2 [70, 1 1 ] RPSF /2 [70, 1 1 ] EPSF (1905)F 35 **** < 100 > 162 Exp /2 [56, ] RPSF /2 [56, ] EPSF (1910)P 31 **** Exp /2 [56, ] RPSF /2 [56, ] EPSF (1920)P 33 *** (P ) Exp (F ) /2 [56, ] RPSF /2 [56, ] EPSF (1930)D 35 *** Exp /2 [70, 2 1 ] RPSF /2 [70, 2 1 ] EPSF (1950)F 37 **** < 34 Exp /2 [56, ] RPSF /2 [56, ] EPSF 3* and 4* states

35 U(7) Model Results, arxiv: * and 4* states TABLE V: As Table III, but for Σ and Σ resonances. Baryon Status M [MeV] NK Σπ Λπ Ση ΞK K Σ π NK Σρ Λρ Σω Σ(1660)P 11 *** seen seen Exp /2 [56, ] RPSF Σ(1670)D 13 **** Exp /2 [70, 1 1 ] RPSF Σ(1750)S 11 *** < 13 seen 9 88 Exp /2 [70, 1 1 ] RPSF Σ(1775)D 15 **** Exp /2 [70, 1 1 ] RPSF Σ(1915)F 15 **** seen seen < 8 Exp /2 [56, ] RPSF Σ(1940)D 13 *** < 60 seen seen seen seen seen Exp /2 [56, 1 1 ] RPSF Σ (1385)P 13 **** Exp /2 [56, ] RPSF Σ (2030)F 17 **** < Exp /2 [56, ] RPSF

36 U(7) Model Results, arxiv: * and 4* states TABLE VI: As Table III, but for Λ and Λ resonances. Baryon Status M [MeV] NK Σπ Λη ΞK Σ π NK Σρ Λω Λ(1600)P 01 *** Exp /2 [56, ] RPSF Λ(1670)S 01 **** Exp /2 [70, 1 1 ] RPSF Λ(1690)D 03 **** Exp /2 [70, 1 1 ] RPSF Λ(1800)S 01 *** seen seen Exp /2 [70, 1 1 ] RPSF Λ(1810)P 01 *** seen Exp /2 [70, ] RPSF Λ(1820)F 05 **** Exp /2 [56, ] RPSF Λ(1830)D 05 **** > 9 Exp /2 [70, 1 1 ] RPSF Λ(1890)P 03 **** seen Exp /2 [56, ] RPSF Λ(2110)F 05 **** seen Exp /2 [70, ] RPSF Λ (1405)S 01 **** Exp /2 [70, 1 1 ] RPSF Λ (1520)D 03 **** Exp /2 [70, 1 1 ] RPSF

37 U(7) Model Results, arxiv: * and 4* states TABLE VII: As Table III, but for Ξ and Ξ resonances. Baryon Status M [MeV] ΣK ΛK Ξπ Ξ π Ξ(1690)S 11 *** Exp /2 [70, 1 1 ] RPSF Ξ(1820)D 13 *** Exp /2 [70, 1 1 ] RPSF Ξ (1530)P 13 **** Exp /2 [56, ] RPSF

38 U(7) Model Results, arxiv: Missing resonances TABLE VIII: Strong decay widths of missing nucleon resonances (in MeV), calculated with the U(7) Model of Sec. II A and Refs. [39, 40], in combination with the relativistic phase space factor of Eq. (21) and the values of the model parameters of Table II (second column). Tentative assignments of one and two star resonances are labeled by. N Mass Nπ Nη ΣK ΛK π Σ K Nρ Nω ΣK ΛK ρ 2 8 J [20, ] /2 [70, ] /2 [70, ] J [70, 2 1 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ] J [70, 2 1 ] /2 [56, 1 1 ] /2 [56, 1 1 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ]

39 U(7) Model Results, arxiv: Missing resonances TABLE XII: As Table VIII, but for missing Ξ (top) and Ξ (bottom) resonances. Ξ Mass ΣK ΛK Ξπ Ξη Σ K Ξ π ΛK 2 8 1/2 [70, ] /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, 1 1 ] J[20, ] /2 [56, ] /2 [56, ] /2 [70, ] /2 [56, ] /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ] TABLE XIII: As Table VIII, but for missing Ω resonances. Ω Mass ΞK Ξ K /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ]

40 U(7) Sigma missing states Missing resonances Mass NK fi fi K K ú fi ú 4 8 1/2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [20, ] /2 [20, ] /2 [56, ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, 2 1 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ]

41 U(7) Sigma missing states II Missing resonances Mass NK fi fi K K ú fi ú ú 4 8 1/2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ]

42 U(7) Model Results, arxiv: Missing resonances TABLE XII: As Table VIII, but for missing Ξ (top) and Ξ (bottom) resonances. Ξ Mass ΣK ΛK Ξπ Ξη Σ K Ξ π ΛK 2 8 1/2 [70, ] /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, 1 1 ] J[20, ] /2 [56, ] /2 [56, ] /2 [70, ] /2 [56, ] /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ] TABLE XIII: As Table VIII, but for missing Ω resonances. Ω Mass ΞK Ξ K /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ]

43 U(7) Sigma missing states Missing resonances Mass NK fi fi K K ú fi ú 4 8 1/2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [20, ] /2 [20, ] /2 [56, ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, 2 1 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ]

44 U(7) Sigma missing states II Missing resonances Mass NK fi fi K K ú fi ú ú 4 8 1/2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ]

45 U(7) Model Results, arxiv: Missing resonances TABLE IX: As Table VIII, but for missing resonances. Mass Nπ ΣK π η Σ K Nρ /2 [70, ] /2 [70, 2 1 ] /2 [70, ] /2 [70, ] /2 [70, 1 2 ] /2 [70, 1 2 ]

46 U(7) Model Results, arxiv: Missing resonances TABLE XII: As Table VIII, but for missing Ξ (top) and Ξ (bottom) resonances. Ξ Mass ΣK ΛK Ξπ Ξη Σ K Ξ π ΛK 2 8 1/2 [70, ] /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, 1 1 ] J[20, ] /2 [56, ] /2 [56, ] /2 [70, ] /2 [56, ] /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ] TABLE XIII: As Table VIII, but for missing Ω resonances. Ω Mass ΞK Ξ K /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ]

47 U(7) Sigma missing states Missing resonances Mass NK fi fi K K ú fi ú 4 8 1/2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [20, ] /2 [20, ] /2 [56, ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, 2 1 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ]

48 U(7) Sigma missing states II Missing resonances Mass NK fi fi K K ú fi ú ú 4 8 1/2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 2 1 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ]

49 U(7) Sigma ú missing states III Mass NK fi fi K K ú fi /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [70, ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [70, ] /2 [70, ] J [70, 2 1 ] /2 [56, ] /2 [70, 1 2 ] /2 [70, 1 2 ]

50 U(7) Model Results, arxiv: Missing resonances TABLE XI: As Table VIII, but for missing Λ (top) and Λ (bottom) resonances. Λ Mass NK Σπ Λη ΞK Σ π Ξ K NK Σρ Λω 4 8 3/2 [70, 1 1 ] J [20, ] /2 [70, ] /2 [70, ] /2 [70, ] J [70, 2 1 ] J [70, 2 1 ] /2 [70, ] /2 [70, ] /2 [70, ] J [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, ] J [20, ] /2 [70, ] /2 [70, ] J [70, 2 1 ] J [70, 1 2 ]

51 Results for Hypercentral Model 3* and 4* states Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase TABLE XV: Strong decay widths of three- and four-star nucleon resonances(in MeV), calculated with the Hypercentral QM of Sec. II B and Refs. [41, 46], in combination with the relativistic phase space factor (RPSF) of Eq. (21) and the values of the model parameters of Table XIV. The experimental values are taken from Ref. [1]. Decay channels labeled by are below threshold. The symbols (S) and(d) standfors and D-wave decays, respectively. Resonance Status M [MeV] Nπ Nη ΣK ΛK π Nρ Nω N(1440)P 11 **** Exp /2 [56, ] RPSF N(1520)D 13 **** Exp /2 [70, 1 1 ] RPSF N(1535)S 11 **** < 2 Exp /2 [70, 1 1 ] RPSF N(1650)S 11 **** Exp /2 [70, 1 2 ] RPSF N(1675)D 15 **** < Exp /2 [70, 1 1 ] RPSF N(1680)F 15 **** Exp /2 [56, ] RPSF N(1700)D 13 *** < (S) Exp. < 50 (D) 2 8 3/2 [70, 1 2 ] RPSF N(1710)P 11 *** Exp /2 [70, ] RPSF N(1720)P 13 **** Exp /2 [56, ] RPSF N(1875)D 13 *** (S) Exp (D) Exp /2 [70, 1 1 ] RPSF N(1900)P 13 *** Exp /2 [70, ] RPSF

52 Results for Hypercentral Model Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase 3* and 4* states TABLE XVI: As Table III, but for resonances. The symbols (S), (P ), (D) and(f )standfors-, P -, D- andf -wave decays, respectively. Resonance Status M [MeV] Nπ ΣK π η Σ K Nρ (1232)P 33 **** Exp /2 [56, ] RPSF (1600)P 33 *** < 88 Exp /2 [56, ] RPSF (1620)S 31 **** Exp /2 [70, 1 1 ] RPSF (1700)D 33 **** (S) Exp (D) /2 [70, 1 1 ] RPSF (1905)F 35 **** < 100 > 162 Exp /2 [56, ] RPSF (1910)P 31 **** Exp /2 [56, ] RPSF (1920)P 33 *** (P ) Exp (F ) /2 [56, ] RPSF (1950)F 37 **** < 34 Exp /2 [56, ] RPSF

53 Results for Hypercentral Model Missing resonances Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase TABLE XVII: Strong decay widths of missing nucleon resonances (in MeV), calculated with the Hypercentral QM of Sec. II B and Refs. [41, 46], in combination with the relativistic phase space factor of Eq. (21) and the values of the model parameters of Table XIV. Tentative assignments of one and two star resonances are labeled by. N Mass Nπ Nη ΣK ΛK π Σ K Nρ Nω ΣK ΛK ρ 4 8 3/2 [70, ] /2 [20, ] /2 [20, ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, 1 1 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [56, ] /2 [70, 1 2 ]

54 Results for Hypercentral Model Missing resonances Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase TABLE XVIII: As Table XVII, but for missing resonances. Mass Nπ ΣK π η Σ K Nρ /2 [70, ] /2 [70, ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, ] /2 [56, ]

55 Results for Hypercentral Model Missing resonances Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase TABLE XIX: As Table XVII, but for missing Σ (top) and Σ (bottom) resonances. Σ Mass NK Σπ Λπ Ση ΞK K Σ π Σ η Ξ K NK Σρ Λρ Σω K 2 8 3/2 [56, ] /2 [70, 1 1 ] /2 [56, ] /2 [70, ] /2 [70, ] /2 [70, 1 2 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ] J [20, ] J [70, 1 2 ] /2 [56, ] /2 [56, ] /2 [70, ] /2 [70, ] J [70, 1 2 ]

56 Results for Hypercentral Model Missing resonances Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase TABLE XXI: As Table XVII, but for missing Ξ (top) and Ξ (bottom) resonances. Ξ Mass ΣK ΛK Ξπ Ξη Σ K Ξ π ΛK ΣK Ξρ Ξω 2 8 1/2 [56, ] /2 [70, 1 1 ] /2 [56, ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ] J [20, ] J [70, 1 2 ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [56, ]

57 Results for Hypercentral Model TABLE XX: As Table XVII, but for missing Λ (top) Missing and Λ resonances (bottom) resonances. Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase Λ Mass NK Σπ Λη ΞK Σ π Ξ K NK Σρ Λω 4 8 3/2 [70, 1 1 ] /2 [70, ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, ] /2 [70, ] /2 [70, ] /2 [70, ] J [20, ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [70, 1 2 ]

58 Results for Hypercentral Model Missing resonances Strong decay widths of three and four star nucleon resonances (in MeV), calculated with the relativistic phase TABLE XXII: As Table XVII, but for missing Ω resonances Ω Mass ΞK Ξ K Ωη ΞK /2 [70, 1 1 ] /2 [70, 1 1 ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [56, ] /2 [70, 1 2 ] /2 [70, 1 2 ] /2 [56, ]

59 Comparison We computed the open-flavor strong decays of light baryons (i.e. made up of u, d, s valence quarks) into baryon-pseudoscalar and baryon- vector mesons using a 3 P 0 pair-creation model. We studied the strong decays in two di erent constituent quark Models. Some resonances have di erent assignments then we have di erent predictions. We to suppress heavier quark pair creation, like s s with respect to uū(d d) Alargenumberofdecaysweredescribedwithafewparameters. Maybe the deviations are due to the meson cloud e ects or the contribution of the higher Fock components.

60 We extended the predicnons of CapsNck and Roberts in the 3P0 model to the hyperons and we also included the decays into baryons + vector mesons. We calculated the strong decays 3P0 predicnons for two models: the U(7) and the hypercentral: they came out to be different in parncular for the missing states For the first Nme 3P0 decays have been calculated for baryons taking into account the strangeness suppression and all the analyncal formula and couplings are in the appendix in closed form- à so they can be used with other models. Different quark models have different missing states and so different predicnons (but also in some known states they can give different predicnons)- à >> tool to disnnguish between Different models of structure.

61 Thanks!

62 One may wonder whether there is a unique spectral signature for quark-diquark models. One of these signatures is the detection of 1 + states which are antisymmetric in all three quarks. These states, originating from the omitted diquark representation 15 of SU sf (6) are not present in the quark-diquark model and occur (at different masses)inallmodelswith three quarks. These missing states may, however, be very difficult to detect since they are decoupled and cannot be excited with electrons or photons. To excitethesestates, strongly interacting particles are needed, for example ( p, p )withspintransfer. Anotherpossibility E. Santopinto, PRC72, (2005)

63 TABLE II: 3 P 0 model parameter values used in the calculations, in combination with the relativistic phase space factor of Eq. (21) (column 2) and the effective phase space factor of Eq. (22) (column 3). The parameter values are obtained in a fit to the experimental strong decay widths. See App. A, Table XXIII, last column. The values of the constituent quark masses m n (n = u, d) andm s are used in the vertex factor of Eq. (A2), where the pair-creation strength, γ 0,is substituted by an effective one [see Eq. (24)]. α b is the harmonic oscillator parameter of baryons A and B, α c that of meson C and α d is the quark form factor parameter. Parameter Rel. PSF Eff. PSF γ α b 2.99 GeV GeV 1 α c 2.38 GeV GeV 1 α d 0.52 GeV GeV 1 m n 0.33 GeV 0.55 GeV m s TABLE XIV: Parameter values used in the calculations, in combination with the relativistic phase space factor of Eq. (21). The parameter values are fitted to a sample of 9 transitions: Nπ, N(1520) Nπ, N(1535) Nπ, N(1650) Nπ, N(1680) Nπ, N(1720) Nπ, (1905) Nπ, (1910) Nπ and (1920) Nπ. The quantum number assignments for the decaying states are now taken from the hqm results of Ref. [41, 46] and Table XV. Parameter Value γ α b α c α d 0 m n 0.33 m s 0.55