Why? How? to test strong QCD! SU(3) Chiral Perturbation Theory Threshold γn ΚΛ amplitudes K +, K 0, Λ form factors, polarizabilities Lattice QCD

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1 Why? to test strong QCD! How? SU(3) Chiral Perturbation Theory Threshold γn ΚΛ amplitudes K +, K 0, Λ form factors, polarizabilities Lattice QCD Cornelius Bennhold George Washington University Excitation spectrum of the nucleon Missing and exotic resonances Cornelius Bennhold, George Washington University HYP2003, page 1

2 What do we want? New Topic Cornelius Bennhold, George Washington University HYP2003, page 2

3 short table gives the name, the quantum numbers (where known), and the status of baryons in the Review. Only the baryons with 3- This 4-star status are included in the main Baryon Summary Table. Due to insucient data or uncertain interpretation, the other entries in the or table are not established as baryons. The names with masses are of baryons that decay strongly. For N,, and resonances, the partial short is indicated by the symbol L 2I 2J, where L is the orbital angular momuntum (S, P, D, :::), I is the isospin, and J is the total angular wave + c 0 b, ; b c *** Quantum Chromodynamics (QCD) --- the fundamental theory of the strong interaction (in terms of quarks and gluons) L 1 µν µ QCD = TrF F q( D + µν + γ µ mq ) q Baryon Summary Table momentum. For and resonances, the symbol is L I 2J. p P11 **** (1232) P33 **** P01 **** + P11 **** 0, ; P11 **** n P11 **** (1600) P33 *** (1405) S01 **** 0 P11 **** (1530) P13 **** N(1440) P11 **** (1620) S31 **** (1520) D03 **** ; P11 **** (1620) * N(1520) D13 **** (1700) D33 **** (1600) P01 *** (1385) P13 **** (1690) *** N(1535) S11 **** (1480) * (1750) P31 * (1670) S01 **** (1820) D13 *** N(1650) S11 **** (1900) S31 ** (1690) D03 **** (1950) *** (1560) ** N(1675) D15 **** (1905) F35 **** (1800) S01 *** (2030) *** (1580) D13 ** N(1680) F15 **** (1910) P31 **** (1810) P01 *** (2120) * (1620) S11 ** N(1700) D13 *** (1660) P11 *** (1920) P33 *** (1820) F05 **** (2250) ** N(1710) P11 *** (1930) D35 *** (1830) D05 **** (1670) D13 **** (2370) ** N(1720) P13 **** (1940) D33 * (1890) P03 **** (2500) * (1690) ** N(1900) P13 ** (1950) F37 **** (2000) * (1750) S11 *** N(1990) F17 ** (2020) F07 * (1770) P11 * ; **** (2000) F35 ** N(2000) F15 ** (2150) S31 * (2100) G07 **** (1775) D15 **** (2250) ; *** N(2080) D13 ** (1840) P13 * (2380) ; ** (2200) G37 * (2110) F05 *** N(2090) S11 * (1880) P11 ** (2470) ; ** (2300) H39 ** (2325) D03 * N(2100) P11 * (2350) D35 * (2350) H09 *** (1915) F15 **** N(2190) G17 **** (2390) F37 * (2585) ** (1940) D13 *** **** N(2200) D15 ** (2000) S11 * c (2593) + *** (2400) G39 ** N(2220) H19 **** (2030) F17 **** c (2625) + *** (2420) H3 11 **** N(2250) G19 **** (2070) F15 * c (2765) + * (2750) I3 13 ** (2080) P13 ** c (2880) + ** N(2600) I1 11 *** (2950) K3 15 ** N(2700) K1 13 ** (2100) G17 * c (2455) **** (2250) *** c (2520) *** (2455) ** (2620) ** + c, 0 c *** 0+ c, 00 (3000) * c (2645) *** (3170) * c (2790) *** c (2815) *** 0 c *** 0 b *** Cornelius Bennhold, George Washington University HYP2003, page 3 *

4 Comparison with lattice results What is the nature of the Roper (P 11 (1440) 1/2 + ) resonance? Mass (GeV) S 11 (1535) 1/2 - P 11 (1440) 1/2 + N(938) 1/2 + Naïve quark model gives the wrong ordering h ω h ω N(1440)1/2+ N(1535)1/2- N(938)1/2+ - Hybrid state (qqqg)? - Dynamical meson-baryon state? Cornelius Bennhold, George Washington University HYP2003, page 4

What is the nature of the Roper (P 11 (1440) 1/2 + ) resonance? P 11 (1440) 1/2 + 2.5 Mass (GeV) 2.0 1.5 1.0 0.

5 What is the nature of the Roper (P 11 (1440) 1/2 + ) resonance? P 11 (1440) 1/ Mass (GeV) S 11 (1535) 1/2 - P 11 (1440) 1/2 + N(938) 1/2 + m π = 180 MeV! N(938) 1/2 + F.X. Lee et al., 2003 Answer: The Roper (P 11 (1440) 1/2 + ) is just a regular 3-quark state! Cornelius Bennhold, George Washington University HYP2003, page 5

Can we understand the level ordering? 2.5 Mass (GeV) 2.0 1.5 1.0 0.5 S 11 (1535) 1/2 - P 11 (1440) 1/2 + N(938) 1/2 + F.X.

6 Can we understand the level ordering? 2.5 Mass (GeV) S 11 (1535) 1/2 - P 11 (1440) 1/2 + N(938) 1/2 + F.X. Lee et al., 2003 Cross over occurs very close to chiral limit! Cornelius Bennhold, George Washington University HYP2003, page 6

7 What about Hyperons? The Λ(1405)? 2.5 Λ(1600) 1/2 + Mass (GeV) Λ(1600) 1/2 + Λ(1405) 1/2 - Λ(1115) 1/2 + Λ(1115) 1/2 + Λ(1405) 1/2 - Talk by Frank Lee on Friday Cornelius Bennhold, George Washington University HYP2003, page 7

8 How do we find the resonances? New Topic Cornelius Bennhold, George Washington University HYP2003, page 8

9 N* spectral lines don t quite look like this: but more like this: σ (µb) Nucleon resonances are broad and overlapping! Eγ (MeV) Cornelius Bennhold, George Washington University HYP2003, page 9

γn πn, ππn, ηn, ΚΛ, σtotal χpt Resonance Region High-t pqcd Low-t Regge Threshold low W 1.

10 γn πn, ππn, ηn, ΚΛ, σtotal χpt Resonance Region High-t pqcd Low-t Regge Threshold low W Intermediate W High W W (GeV) Cornelius Bennhold, George Washington University HYP2003, page 10

11 We cannot directly compare experiment to QCD therefore, we must use an intermediary : QCD Lattice, Quark models M N*, Γ πn, A 1/2 Dynamical Models: mesons + Baryons Multipoles Phase shifts Experiments: γn πn, ππn ηn, ΚΛ, πn πn, ππn ηn, ΚΛ, Theoretical challenge: Resolution of broad, overlapping resonances in a strongly-coupled, multi-channel system Cornelius Bennhold, George Washington University HYP2003, page 11

12 A theorist s approach to finding N*s Step 1: Measure all observables for all channels at all energies and all angles! Step 2: Perform partial wave analysis Step 3: Fit model parameters to extracted partial waves Step 4: Separate background from resonance contributions Step 5: Extract resonance properties and compare to lattice Cornelius Bennhold, George Washington University HYP2003, page 12

13 How does a partial-wave amplitude behave at E = E res? 40 γn πn multipole Im M 1+ = max M 1+ (3/2) (10-3 /m π ) 20 0 Re M 1+ = 0 Tl (E) ~ ~ Γ/2 (E-E R ) - iγ/2 Γ/2 (E-E R ) 2 + (Γ /2) 2 ReT l ω L (MeV) ((E-E R ) + iγ/2) W = 1232 MeV ImT l Caution: Single resonance, elastic, no background! Cornelius Bennhold, George Washington University HYP2003, page 13

14 Scattering amplitude: M = V + V G 0 T Hadronic rescattering amplitude: The physics is in the driving terms π K π K π, η, K, ππ π = + K Cornelius Bennhold, George Washington University HYP2003, page 14

15 Driving (potential) terms SU(3) chiral dynamics: Derivative couplings Contact terms to a given order At high energies: t-channel contributions Regge behavior A 1/2, A 3/2 helicity amplitudes Resonance contributions N*, * masses Cornelius Bennhold, George Washington University HYP2003, page 15 N* Free parameters adjusted to data πn ηn KΛ ΚΣ branching ratios

16 How many N* do we have? State-of-the-art multi-channel analyses find, for a given partial wave: Ground states (1 st tier): P 33 (1232), D 13 (1520), Clear resonance signal, Mass known to within a few %. A 1/2, Γ total, partial widths fairly well known Exceptions: S 31 (1620), 2 nd tier states: P 33 (1600), D 13 (1700), Existence confirmed, but poorly understood 3 rd tier states: P 33 (1920), D 13 (2080), Existence controversial. Where is everybody? How many N* do we need? Cornelius Bennhold, George Washington University HYP2003, page 16

17 What are missing Resonances? New Topic Cornelius Bennhold, George Washington University HYP2003, page 17

18 Current spectrum of baryon resonances: Gap of almost 200 MeV with no N* P11 **** p P11 **** n P11 **** N(1440) D13 **** N(1520) S11 **** N(1535) P33 **** (1232) P33 *** (1600) S31 **** (1620) D33 **** (1700) P31 * (1750) N(1650) S11 **** (1900) S31 ** N(1675) D15 **** (1905) F35 **** N(1680) F15 **** (1910) P31 **** N(1700) D13 *** (1920) P33 *** N(1710) P11 *** (1930) D35 *** N(1720) P13 **** (1940) D33 * N(1900) P13 ** (1950) F37 **** Gap of 450 MeV between 4-star N* F17 ** N(1990) F15 ** N(2000) D13 ** N(2080) S11 * N(2090) P11 * N(2100) F35 ** (2000) S31 * (2150) G37 * (2200) H39 ** (2300) D35 * (2350) Gap of 450 MeV between 4-star * N(2190) G17 **** (2390) F37 * N(2200) D15 ** (2400) G39 ** N(2220) H19 **** (2420) H3 11 **** N(2250) G19 **** (2750) I3 13 ** N(2600) I1 11 *** (2950) K3 15 ** N(2700) Cornelius Bennhold, George K1 13 ** Washington University HYP2003, page 18

Compare experimental N* and quark model states experimentally uncertain N* Quark model predictions experimentally known N* Capstick and Roberts quark model Quark

19 Compare experimental N* and quark model states experimentally uncertain N* Quark model predictions experimentally known N* Capstick and Roberts quark model Quark models predict many more states than are seen experimentally! 1/2 + 3/2 + 5/2 + 7/2 + 1/2-3/2-5/2-7/2 - Cornelius Bennhold, George Washington University HYP2003, page 19

20 True for all models based on three constituent quarks Quark model predictions Metsch and Petry quark model Cornelius Bennhold, George Washington University HYP2003, page 20

21 Nucleon flux-tube hybrids: SCapstick and P. Page, PRD60 (1999) Even more missing states!!! Cornelius Bennhold, George Washington University HYP2003, page 21

22 Let s focus on the P 13 (3/2 + ) states: Five extra states below W = 2100 MeV! experimentally uncertain N* Light hybrids Quark model predictions experimentally known N* Cornelius Bennhold, George Washington University HYP2003, page 22

23 How many N* do we have? State-of-the-art multi-channel analyses find, for a given partial wave: Ground states (1 st tier): P 33 (1232), D 13 (1520), Clear resonance signal, Mass known to within a few %. A 1/2, Γ total, partial widths fairly well known Exceptions: S 31 (1620), 2 nd tier states: P 33 (1600), D 13 (1700), Existence confirmed, but poorly understood 3 rd tier states: P 33 (1920), D 13 (2080), Existence controversial. Where is everybody? How many N* do we need? Possibly 4-5 N* for selected partial waves! Cornelius Bennhold, George Washington University HYP2003, page 23

24 looking in places: γn ΚΛ(Σ) New Topic Cornelius Bennhold, George Washington University HYP2003, page 24

25 Scattering amplitude: M = V + V G 0 T From coupled channels to single channel: T πν πν T ην πν T γν πν T ρν πν T σν πν T ΚΛ πν T ΚΣ πν T= T πν ην T ην ην T γν >ην T ρν ην T σν ην T ΚΛ ην T ΚΣ ην T πν γν T ην γν T γν γν T ρν γν T σν γν T ΚΛ γν T ΚΣ >γν T πν ρν T ην ρν T γν ρν T ρν ρν T σν ρν T ΚΛ ρν T ΚΣ ρν T πν σν T ην σν T γν σν T ρν σν T σν σν T ΚΛ σν T ΚΣ σν T γν ΚΛ T πν ΚΛ T ην ΚΛ T γν ΚΛ T ρν ΚΛ T σν ΚΛ T ΚΛ ΚΛ T ΚΣ ΚΛ T πν ΚΣ T ην ΚΣ T γν ΚΣ T ρν ΚΣ T σν ΚΣ T ΚΛ ΚΣ T ΚΣ ΚΣ Cornelius Bennhold, George Washington University HYP2003, page 25

26 Background: tree level with SU(3) couplings Hadronic form factors: Vertex F(s,t,u) Meson Baryon Baryon resonance background ω(mev) Cornelius Bennhold, George Washington University HYP2003, page 26

27 γn ΚΛ fits Database: diff. cross section from SAPHIR or Jlab (not both!) Recoil polarization from SAPHIR or Jlab Photon asymmetry (SPring 8) 1300 data points Model: Born terms with form factors + 2 Y* in u-channel + K* in t-channel 6-88 N* states parameters χ Cornelius Bennhold, George Washington University HYP2003, page 27

28 Polarization observables for γn ΚΛ Polarized photons Photon Polarization Σ Λ Recoil Cornelius Bennhold, George Washington University HYP2003, page 28

Divide energy region into three parts: Threshold region (1.61 1.75 GeV): S 11 (1650), P 11 (1710), P 13 (1720) Missing N* region (1.75 2.1 GeV): D 13 (1900), High-spin N* region (2.1 2.

29 Divide energy region into three parts: Threshold region ( GeV): S 11 (1650), P 11 (1710), P 13 (1720) Missing N* region ( GeV): D 13 (1900), High-spin N* region ( GeV): G 17 (2190), γn ΚΛ σtotal S 11 (1650), P 11 (1710), P 13 (1720) Missing N* Region High-spin N* and Regge W (GeV) Threshold Intermediate W High W Cornelius Bennhold, George Washington University HYP2003, page 29

30 Threshold Region New Topic Cornelius Bennhold, George Washington University HYP2003, page 30

31 Threshold Region: S 11 (1650), P 11 (1710), P 13 (1720) What does the quark model predict? (Capstick, Roberts) Result of coupled-channels analysis for: γp Κ + Λ and π p Κ 0 Λ N* Γ ΚΛ S 11 (1650) large D 15 (1675) F 15 (1680) D 13 (1700) P 11 (1710) P 13 (1720) zero zero small large large s-wave Onset of p- wave New result (prelim.): S 11 (1650) MeV P 11 (1710) P (1720) 1650 or 1730 MeV possibly 2 different N*? but total width is MeV! Cornelius Bennhold, George Washington University HYP2003, page 31

32 Another signal for a new P 13 around 1700? Cornelius Bennhold, George Washington University HYP2003, page 32

33 Missing N* region New Topic Cornelius Bennhold, George Washington University HYP2003, page 33

34 Before 2003: suggestion for a new resonance, D 13 (1900). No sign of any other states. Cornelius Bennhold, George Washington University HYP2003, page 34

35 Bump around 1900 MeV is also in the new data, but less pronounced SAPHIR data: talk by K.H. Glanders Cornelius Bennhold, George Washington University HYP2003, page 35

36 New resonances in γn ΚΛ in the region 1.75 < W < 2.1 GeV (preliminary) N* State Mass range (MeV) P D D D F Particle Data Group P 13 (1900)**? D D 13 (2080)**? D F 17 (1900)**? Cornelius Bennhold, George Washington University HYP2003, page 36

37 Comparison with C-R quark model in the region 1.75 < W < 2.1 GeV Quark model state PDG Γ ΚΛ our result [P 13 ] 2 (1870±50) missing small - [P 13 ] 3 (1910±50) P 13 (1900)** zero - [P 13 ] 4 (1950±100) missing large P 13 ( ) [P 13 ] 5 (2030±100) missing small - [D 13 ] 3 (1960±50) missing very large D 13 ( ) [D 13 ] 4 (2055±100) missing large D 13 ( ) [D 13 ] 5 (2095±100) D 13 (2080)** zero - [D 15 ] 2 (2080±50) missing large D 13 ( ) [D 15 ] 3 (2095±50) missing large [F 15 ] 2 (1980±50) missing zero - [F 15 ] 3 (1995±50) F 15 (2000)** zero - [F 17 ] 1 (2000±50) F 17 (1900)** zero F 17 ( ) Cornelius Bennhold, George Washington University HYP2003, page 37

38 High energy (Regge) region New Topic Cornelius Bennhold, George Washington University HYP2003, page 38

39 At high W, but low t: Regge trajectories γn ΚΛ 5 GeV 8 GeV 11 GeV 16 GeV Cornelius Bennhold, George Washington University HYP2003, page 39

40 How does Regge theory work in the N* region? Magnitude okay within factor 2 but no structure! How to transition from N* into Regge region?? Cornelius Bennhold, George Washington University HYP2003, page 40

41 Conclusions: New resonances in γn ΚΛ (preliminary) Four new resonances for γn ΚΛ, in addition to D 13 (1900) In comparison to Capstick-Roberts quark model: Only one N* with small or zero couplings to ΚΛ channel appears. Nine others do not appear. All of the N* with large couplings to ΚΛ channel appear. The D 13 (1900) with a very large coupling has already been seen in previous SAPHIR data. Are the missing N* finally appearing? Must follow up with: Must follow up with: Partial-wave analysis need polarization observables! Full coupled channels analysis (talk by A. Waluyo) Cornelius Bennhold, George Washington University HYP2003, page 41

Cornelius Bennhold George Washington University

Cornelius Bennhold George Washington University The past 7 years Low-lying baryon resonances Missing and exotic (hybrid) resonances How many N* do we need? How many do we have? Resonance form factors The