Progress and open questions in hadron spectroscopy

Transcription

1 Progress and open questions in hadron spectroscopy SFB/TR6 E. Klempt Helmholtz-Institut für Strahlen und Kernphysik Universität Bonn Nußallee 4-6, D-535 Bonn, GERMANY QCD Workshop, Graz, November 5-6

2 Mesons. πn scattering Cross section (mb) π + p total In 95, E. Fermi and collaborators measured the cross section for π + p π + p and found it steeply raising. H. L. Anderson, E. Fermi, E. A. Long and D. E. Nagle, Phys. Rev. 85 (95) 936. Today: ++ (3), + (3), (3), (3) width 5 MeV /Γ.45 3 s Cross section (mb) π + p elastic - πp πd Center of mass energy (GeV) π ± d total π p total π p elastic - Laboratory beam momentum (GeV/c)

3 Maximum cross section: σ tot,π + p = mb σ el,π + p = mb σ tot,π p = 7 mb σ el,π p = 3 mb WHY? Cross section (mb) Cross section (mb) π + p total π + p elastic - πp πd Center of mass energy (GeV) π ± d total π p total π p elastic - Laboratory beam momentum (GeV/c)

4 . Mesons and their quantum numbers spin S baron number B flavor charge Q Parity Quarks q / /3 u, d, s /3,-/3,-/3 Antiquarks q /; -/3 ū, d, s -/3,/3,/3 - Quark and antiquark combine to B = and to spin S = or S =. The total spin S and the orbital angular momentum L between quark and antiquark couple to the total angular momentum J: J = L + S. Mesons have quantum numbers J P C and a flavor content. These are conventional mesons. Other kinds of mesons may exist as well: glueballs, hybrids, tetraquarks, molecules. q q mesons they may have the following properties:.. Parity P = ( ) L+ The parity of a meson is due to the orbital angular momentum between quark and antiquark P = ( ) L multiplied with their intrinsic parities P q P q = -.

5 .. C-Parity C = ( ) L+S The total wave function of a meson is antisymmetric w.r.t. the exchange of quark and antiquark. The symmetry of the wave function is given by the product of symmetries of the spatial and spin wave function, and by the C-parity: Spins: ( ) S+ Space: ( ) L The product is -, hence Charge: C C( ) S+L+ = and C = ( ) S+L..3 Isospin Proton and neutron form an isospin doublet and so do the up and the down quark. We may construct states of or 3 quarks; the isospin of the system is determined by adding the quark isospins using Clebsch-Gordan coefficients. We could also define ū and d as isospin doublet in a isospin space of antiparticles and invent a new table of Clebsch-Gordan coefficients. Or we can define iso-doublets in a way that the doublets of antiparticle transform under isospin rotations like those of particle doublets. These are, e.g.:

6 neg. n p p u n d neg. d ū K+ K neg. K K neg. Kstar+ K star K star neg.k star/neg. We now can construct q q mesons like pions or η s. I =, I 3 = > = u d > = π + > I =, I 3 = > = ( uū > d d >) = π > I =, I 3 = > = dū > = π > I =, I 3 = > = ( uū > + d d >) = η > The three states π +, π, and π form an iso-triplet, η and η both form isosinglets...4 G-parity P = ( ) L++I The C-parity has a defined eigenvalue only for particles which are their own antiparticles. The action of C-parity on other states leads to their antiparticles. We define C π = + π ; C π + = π ; C π = π +

7 It is useful to introduce also a G-parity as C-parity followed by a rotation in isospin space by 9 about the y-axis. The rotation by 8 in isospin space around y-axis are given by e iπi y We define: G = C e iπi y and introduce Cartesian states: π ± = π x ± iπ y > Then : G π ± > = C e iπiy π x ± iπ y > C π x ± iπ y >= ( )C π >= π ± > G π > = Ce iπiy π >= C π >= π > Thus we have: G π >= π > G-parity is conserved in strong interactions. For mesons decaying into n π pions we have the relation G = ( ) I C = ( ) L+S+I = ( ) n π

8 Maximum cross section: σ tot,π + p = mb σ el,π + p = mb σ tot,π p = 7 mb σ el,π p = 3 mb WHY? Cross section (mb) Cross section (mb) π + p total π + p elastic - πp πd Center of mass energy (GeV) π ± d total π p total π p elastic - Laboratory beam momentum (GeV/c)

9 / / + +/ +/ +/ / / / / +/ / / 3/ +3/ + +/ / / / / +/ / +/ 3 + / +/ + / /3 /3 3/ / +/ /3 /3 / / / / + /3 /3 3 + /3 / / / + /5 8/5 6/5 /3 /3 3/ /3 /3 3/ / / / + + /6 / /3 /3 /3 + /6 / /3 /3 /6 / + + / / + 3/5 3/ / 3 /5 3/5 /5 3/ 5/ +5/ 5/ +3/ + +3/ / / +3/ +/ 3/ /5 3/ /5 8/5 /5 /5 3/5 +3/ +/ / / /6 /3 / + 3/ +3/ 3/5 /5 5/ +5/ / 5/ 3/ /5 4/5 3/ +3/ 4/5 /5 5/ +/ + / /5 3/5 +/ 3/5 /5 + +3/ +/ + 5/ 3/ / +/ +/ +/ / +/ +3/ / /4 3/4 +/ +/ 3/4 /4 +/ / 3/ + 3/ 3/5 / 8/5 /5 /5 5/ / 3/5 /5 / /5 / 3/5 /5 /3 5/ 3/ / + 3/ 8/5 /6 / / / / 3/ 3/5 + / + +/ 3 3/ / /3 /3 /3 / / +/ + +/ / / / / +/ / / / / 3/ +/ 3/ / /5 5/ 3/ 3/5 3/ 3/ / +/ /6 /3 5/ / 3/ / 3/ Notation: m m 3/5 /5 3/ 3/ /5 3/5 3/ J M 4/5 /5 /5 4/5 5/ 5/ / 3/4 /4 /4 3/4 3/ / 5/ 5/ J M m m Coefficients / 7/ +7/ 7/ 5/ + +3/ +5/ +5/ 3/ 3/ +3/ +3/ +3/ +/ / / / 3 +3/ / / + + +

10 σ tot,π + p = σ π + p π + p = CG (I=/,I3 =/)+(I=,I 3 =) (I=3/,I 3 =3/) CG (I=3/,I3 =3/) (I=/,I 3 =/)+(I=,I 3 =) = mb σ el,π + p = σ π + p π + p = CG (I=/,I3 =/)+(I=,I 3 =) (I=3/,I 3 =3/) CG (I=3/,I3 =3/) (I=/,I 3 =/)+(I=,I 3 =) = mb σ tot,π p = σ π p π p + σ π p π n = CG (I=/,I3 =/)+(I=,I 3 = ) (I=3/,I 3 = /) + CG (I=/,I3 = /)+(I=,I 3 =)+(I=3/,I 3 = /) = /3 /3 + /3 /3 7 mb σ el,π p = σ π p π p = CG (I=/,I3 =/)+(I=,I 3 = ) (I=3/,I 3 = /) CG (I=3/,I3 = /) (I=/,I 3 =/)+(I=,I 3 = ) = /3 /3 3 mb

11 .3 Particle decays.3. The transition amplitude The transition rate for particle decays are given by Fermi s golden rule: T if = π M ρ(e f ) T if is the transition probability per unit time. With N particles the number of decays in the time interval dt is NT if dt or dn = NT if dt and N = N e T if t = N e (t/τ) = N e Γt Γτ = = (uncertainty priniple).

12 .3. Short-lived states in QM Consider a state with energy E = ω; it is characterized by a wave function ψ(t) = ψ (t)e ie t Now we allow it to decay: = ψ (t)ψ (t) = ψ (t = )ψ (t = )e t/τ. Probabilty density must decay exponentially. ψ(t) = ψ(t = )e ie t e t/τ

13 A damped oscillation contains not only one frequency. The frequency distribution can be calculated by the Fourier transformation: = f(ω) = f(e) = ψ(t = ) (E E) i/ (τ ) ψ(t = )e ie t t/τ e iet dt = ψ(t = )e i((e E)t /τ )t dt Probability to find the energy E: f (E)f(E) = (τ = /Γ) ψ(t = ) (E E) + / (τ ) (Γ/) (E E) + (Γ/)

14 .3.3 The Breit-Wigner amplitude BW (E) = Γ/ (E E) iγ/ = / (E E) /Γ i/ With (E E) /Γ = cot δ : f(e) = cot δ i = eiδ sin δ = i ( e iδ ) This formula is derived from S matrix. δ is called phase shift. The amplitude is zero for Γ/(E E ) << and starts to be real and positive with an small positive imaginary part. For Γ/(E E ) >> the amplititude is small, real and positive with an small negative imaginary part. The amplitude is purely imaginary (i) for E = E. The phase δ goes from to π/ at resonance and to π at high energies. Argand circle

15 Scattering amplitude T in case of inelastic scattering. Definition of phase δ and inelasticity η.

16 Elastic channel (upper curve), πp ππp (lower curve), difference πp ηp or πp ΛK Argand diagram and cross section for π p π p via formation of the N(65)D,5 resonance (L=). D. M. Manley, Multichannel analyses of anti-k N scattering, PiN Newslett. 6 () 74.

17 .3.4 The Dalitz plot Events are represented in a Dalitz plot by one point in a plane defined by m in x and m 3 in y direction. Since the Dalitz plot represents the phase space, the distribution is flat in case of absence of any dynamical effects. An example is the Dalitz plot for K L π+ π π Resonances in m are given by a vertical line, in m 3 as horizontal lines. Since m 3 = (M p + m + m + m 3 ) (m m 3 ) particles with defined m 3 mass are found on the second diagonal. From the invariant mass of particles and 3 m 3 = (E + E 3 ) ( p + p 3 ) we derive m 3 = (m + m 3 + E E 3 ) ( q q 3 ) cos θ with being the angle between q and q 3. This can be rewritten as m 3 = [( m 3 ) max + ( m 3 ) min ] [( ) + m 3 ( m ) max 3 min ] cos θ For a fixed value of m, the momentum vector p 3 has a cos θ direction w.r.t. the recoil p which is proportional to m 3.

18 Example: x x The π + π π Dalitz plot in p p annihilation at rest, and ρ+ (a), ρ (b) and ρ (c) decay angular distributions.

19 .4 Meson nonets.4. The pseudoscalar mesons The pseudoscalar quantum numbers are J P C = +. From atomic physics we take the spectroscopic notation n s+ L J = S. From the 3 quarks u, d, s and their antiquarks the following SU(3) eigenstates can be constructed: K = d s K + = u s π = dū π = (uū d d) π + = u d η 8 = K = sū K = s d 6 (uū + d d s s) η = 3 (uū + d d + s s) The 9 states are orthogonal; one of them, the η, is invariant under rotations in SU(3). The nonet structure is seen in the well-known nonet representation:

20 K S Octet K + π π η 8 η I 3 I 3 π + S Singlet K K The octet state and the singlet state are the SU(3) eigenstates. They have the same quantum numbers and can mix. The mixing angle is called pseudoscalar mixing angle Θ P S. The physical states are given by η >= cos Θ P S η 8 > sin Θ P S η > η >= sin Θ P S η 8 > + cos Θ P S η >

21 We can write down the flavor wave function for a few angles: Θ P S = η > = η > = ( ) 6 uū + d d s s ( ) 3 uū + d d + s s Θ P S =. η > = η > = Θ P S = 9.3 η > = η > = ( (uū + d d) s s ) ( (uū + d d) + s s ( 3 uū + d d s s ) ( ) 6 uū + d d + s s ) Θ P S = 35.3 η > = s s ( η > = uū + d d ) The large mixing between the (uū + d d) (which we abbreviate as n n) and the s s component in the η and η wave functions has led to speculations that the η and in particular the η may contain a large fraction of glue, that they are gluish. This requires an

22 extension of the mixing scheme by introduction of a non-q q or inert component, with a third state of unknown mass which is dominantly a glueball. η > = X η η > = X η ( uū + d d) + Yη (s s) + Z η (glue) ( uū + d d) + Yη (s s) + Z η (glue) light quark strange quark inert Z η = Z η At present there is no convincing evidence for a glueball content in the η wave function; nevertheless the η is still suspect of being produced preferentially in glue-rich processes or in glueball decays.

23 .4. Vector and tensor mesons Both nonets have a nearly ideal mixing angle Θ ideal = 35.3 for which one meson is a purely s s state. Note that the mass difference between the s s and the uū + d d state is about 5 MeV. S K Octet K + The vector mesons J P C = ρ ρ ω 8 ω I 3 I 3 ρ + S Singlet K K ω = Φ = 3 ω ω 8 3 ω 3 ω

24 K (43) S Octet K + (43) The tensor mesons J P C = ++ a (3) f (8) f () I 3 I 3 a (3) a + (3) S Singlet K (43) ω = K (43) Φ = 3 ω ω 8 3 ω 3 ω Θ V,T = 35.3 ω > = ( uū + d d) f (7) Φ > s s = f (55)

25 .4.3 The Gell-Mann-Okubo mass formula You can derive a relation between the masses within a meson nonet by ascribing to mesons of one nonet a common mass M plus the (constituent) masses of the quark and antiquark it is composed of. The pion mass is given by M π = M + M q where M q is the mass of the up or down quark, and the Kaon mass by M K = M + M q + M s with M s as strange quark mass. The η contains masses from both the singlet and octet component which we weight according to their fractions: M η = M 8 cos Θ + M sin Θ M η = M 8 sin Θ + M cos Θ Similarly we determine the singlet and octet masses from the flavor decomposition of their wave functions. M = M + 4/3M q + /3M s M 8 = M + /3M q + 4/3M s

26 Thus we arrive at the linear mass formula: cos Θ = 3M η + M π 4M K 4M K 3M η M π Often, the linear GMO mass formula is replaced by the quadratic GMO formula which is given as above but with M values instead of masses. It reads cos Θ = 3M η + M π 4M K 4M K 3M η M π Nonet members Θ linear Θ quad π, K, η, η 3 ρ, K, Φ, ω a (3), K (43), f (55), f (7) 6 9 ρ 3 (69), K3 (78), Φ 3(85), ω 3 (67) 9 8

27 .4.4 Meson decays The decays of mesons belonging to a given nonet are related by SU(3) symmetry. The coefficients governing these relations are called SU(3) isoscalar factors and listed by the Particle Data Group. Two simple examples. A glueball is a flavor singlet. It may decay into two octet mesons: 8 8. In the listings we find (Λ) (N K Σπ Λη ΞK) = 8 ( 3 ) / The particles stand for their SU(3) assignment, the Λ can be octet or singlet. The / is understood for every coefficient. Decays of a flavor singlet meson into two pseudoscalar mesons: (glueball) (K K ππ η 8 η 8 KK) = 8 ( 3 ) / Hence glueballs have squared couplings to K K, ππ, η8 η 8 of 4 : 3 :. The decay into two isosinglet mesons η η has an independent coupling and is not restricted by these SU(3) relations. The decay into η η 8 is forbidden for any pseudoscalar mixing angle.

28 Second example: decays of vector mesons into two pseudoscalar mesons, comparing K Kπ and ρ ππ, decays of octet particles into two octet particles: Two octets can couple to an octet with symmetry or antisymmetry w.r.t. their exchange. The two pions in ρ decay must be antisymmetric, hence use the isoscalar factors for (K ) (Kπ Kη πk ηk) = ( ) / (ρ) (K K ππ ηπ πη KK) = ( 8 ) / Thus, K Kπ+πK 6, ρ ππ 8, or Γ K Kπ+πK Γ ρ ππ = 6 8 ( ).9 3 =.4 (Exp. =.34).358 The latter factor is the ratio of the decay momenta q to the 3rd power. The transition probability is proportional to q; for low momenta, the centrifugal barrier scales with q l where l is the angular momentum. Relation o.k. at the level of %, the typical level of SU(3) breaking effects. We have neglected angular barrier factors and that ρ and K may have different sizes,.

29 .4.5 Other meson nonets A meson nonet is fully described by just 4 names. The pseudoscalar nonet contains 3 pions, four kaon, the η and the η. In Table some meson nonets are collected. The f (5) is chosen as s s state instead of the f (4) as only the former has mass and decay modes compatible with values expected from SU(3) arguments. The η(95) is mostly considered to be the radial excitation of the η ground state. This assignment is challenged by its non-observation in radiative J/ψ decays, in pp annihilation and in -photon collisions while the η(44) is observed in all three reactions.

30 L S J n I= I=/ I= I= J P C n s+ L J π K η η + S ρ K Φ ω 3 S b (35) K B h (38) h (7) + P a (45) K (43) f (7) f (37) ++ 3 P a (6) K A f (5) f (85) ++ 3 P a (3) K (43) f (55) f (7) ++ 3 P π (67) K (77) η (87) η (645) + D ρ(7) K (68) ω(65) Φ(????) 3 D ρ (????) K (8) ω (????) Φ (????) 3 D 3 ρ 3 (69) K 3 (78) ω 3(67) Φ 3 (85) 3 3 D 3 π(37) K (46) η(475) η(95) + S ρ(45) K (45) Φ(68) ω(4) 3 S Table : The light mesons. The two mesons K A and K B mix to form the observed resonances K (8) and K (4). In some cases, mesons still need to be identified. The scalar and excited pseudoscalar mesons need a more detailed discussion.

31 .5 QCD on the lattice ] [GeV M 6 π (36) 4 π (7) π (8) π (3) π (4) 3 4 n No evidence for states beyond q q! Caution: π (6)

32 Glueballs + Four-quark states (Jaffe) r m G * * + * PC 4 3 m G (GeV) S d suū u sd d (uū + d d)s s u ddū dūs s u ds s (uū d d)s s sūd d s duū - I 3 f, a = κ = n sn σ = n nn M qq q q,l= < M q q,l= C. J. Morningstar and M. J. Peardon, Phys. Rev. D 6, 3459 (999). R. L. Jaffe, Phys. Rev. D 5, 67 (977). f (37) f (5) f (7) True for higher excitations? n n + glueball + s s? Scalar resonances f (37), f (7), a (45), K (4) Glueball f (5)

33 .6 Glueballs and hybrids.6. Is there evidence for a scalar glueball? f (37) and f (5) Crystal Barrel Collaboration x 3 m (ηη, ) [MeV /c 4 ] x 3 m (π η, ) [MeV /c 4 ] m(π π π π ) m(π π π π ) Dalitz plots for p p at rest into 3π, π η, π ηη, KL K L π, and 4π. Invariant mass for pn π 4π with one and two scalar states.

34 δ (s) Solution B Solution A Solution C Grayer et al. Solution D Solution E Protopopescu et al. (Table VI) Estabrooks & Martin s-channel Estabrooks & Martin t-channel Kaminsky et al. PY from data s / (MeV) 3 4 s / (MeV) Kaminsky Polychronatos Cohen Etkin Wetzel Hyams Protopopescu PY from data PY alternative h (s) Small inelasticity: f (37) ππ is small, f (37) 4π must be large!

35 [GeV/c ] Data from: D. Barberis et al., Phys. Lett. B47 (). Data from: Abele et al. EPJC 9, 667 (). No f (37) 4π. Fit: f (37) and f (5); Phase: only f (5) f (37) unlikely to exist: There is no evidence for supernumerosity, no evidence for a scalar glueball! M (Gev ) K * (95) K * (43) f () a () f (76) a (475) f (5).5 A view of scalar mesons:.5 a (98) f (98) K * (7) f (465) {} / {8} Isospin

36 .6. A pseudoscalar glueball? Strong signal in radiative J/ψ decay Z. Bai et al., Phys. Rev. Lett. 65 (99) 57. η(95) M =94±4, Γ=55± 5 MeV. η L a (98)π M =45± 5, Γ=56± 6 MeV η H K K + K K M =475± 5, Γ=8± MeV. Are η(95) and η(475) the n n and s s states and is η(45) the pseudoscalar glueball? 95 MeV 44 MeV 3 η states between 8 and 48 MeV?

37 Two quantitative tests for the glueball naturewere proposed: Stickiness S = N l ( mr ) l+ Γ J γr K J γr Γ R γγ F. E. Close, G. R. Farrar and Z. p. Li, Phys. Rev. D 55 (997) 5749., ( α ) Γ R gg Gluiness G = 9 e4 q α s Γ R γγ, L3 collaboration: S η = S η = 3.6 ±.3 S η(44) = 79 ± 6. G η = 5. ±.8 G η(44) = 4 ± 4. M. Acciarri et al., Phys. Lett. B 5 ().

38 From PDG 4 onwards: The η(44) is split π η η K π(3) η(95) η(45) η(475) K(46) n n n n glueball s s n s same masses ideally mixed From decays: η(45) a (98)π, ση Can be SU(3) singlet η(475) K K + KK Must have SU(3) octet component

39 However, (95) seen in N scattering only, not in any production experiment. (95) is fake? Is splitting of η(44) due to wave function node? Amplitudes for (44) decays to T.Barnes, F.E.Close, P.R.Page, E.S.Swanson, PRD 55, 457 (997). a π ση : K K Breit-Wigner functions (left) squared decay amplitudes (center) final squared transition matrix element (right).

40 Phase motion Complex amplitude and phase motion of a (98)π. From 3 to 5 MeV, phase varies by π. Only one resonance in mass interval. The ση exhibits the same behavior. What is η(95)? Not q q, exotic? Deck type background? Feed-through?

41 Summary on η(44). The η(95) is not a q q meson. The η(44) wave function has a node leading to two apparently different states η(45) and η(475). The node suppresses OZI allowed decays into a (98)π and allows K K decays. There is only one η state, the η(44) in the mass range from to 5 MeV and not 3! The η(44) is the radial excitation of the η. The radial excitation of the η is expected at about 8 MeV; it might be the η(835). S π η η K S π(3) η(835) η(44) K(46)

42 .6.3 Do exotic mesons exist?

43 .6.4 Are there charged bottononium states? Mass (MeV) ϒ() η b (3S) ππ ππ ϒ(86) ππ ϒ(4S) ϒ(3S) ππ ππ h b (P) χ (P) b χ b (3P) χ (P) b χ (P) b Thresholds: B s B s B*B* BB 3 ϒ( D ) 99 η b (S) ππ KK ϒ(S) ππ η π ππ h b (P) χ (P) b ω ππ χ (P) b ππ χ (P) b π π 97 ππ η 95 η b (S) ϒ(S) 93 PC J =

44 8 (Events/ MeV/c ) 6 4 (a) M(π + π - )>.447 GeV (Events/5 MeV/c ) (b) M(π + π - )>.374 GeV (Events/4 MeV/c ) (c) M (π + π - )>.36 GeV M(Y(S)π) max, (GeV/c ) M(Y(S)π) max, (GeV/c ) M(Y(3S)π) max, (GeV/c ) Events / MeV/c (d) M miss (π), GeV/c Events / MeV/c (e) M miss (π), GeV/c Invariant mass spectra of the (a) Υ(S)π ±, (b) Υ(S)π ±, (c) Υ(3S)π ±, (d) h b (P )π ± and (e) h b (P )π ± combinations.

45 Z b (6) Z b (65) Υ(S)π + π - Υ(S)π + π - Υ(3S)π + π - h b (P)π + π - h b (P)π + π - Average M, MeV Γ, MeV M, MeV - Γ, MeV Z + b resonance or dynamical effect? Minimal quark configuration: b bu d

46 RPP, Summary nn RPP, ss Bugg 4, 3* - 4* Bugg 4, * - * RPP, Omitted from Summary RPP, Further States Large number of meson resonances expected and observed! I G (J P C ) M GeV

47 Baryons. New results J. Beringer et al. (Particle Data Group), Phys. Rev. D86, (). Resonance Rating Npp Resonance Rating Npp Resonance Rating Npp N(44)/ + **** 3 N(5)3/ **** 7 N(535)/ **** 5 N(65)/ **** 8 N(675)5/ **** 4 N(68)5/ + **** 7 N(685) * N(7)3/ *** 5 N(7)/ + *** 4 N(7)3/ + **** 7 N(86)5/ + ** 9 N(875)3/ *** 6 N(88)/ + ** N(895)/ ** 7 N(9)3/ + *** 8 N(99)7/ + ** 9 N()5/ + ** N(4)3/ + * N(6)5/ ** 3 N()/ + * N(5)3/ ** N(9)7/ **** N()7/ **** 7 N(5)9/ **** N(6)/ *** N(7)3/ + ** (3) **** 8 (6)3/ + *** (6)/ **** (7)3/ **** (75)/ + * (9)/ ** 3 (95)5/ + **** (9)/ + **** 3 (9)3/ + *** (93)5/ *** (94)3/ * 5 (95)7/ + **** 3 ()5/ + ** (5)/ * ()7/ * (3)9/ + ** (35)3/ * (39)7/ + * (4)/ + **** (4)9/ **** (75)3/ ** (95)5/ + ** E.g.: V. Kuznetsov et al., Phys. Lett. B 647, 3 (7); V. Kuznetsov et al., Phys. Rev. C 83, (); I. Jaegle et al., Eur. Phys. J. A 47, 89 (). M. Ablikim et al. [BES Collaboration], Phys. Rev. D 8, 54 (9). A. V. Anisovich, R. Beck, E. Klempt, V. A. Nikonov, A. V. Sarantsev and U. Thoma, Eur. Phys. J. A 48, 5 (); Npp particle properties were determined; 4 in total. Be cautious, there are ambiguities! Promoted to three-star resonance

48 . What is the origin of mass?.. From Atoms to quarks, from compositeness to structure Search for the basic constituents of matter: Atoms Nuclei and electrons Nucleons Quarks Preons?

49 .. 3 Generations of quarks Mass (MeV) n Octet S p Decuplet S Thresholds: D s*d s* D s*d s D*D* D s D s D D* DD η c (S) X(466) ψ (445) X(436) X(46) ψ (46) ψ (44) ψ (377) π π η π ψ (S) π π π π h c (P) χ c (P) X(387) -+ (?) χ c (P) χ c χ c (P) (P) Λ Σ Σ Σ + I 3 Σ Σ Σ + I Mass (MeV) PC J = η c (S) + π π J /ψ π π π η (S) π π ϒ() Ξ Ξ Ξ Ξ η b (3S) ππ ππ ϒ(86) ππ ϒ(4S) ϒ(3S) ππ ππ h b (P) χ b (P) χ b (3P) χ (P) b χ b (P) Thresholds: B sb s B*B* BB 3 ϒ( D ) Ω : Predicted by Gell-Mann in 964: Ω η b PC J = η b (S) (S) + ππ KK ππ η ϒ(S) ππ η ϒ(S) π ππ h b (P) + χ b (P) + + ω ππ χ (P) b + + ππ χ b (P) + + π π Found by V. E. Barnes et al. in 964 Triumph of SU(3) Spectroscopy suggests: Constituent quarks of 35 MeV. Later: charm, bottom, top

50 ..3 The Standard Model ( u d) ( c s) ( t b) ( u d) ( u d ) ( c s) ( c s) ( t b) ( t b) QCD, 8 gluons ( νe e ) ( νµµ ) ( ντ τ ) QFD, γ, W, Z The quarks and leptons are eigenstates of the weak interaction operator. They are linked to the mass eigenstates via the (3 3) Cabibbo-Kobayashi-Maskawa matrix. Masses: m e =.5 MeV; m µ = 5.66 MeV; m τ = 776.8±.6 MeV; < m ν e < ev; < m νµ <.9 MeV; < m ντ < 8. MeV; m u =.5±.5 MeV; m d = 4.7±. MeV; m s = 93.5±.5 MeV; m c =.75±.5 GeV; m b = 4.8±.3 GeV; m t = 73.5±. GeV A wide range of masses. Fundamental? Where does the mass come from?

51 ..4 Nobel price 3 in physics: The Higgs particle. Events / GeV 8 6 ATLAS Data + SM Higgs boson m =6.8 GeV (fit) H Bkg (4th order polynomial) H γγ Events/5 GeV Data + SM Higgs Boson m H =4.3 GeV (fit) Background Z, ZZ* Background Z+jets, tt Syst.Unc. ATLAS H ZZ* 4l s = 7 TeV s = 8 TeV - Ldt = 4.6 fb Ldt =.7 fb s = 7 TeV Ldt = 4.8 fb - s = 8 TeV Ldt =.7 fb 5 Events - Fitted bkg m γγ [GeV] [GeV] m 4l Higgs gives masses to quarks, leptons, and weakly interaction bosons but there is more mass in the Universe than the Higgs provides!

52 ..5 The mass of the Universe Mass of the Universe: Dark energy 73% Dark matter 3% Intergalactic gas 3.6% } atoms Stars.4% Mass of atoms Mass of quarks Mass of electrons Field energy % due to Higgs.% due to Higgs 99% due to strong QCD Binding energies H atom ev / GeV 8 Nuclei 8 MeV / GeV Nucleons.99 GeV / GeV Mass of atoms is due to self-interactions! How does this work?

53 ..6 How to explore the internal structure of the nucleon? Spectroscopy and scattering! Bohr and Rutherford Quantum Electro Dynamic very well understood Praktikumsversuch, Universität Stuttgart

54 Nucleon tomography: Goal: Distribution of linear and angular momenta Collectivity is lost! x f(x) x There are 3 valence quarks in a proton Quarks carry /3 and -/3 charges Quarks have spin / Quarks are confined With increasing resolution more and more q q pairs show up Gluons carry a large fraction of the proton momentum Quarks make little contributions to the proton spin Quarks carry colour red, green, blue and interact by exchange of gluons Gluons themselves carry color and interact Their interaction leads to perturbative quark-gluon and gluon-gluon interactions, and to non-perturbative interactions,.5 Confinement potential: β=6. β=6. fit including confinement Caution:. The q q potential: static quarks! V (r)/gev.5. fm 4 3 αs r V (r) = a r. α s undefined in spectroscopy! -.5α s : r/fm..4.6

55 Nucleon spectroscopy: σ tot 5 [µb] E γ [GeV] / + 3/ - 5/ ρ-ω W [GeV] (CB-ELSA collab.) Wave length matches the size of constituents α s : Explores collective response! For massless quarks, the QCD Lagrangian respects chiral symmetry This should lead to identical masses for π and f (5) N and N(535)/ Chiral symmetry is obviously broken (spontaneously broken) even in the regime of light quarks Quarks acquire an effective mass; M ρ, M ω 75 MeV, M N MeV, Constituent quark masses evolve, m u =m d =35 MeV, m s =5 MeV Chiral symmetry could be restored at high temperature Is chiral symmetry restored in high-mass hadrons?

56 ..7 Current and constituent quarks (-) From lattice QCD: P. O. Bowman et al., Phys. Rev. D 7, 5457 (5). (-) By expelling the chiral condensate: A. Chodos, R. L. Jaffe, K. Johnson and C. B. Thorn, Phys. Rev. D, 599 (974). < ψψ >= (.3) 3 GeV 3 (-) From instantons: D. Diakonov and V. Y. Petrov, Sov. Phys. JETP 6, 4 (985) [Zh. Eksp. Teor. Fiz. 89, 36 (985)]. L R L R (-) Gluon propagator from Dyson-Schwinger equation: M. S. Bhagwat, M. A. Pichowsky, C. D. Roberts and P. C. Tandy, Phys. Rev. C 68, 53 (3). = -

57 ..8 Photoproduction Study of coupled channels very important! σ tot, µb γp π p a) / 3/ / 5/ + 3/ 7/ σ tot, µb γp ηp c) / / / 3/ + / 5/ σ tot, µb γp K + Λ g) / / / 5/ + / 7/ + / 7/ σ tot, µb γp K + Σ d) / / / 3/ 3/ 7/ σ tot, µb γp K Σ + e / / / 3/ / 3/ M(γp), MeV M(γp), MeV M(γp), MeV 8 4 M(γp), MeV M(γp), M 4 σ tot, µb CB-ELSA CB-ELSA TAPS GRAAL CB-ELSA pπ / 3 σ tot, µb GRAAL MAMI CB/TAPS CB/TAPS D 33 P 33 η N(535)π a (98)p M(γp), GeV/c E γ, MeV

58 Cx (γp KΛ).5 W=838 W=939 dσ/dω, µb/sr Σ cos θ cm W= Cz (γp KΛ) W=35 W= W=8 cos θ cos θ cm W= W= cos θ cos θ cm

59 ) ) ) )..9 Dalitz plots for pπ π and pπ η ) ) (GeV (pπ M ) ) (GeV (pπ M ) ) (GeV (pπ M M (pπ ) (GeV ) M (pπ ) (GeV ) M (pπ ) (GeV ) M (pπ ) (GeV ) ) (pπ ) (GeV M ) (pπ ) (GeV M (3) (3) a a(98) a (98) (3) (3) (3) 4.5. (3) 4 (3) (3) M (π η) (GeV M (π η) (GeV ) ) (pπ ) (GeV M a a(98) a (98) (3) (3) (3) 4.5. (3) 4 (3) (3) M (π η) (GeV M (π η) (GeV ) ) (pπ ) (GeV M.4.6 ) (pπ ) (GeV.4 M ) (pπ ) (GeV M (3) a 8 (98) (3) (3) (3) a (98) a (98) (3) (3) (3) 4.5. (3) 4 (3) M (πm η) (π (GeV η) (GeV ) ) (pπ ) (GeV M aa (98) a (98) a (98) (3) (3) (3) 4.5. (3) 4 (3) (3) M (π η) (GeV M (π η) (GeV ) ) (pπ ) (GeV M

60 .3 The wave function Total wave function ψ >= flavor > space > spin > color > Example ++ (3) ground state with J = 3/: L = and S, S z = 3/, 3/. = u u u 3 flavor > space > spin > fully symmetric color! Pauli principle: The color wave function is fully antisymmetric, the spin-space-flavor wave function fully symmetric. u u u 3 u u u 3 u u u 3

61 .3. The spin wave function S = 3/ : fully symmetric S = / : ( ) mixed symmetry.3. The flavor wave function SU() SU(3) = SU(6) = 56 S 7 M 7 M A 56 = = = 8 4.

62 .3.3 The spatial wave function Two oscillators (assume harmonic); ρ = ( x x ) λ = 6 ( x + x x 3 ) ρ λ X = ( x + x + x 3 ) S space spin isospin κ gd S SSS S S(M ρ M ρ + M λ M λ ) / S 3 (M ρ M ρ + M λ M λ )S S 4 (M λ M λ M ρ M ρ )M ρ + (M ρ M λ M λ M ρ )M λ /4 S 5 (M ρ SM ρ + M λ SM λ ) S 6 A(M λ M ρ + M ρ M λ )

63 Oscillator states of definite S 3 symmetry, N denotes the number of oscillator excitations, L the total orbital angular momentum, sym. denotes the symmetry: S symmetric, M S mixed symmetric, M A mixed antisymmetric and A antisymmetric. N, L sym. n ρ +n λ l ρ +l λ osc. state [, S φ s ( ρ) φ s ( λ) [, M S φ s ( ρ) φ p ( λ) [, M A φ p ( ρ) φ s ( λ), S, M S, M A, A, S, M S, M A ] ] ] ] [φ s ( ρ) φ s ( λ) [ + φ s ( ρ) φ s ( λ) ] [φ s ( ρ) φ s ( λ) [ - φ s ( ρ) φ s ( λ) [ ] φ p ( ρ) φ p ( λ) [ ] φ p ( ρ) φ p ( λ) [φ s ( ρ) φ d ( λ) [ + φ d ( ρ) φ s ( λ) ] ] ] ] [φ s ( ρ) φ d ( λ) [ - φ d ( ρ) φ s ( λ) [ ] φ p ( ρ) φ p ( λ) ] ]

64 .4 Models.4. Quark models U. Löring, B. C. Metsch, H. R. Petry, Eur. Phys. J. A, 395 (). Ingredients: constituent quarks with defined rest masses confinement potential some residual interaction, e.g. effective one-gluon exchange, meson exchange, instantons ** 6 *** Mass [MeV] 5 * S 9 ** ** ** *** **** **** 44 **** **** 9 8 * ** S S 7 65 *** **** **** **** ** 675 **** 9 **** 5 **** J π L T J 939 **** /+ 3/+ 5/+ 7/+ 9/+ /+ 3/+ /- 3/- 5/- 7/- 9/- /- 3/- P P3 F5 F7 H9 H K 3 S D3 D5 G7 G9 I I 3

65 .4. 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 more states than observed (missing resonances) b Lattice and quark models predict even-odd staggering (exp: parity doublets) c 3/ + : 5 states expected, N(7)3/ +, N(9)3/ +, tentative N(96)3/ +, N()3/ +

66 .4.3 Dynamically generated baryon resonances At low energies the building blocks of hadron resonances could be the ground state mesons and baryons. Resonance properties are derived from chiral Lagrangians. N / (535), e.g., is a quasibound ΛK ΣK state. Are dynamically generated states additional states, atop of quark model states? Or are quark model and dynamically generated resonance dual descriptions? Cross Section (mb) T p (MeV) πp - pp n η h n Examples: N(535)/, Λ(45)/ a (98), f (98), D s (37), X(387), σ(5), κ(7) Are these states additional to the quark model? N. Kaiser, P. B. Siegel and W. Weise, Phys. Lett. B 36, 3 (995).

67 .4.4 Excursion to heavy baryon resonances: Masses (in MeV) of heavy baryons. The isospin of Λ + c /Σ+ c (765) (faint) is unknown. Λ + c 86.5± ±.6 68.± ± ±.4 Σ ++ c 454.±. 58.4± Λ + c : 939.3±.4 Σ + c 45.9± ± ±.4 Σ + c 453.8±. 58.± Ξ + c 467.9± ± ± ± ± ± ± ±.5 3.9±.3 Ξ c 47.± ± ±. 79.9± ±. 97.9± ±. Ω c 697.5± ±3. Ξ + cc : 358.9±.9 Λ b 56.±.6 Σ + b 587.8± ±3.4 Σ b : 585.± ±.8 Ξ b ±3.8 Ω b : 665±7 or 654.4±6.8 Ξ b = (bsd) three generations! Only very few measured spin-parities!

68 (MeV) E MeV 5/ Λ 3/ / / + 3/ / / + Λ c?? / +? 3/ / / + / + Ξ c 3/ /?? / +? 3/ / 3/ + / + The lowest-mass Λ, Λ c, and Ξ c negativeparity states have fully antisymmetric spinflavor wave functions. In the Λ spectrum, the Roper-like state is above the two singlet states, then the two negative-parity octet (mixed symmetry) states follow. The Λ c and Ξ c exhibit the same pattern but spin-parities are not known. Wohl in PDG: The clean Λ c spectrum has in fact been taken to settle the decades-long discussion about the nature of the Λ(45) - true 3-quark state or K p threshold effect? - unambiguously in favor of the first interpretation. Heavy-quark and light-quark spectroscopy benefit from each other!

69 .5 Baryon excitations.5. 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 N 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)

70 .5. Are there dynamically generated resonances not existing in quark models? Im z R [MeV] x=. (I=) 46 (I=) 4 x=. x=.5 Singlet disappear (I=) x=.5 x=.6 x=.5 5 Octet x=. x=.5 x= (I=) 68 (I=) x=. 7 Re z R [MeV] Trajectories of the poles in the scattering amplitudes obtained by changing the SU(3) breaking parameter x gradually. At the SU(3) symmetric limit (x = ), only two poles appear, one is for the singlet and the other for the octet. The symbols correspond to the step size δx =.. Jido, Oller, Oset, Ramos, Meissner, Nucl. Phys. A 75, 8 (3). In the quark model one expects a SU(3) singlet spin-doublet a SU(3) octet spin-doublet a SU(3) octet spin-triplet MeV 6 4 5/ 5/ + / 3/ / / + 3/ /? / +? 3/ / The occurrence of two Λ states with J P = / is - from the quarkmodel point of you - completely unexpected. This is the only place where a resonance is dynamically generated and unexpected in quark The Λ c spectrum is similar. models! Λ / + Λ c / + I m convinced: this is wrong!

71 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: the number of q q mesons and of qqq baryons does not exceed the number of states expected from quark models. The Roper resonance or the f (98) and a (98) can have large molecular components but the raison d être of all hadrons is their q q or qqq component. There are no (additional) unconventional states!

72 .5.3 Is the mass of excited baryons due to chiral symmetry breaking or restoration? ] M [GeV / + 7/ + (3) f (7) a (3) ω (78) ρ (77) 3 / + (95) 7 (4) ω 3 ρ 3 5/ + f 4 a 4 (67) (69) ρ 5 (35) (5) () (95) f 6 a 6 (5) (45) 5 J Nambu: gluon flux between the two quarks concentrated in a rotating flux tube with a homogeneous mass density. This gives the total mass Mc = r and the angular momentum l = c r σdr v /c = πσr σrvdr + const(= /) v /c l + / = πσr c = M πσ c where σ =.8 (GeV) / c =.9 GeV/fm is the string tension, and r (ρ) =.6 fm r (a 6 ) =.86 fm. The linearity of the Regge trajectory suggests a string-like interaction (not one-gluon exchange!) and a quark-diquark picture for baryon excitations.

73 .5.4 AdS/QCD: Analytically solvable model of QCD with constant s. The model which contains only one parameter, size. M = a (L + N + 3/) b α D [ GeV ] a =.4 GeV and b =.46 GeV 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/ +() 7/ + 5/ + 7/ +(39) 9/ +(3) / +(4) 3/ 5/ (35) 7/ 9/ (4) / / 5/ + 7/ + 9/ + / + 9/ + / + 3/ + 5/ +(95) / 3/ (75) N= 7/ 9/ L+N

74 .5.5 Comparison model versus data: Quark model with eff. one-gluon exchange: (δm/m) = 5.6% (7p) S. Capstick and N. Isgur, Baryons In A Relativized Quark Model With Chromodynamics, Phys. Rev. D 34, 89 (986). Quark model with instanton induced forces: (δm/m) = 5.% (5p) U. Loring, B.C. Metsch and H.R. Petry, The light baryon spectrum in a relativ. quark model with instanton-induced quark forces, Eur. Phys. J. A, 395, 447 (). AdS/QCD model with good diquarks : (δm/m) =.5% (p) H. Forkel and E. Klempt, Diquark correlations in baryon spectroscopy and holographic QCD, Phys. Lett. B 679, 77 (9). Skyrme model: (δm/m) = 9.% (p) M. P. Mattis and M. Karliner, The Baryon Spectrum Of The Skyrme Model, Phys. Rev. D 3, 833 (985).

75 .5.6 Restoration of chiral symmetry Chiral multiplets for J = /, 3/, 5/ (first three lines) and for J = /,, 7/ (last four lines) for nucleon and Mass of ground-state baryons due to spontaneous breaking of chiral symmetry. Thus, N / (535) is much heavier than its chiral partner, N / + (94). resonances. N / + (7) N / (65) / + (75) / (6) ** **** **** N 3/ + (7) N 3/ (7) 3/ + (6) 3/ (7) **** *** *** **** N 5/ + (68) N 5/ (675) no chiral partners **** **** N / + (88) N / (95) / + (9) / (9) ** * **** ** N 3/ + (9) N 3/ (86) 3/ + (9) 3/ (94) ** ** *** ** no chiral partners 5/ + (95) 5/ (93) **** *** N 7/ + (99) a N 7/ (9) 7/ + (95) 7/ () ** **** **** * N 9/ + () N 9/ (5) 9/ + (3) 9/ (4) **** **** ** ** At high excitation energies, chiral potential could be irrelevant. details of the Chiral symmetry could be restored. Then: chiral multiplets should occur. Limited predictive power.

76 .6 The Baryon Resonance Spectrum: Perspectives. Baryons provide an excellent tool to study strong QCD. Fundamental questions are at stake: is chiral symmetry breaking - responsible for the mass of ground state baryons - responsible as well for the mass of excited states? Why is AdS/QCD so successful in reproducing the mass spectrum?. There is an ongoing ambitious program: photoproduction of baryon resonances. High-statistics photoproduction experiments with polarized photons and targets (CLAS, ELSA, MAMI-C, SPring-8) Multi-channel partial wave analyses (BnGa, Ebac, Jülich, MAID, SAID, among others). COMPASS has interesting data which may contribute to baryon spectroscopy. The existence and the properties of a few states are decisive for different scenarios like quark models, the role of dynamically generated resonances, gravitational theories, and the conjecture that chiral symmetry may be restored in high-mass excitations. 3. A couple of key questions should be answered: Is the quark model a valid approximation up to the second shell? The quark model predicts a doublet of positive-parity states - N / + and N 3/ + - with L =, S = /. These states have both oscillators excited; one should expect them to decay in a cascade. Based on the mass formula, I

77 expect these states at 78 MeV and to be found in the reaction chain γp N / (535)π Nπη and γp N 3/ (5)π Nππ, respectively. Are dynamically generated resonances additional resonances atop of quark model states or are these dual views onto the same objects? Decide if Λ / (45) split is really into two states, one mainly singlet, one mainly octet. Best experimental chance in J/ψ Λ / (45)Λ / (45). Explore link to heavy baryon spectroscopy. Is chiral symmetry is restored in high-excitation states? What is the mass of 7/? [a] About 95 MeV; then 7/ forms a chiral doublet with 7/ + (95) and supports chiral symmetry restoration. [b] About MeV; then it supports quark models and AdS/QCD.

78 3 Summary Hadron spectroscopy may reveal fundamental aspects of strong QCD. In meson spectroscopy, new results are to be expected from Compass, BESIII, BELLE, PANDA,. Warning: not every particle which is difficult to understand is a glueball, a hybrid or a molecule. Is there a hybrid candidate which shows a significant phase variation with respect to the leading wave? How is mass generated in excited states, Kinetic energy of constituent quarks? Hadrogenesis? Chiral symmetry breaking in an increasing volume? Restoration of chiral symmetry? Photoproduction experiments begin to make a significant impact on the spectrum of baryon resonances

79 Contents Mesons. πn scattering Mesons and their quantum numbers Parity P = ( ) L C-Parity C = ( ) L+S Isospin G-parity P = ( ) L++I Particle decays The transition amplitude Short-lived states in QM The Breit-Wigner amplitude The Dalitz plot Meson nonets

80 .4. The pseudoscalar mesons Vector and tensor mesons The Gell-Mann-Okubo mass formula Meson decays Other meson nonets QCD on the lattice Glueballs and hybrids Is there evidence for a scalar glueball? A pseudoscalar glueball? Do exotic mesons exist? Are there charged bottononium states? Baryons 47. New results What is the origin of mass?

81 .. From Atoms to quarks, from compositeness to structure Generations of quarks The Standard Model Nobel price 3 in physics: The Higgs particle The mass of the Universe How to explore the internal structure of the nucleon? Current and constituent quarks Photoproduction Dalitz plots for pπ π and pπ η The wave function The spin wave function The flavor wave function The spatial wave function Models Quark models

82 .4. Baryons on the lattice Dynamically generated baryon resonances Excursion to heavy baryon resonances: Baryon excitations Are dynamically generated resonances atop of q q or qqq? Are there dynamically generated resonances not existing in quark models? Is the mass of excited baryons due to chiral symmetry breaking or restoration? AdS/QCD: Comparison model versus data: Restoration of chiral symmetry The Baryon Resonance Spectrum: Perspectives Summary 78