Institute of High Energy Physics, CAS
Quark model for hadrons
Qiang Zhao Institute of High Energy Physics, CAS and Theoretical Physics Center for Science Facilities (TPCSF), CAS [email protected]
Hadron School, Rajamangala Univ. of Technology Isan, Nakhon Ratchasima, Thailand, Feb. 29- April 4, 2016 Outline
Some facts about quarks; A brief review of hadron physics, introduction to non-relativistic constituent quark model (NRCQM) for baryons, and the question of “missing resonances” Electromagnetic (EM) and strong interactions of baryons in NRCQM, quark model selection rules and symmetry breakings Probing baryon resonances in meson photo- and electroproduction, and meson-nucleon scatterings References: N. Isgur and G. Karl, Phys.Rev. D18 (1978) 4187 N. Isgur and G. Karl, Phys.Rev. D20 (1979) 1191-1194 S. Godfrey and N. Isgur, Phys.Rev. D32 (1985) 189-231 S. Capstick and N. Isgur, Phys.Rev. D34 (1986) 2809 E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane, and T.-M. Yan, Phys.Rev. D17 (1978) 3090, Phys.Rev. D21 (1980) 313 E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane, and T.-M. Yan, Phys.Rev. D21 (1980) 203 F. E. Close, An introduction to quarks and partons, Academic Press, 1979 S. Capstick and W. Roberts, Prog.Part.Nucl.Phys. 45 (2000) S241-S331 1. Some facts about quarks Time line of sub-atomic physics
1897: electron
Thomson
1919: proton
Rutherford
1932: neutron
Joliet-Curie Chadwick
1933: positron proton proton C.-Y. Chao Anderson pion
1935: pion predicted by Yukawa neutron neutron Yukawa Elementary particle “Zoo” in 1963
“stable” hadrons meson resonances baryon resonances X S L N
K X* p K* m w e Y* r
Two “classes” of hadrons K2*
“strange:”non-strange:” L, S ,n, K, p, K*, p, r,… … D From S. Olsen’s summer lecture in Beijing, 2010 1961: Gell-Mann, Nishijima & Nee’man: The Eightfold Way
Quarks as building blocks of hadrons: meson (qq), baryon (qqq)
Simple rules for quarks (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge. SU(3) multiplets of baryons made of u, d, and s
S SU(3) octet with JP=1/2+ X– (ssd) X0 (ssu) 2 Gell-Mann - Nishijima:
Q=I3+Y/2=I3+(B+S)/2
333 – 1 + S S =(3 6) 3 (sdd) S0, L (sud) (suu) =(18) (810)
I –1 n (dud) 0 p (uud) 1 3 SU(3) multiplets of baryons made of u, d, and s
S SU(3) decuplet 10 – 3 (sss) with JP=3/2+
X*– (ssd) X*0 (ssu) Decuplet 10: 2 –(sss)
– S* 1 S*+ (sdd) S*0 (sud) (suu)
3/2 1 1 3/2 I3 D–(ddd) D0(udd) 0 D+(uud) D++(uuu) m3 Symmetric spin wavefunction: S=3/2 6/2 Symmetric flavor wavefunction: sss m1 r Symmetric spatial wavefunction: L=0 3 m 2r 2 A problem encountered: r1 Violation of the Pauli principle and Fermi-Dirac r2 statistics for the identical strange quark system?
Jacobi coordinate
• An additional degrees of freedom, Colour, is introduced. • Quark carries colour, while hadrons are colour neutral objects.
3 3 3 = (3 6) 3 = (1 8) (8 10) Again: Are quarks real objects? Probe coloured quarks in electron-positron collisions
e e q e * q * e m Hadrons q m e e Electron-Positron annihilations
2 R êq (2/3)2 (1/3)2 (1/3)2 … u d s … 2 R êq q : u(3/2) d(-1/3) s(-1/3) c(2/3) b(-1/3) t(2/3) R
(2/3)2 (1/3)2 (1/3)2 [2/3] [2/3] (2/3)2 [10/9]
[10/9] (1/3)2 [11/9]
[11/9] (2/3)2 [15/9]
But if quark carries color, one should have 2 R 3 êq 2 R 3 êq q : u(3/2) d(-1/3) s(-1/3) c(2/3) b(-1/3) t(2/3) R
(2/3)2 (1/3)2 (1/3)2 [2/3] 2
[2/3] (2/3)2 [10/9]10/3
[10/9] (1/3)2 [11/9]11/3
[11/9] (2/3)2 [15/9] 5 2/3
Particle Data Group 2010 1976 Nobel Prize: B. Richter and S. C.-C. Ting
"for their pioneering work in the discovery of a heavy elementary particle of a new kind"
+ - y Also seen in pNe e X
J
R=2.2 >>2/3 10
J.J. Aubert et al., PRL 33, 1404 (1974) J.E. Augustine et al., PRL 33, 1406 (1974) Quarks are real building blocks of hadrons: meson (qq), baryon (qqq)
• Quarks are not free due to QCD colour force (colour confinement).
• Chiral symmetry spontaneous breaking gives masses to quarks.
• Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles.
Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge. Quantum Chromo-Dynamics: a highly successful theory for Strong Interactions
Conventional hadrons
Meson Confinement Confinement
Baryon
Asymp. freedom Remaining questions: •What are the proper effective degrees of freedom for hadron internal structures? •What are the possible color-singlet hadrons apart from the simplest conventional mesons (qq) and baryons (qqq)? •What’s happening in between “perturbative” and “non- perturbative”? •… … Multi-faces of QCD: Exotic hadrons beyond conventional QM
Hybrid Glueball Tetraquark
Hadronic molecule Pentaquark
The study of hadron structures and hadron spectroscopy should deepen our insights into the Nature of strong QCD. I. A brief review of hadron physics and introduction to non-relativistic constituent quark model (NRCQM) Electromagnetic Probe（电磁探针）
• Atoms – 10–10 m
• Nuclei – 10–14 m
Photon • Nucleons – 10–15 m
Nucleon resonances Photon energy E= 2p×197.3 MeV·fm/ • Quark degrees of freedom: (0.1~0.5)×10–15 m Basic assumptions of NRCQM i) Chiral symmetry spantaneous breaking leads to the presence of massive constituent quarks as effective degrees of freedom inside hadrons. ii) Hadrons can be viewed as quark systems in which the gluon fields generate effective potentials that depend on the spins and positions of the massive quarks.
Thus, meson is a qq system and baryon is made of qqq.
qq meson qqq baryon Quarks as building blocks of hadrons: meson (qq), baryon (qqq)
• Quarks are not free due to QCD colour force (colour confinement).
• Hadrons, with rich internal structures, are the smallest objects in Nature that cannot be separated to be further finer free particles.
Convention (Particle Data Group): 1) Quark has spin 1/2 and baryon number 1/3; 2) Quark has positive parity and antiquark has negative parity; 3) The flavor of a quark has the same sign as its charge. Baryons in SU(6)O(3) symmetric quark model
We concentrate on the baryons made of u, d, s quarks.
Color
Spin Flavor Spin-flavor Spatial s, r, , a
For a three-quark Fermion system, the Pauli principle requires that the total wavefunction is antisymmetric under exchange of any two quarks. Therefore, the total wavefunction must be antisymmetrized.
Baryon wavefunction as representation of 3-dimension permutation group:
symmetric Baryons 22 nucleon resonances (uud, udd) 18 Lambda resonances (uds) Property of dimension-3 permutation group
e.g. The SU(2) spin wavefunction for a three- quark system Spin and flavor wavefunctions of S3 representations
Spin Flavor
Flavor wavefunctions:
SU(3) multiplets of baryons made of u, d, and s
S SU(3) octet with JP=1/2+ X– (ssd) X0 (ssu) 2 Gell-Mann - Nishijima:
Q=I3+Y/2=I3+(B+S)/2
333 – 1 + S S =(3* 6) 3 (sdd) S0, L (sud) (suu) =(18) (810)
I –1 n (dud) 0 p (uud) 1 3 SU(3) multiplets of baryons made of u, d, and s
S SU(3) decuplet 10 – 3 (sss) with JP=3/2+
X*– (ssd) X*0 (ssu) Decuplet 10: 2 –(sss)
– S* 1 S*+ Anti-decuplet 10: (sdd) S*0 (sud) (suu) +(sss)
3/2 1 1 3/2 I3 D–(ddd) D0(udd) 0 D+(uud) D++(uuu) 333 SU(6) Spin-flavor wavefunctions of S3 representations The spin-independent potential for quark-quark interactions Spatial wavefunction in a spin-independent potential m3 Hamiltonian m1 6/2 r 3 m 2r 2
r1 r2
Jacobi coordinate
2 With an equal mass for u, d, and s quark, and k=mqwh /3, the Hamiltonian can be expressed as
Isgur, and Karl, PLB109, 72(1977); PRD18, 4187(1978); PRD19, 2653(1979) Spatial wavefunction in a spin-independent potential m3 Jacobi coordinate m1 6/2
r3 2r
r1 r2
Harmonic oscillator wavefunction Taking the notation of Karl and Obryk, the harmonic oscillator wavefunction can be written as Total wavefunction of SU(6)O(3) symmetry
Isgur, and Karl, PLB109, 72(1977); PRD18, 4187(1978); PRD19, 2653(1979)
Anharmonic and spin-dependent potential
Based on the SU(6)O(3) symmetry, the quark model succeeded in the classification of the baryon spectrum. But quantitative results could not be expected since more elaborate details about the dynamics were needed. For instance, the Roper resonance P11(1440) was assigned to the radial excitation state with N = 2, and L = 0, which was found to have lower mass than the first orbital excition multiplets S11(1535) etc with N = 1 and L = 1. The inclusion of the anharmonic and spin-dependent quark potential turned to be necessary.
S11(1535)
P11(1440)
n is the radial quantum number, and L is the orbital angular N1/2 N1/2 momentum. N=2, L=0 N=1, L=1
Electromagnetic moments of ground state baryons
One of the most impressive successes of the NRCQM could be its description of the electromagnetic moments of ground state baryons. The simple assumption is that all constituent quarks are in S-wave orbitals, i.e. except for the spin of the constituents, no orbital angular momentum would contribute to the electromagnetic moment.
Question 1: Please work out the neutron’s magnetic moment, and prove Eq. (51). One essential point is that one cannot neglect the “color” degrees of freedom at all. If one anti-symmetrizes the total wavefunction without the color part taken into account, the ratio of the magnetic moment between proton and neutron will be -1/2, which is far away from reality. The CQM is indeed tackling something essential, we are however confronted with big difficulties to disentangle it based on this model itself. More elaborate models are needed for the study the baryon properties at more accurate level. Lattice QCD studies, which are base on the first principle, are also needed for understanding not only the non-perturbative phenomena, but also successes of phenomenological models. Baryon spectroscopy and “Missing resonances”
Are the constituent quarks good degrees of freedom for the description of baryon spectroscopy? Could it be possible to classify all baryon states observed in experiment in the framework of QM? How many have been seen, and how many are still missing? What are the deviations? What causes the deviations? Where the constituent quark model scenario must break down? Does the Nature allow the existence of exotic hadrons, e.g. pentaquarks? Where to look for the anti-symmetric 20-plets? How the constituent picture in the non-perturbative region is connected to the partonic one in the perturbative region? …… “Missing baryon resonances in pN scattering
• The non-relativistic constituent quark model (NRCQM) makes great success in the description of hadron spectroscopy: meson (qq), baryon (qqq).
• However, it also predicted a much richer baryon spectrum, where some of those have not been seen in pN scatterings. – “Missing Resonances”.
p, 0 P33(1232) D P11(1440) N*, L2I,2J S11(1535) D (1520) N, ½+ 13 … Dilemma: a) The NRCQM is WRONG: quark-diquark configuration? …
b) The NRCQM is CORRECT, but those missing states have only weak couplings to pN, i.e. small gpN*N. (Isgur, 1980)
Looking for “missing resonances” in N* N, KS, KL, rN, wN, N, N …
(Exotics …) u r d N* u u d d u n d • Baryons excitations via strong and EM probes
p, 0 P33(1232) D P11(1440) N*, D*, L2I,2J S11(1535) D13(1520) N, ½+ … , 1 D + p N*, D*
D13 + N, ½ F15 PDG2006: 22 nucleon resonances
Moorhouse and L selection rule violated
(**) not well- established Brief summary
The quark model achieved significant successes in the interpretation of a lot of static properties of nucleons and the excited resonances.
However, it also raised the famous puzzle of “missing resonances”, which were predicted by the quark model in the baryon spectroscopy, but have not been found in the p-N scattering experiments.
By studying the baryon spectroscopy, baryon EM form factors, and baryon couplings to mesons in meson photo- and electroproduction, and meson-nucleon scatterings, we could extract important information about the structure of baryons and non-perturbative QCD dynamics.
For the heavy flavor system, the Cornell model was one of the pioneering approaches and many consequent implications will be covered by lectures on the NRQCD (Eichten) and NREFT (Guo and Wang).