Cornelius Bennhold George Washington University

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1 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 next 7 years Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 1

2 Quantum Chromodynamics (QCD) fundamental theory of the strong interaction 1 µν µ LQCD = TrFµν F + q( γ Dµ + mq) q 2 21 N*: P11(1440) - K1,13(2700) 22 *: P33(1232) - K3,15(2950) 17 Λ* 21 Σ* 10 Ξ * 3 Ω * 6 charmed Λ *, Σ*, Ξ* 100 baryon resonances! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 2

3 Comparison with lattice QCD for low-lying states Nature of the Roper (P 11 (1440) 1/2 + )? P 11 (1440) 1/ Mass (GeV) S 11 (1535) 1/2 - P 11 (1440) 1/2 + N(938) 1/2 + m p = 180 MeV! N(938) 1/2 + Kentucky group, 2003 Roper (P 11 (1440) 1/2 + ) is a radial excitation? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 3

4 Can we understand the level ordering? Mass (GeV) S 11 (1535) 1/2 - P 11 (1440) 1/2 + N(938) 1/2 + Kentucky group, 2003 Cross-over occurs very close to chiral limit! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 4

5 What about Hyperons? The L (1405)? different story!! L(1600) 1/2 + Mass (GeV) L(1600) 1/2 + L(1405) 1/2 - L(1115) 1/2 + Baryon Mass (GeV) L(1115) 1/2 + L(1405) 1/2-0.5 Kentucky group, 2004 Behold the strange quark! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 5

6 Question: Why not just compare low-lying N* and Y* with lattice results and declare victory? Un-quench lattice calculations Compute N* and Y* widths What are the effective degrees of freedom in baryons? Constituent quarks? Interacting via Gluons, Bosons, Instantons? Di-quark cluster + quark? Collective excitations of string-like model? Chiral symmetry restoration in N* spectrum above 2 GeV? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 6

7 Where are the missing Resonances? New Topic Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 7

8 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 2004 Jlab User s Meeting: The Next 7 Years, page 8

9 True for all models based on three constituent quarks Quark model predictions Metsch and Petry quark model Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 9

10 How many N* do we have? How many N* do we need? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 10

11 Example: the P 33 partial wave P 33 (1232): Mass: 1232 MeV Width: 110 MeV A 1/2 = -140 ± 10 A 3/2 = -255 ± 12 P 33 (1600): Mass: MeV Width: MeV A 1/2 = A 3/2 = P 33 (1920): Mass: MeV? Width: MeV? Existence controversial! gn fi p N multipole Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 11

12 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), F 15 (1680) Clear resonance signal, Mass known to within a few %. A 1/2, Γ total, partial widths fairly well known Exceptions: S 31 (1620), P 13 (1720), 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 2004 Jlab User s Meeting: The Next 7 Years, page 12

13 Nucleon flux-tube hybrids: Hybrids: Even more missing states!!! SCapstick and P. Page, PRD60 (1999) Pentaquarks, anyone? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 13

14 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 2004 Jlab User s Meeting: The Next 7 Years, page 14

15 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), F 15 (1680) Clear resonance signal, Mass known to within a few %. A 1/2, Γ total, partial widths fairly well known Exceptions: S 31 (1620), P 13 (1720), 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? At least 4-5 N* for selected partial waves! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 15

16 How do we find the resonances? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 16

17 N* spectral lines don t quite look like this: but more like this: s (mb) Nucleon resonances are broad and overlapping Eγ (MeV) Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 17

18 How does a partial-wave amplitude behave at E = E res? 40 γn π N multipole Im M 1+ = max M1+ (3/2) (10-3 /m π ) 20 0 Re M 1+ = 0 Tl (E) ~ ~ Γ/2 (E-ER ) - iγ/2 Γ/2 (E-E R ) 2 + (Γ /2) 2 ReT l w L (MeV) ((E-E R ) + iγ /2) W = 1232 MeV ImT l But: Single resonance, elastic, no background! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 18

19 If only all resonances could behave that way then finding N* would be easy! Step 1: Measure all observables for all channels at all energies and all angles! Step 2: Perform the perfect partial wave analysis Step 3: Extract resonance properties Done! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 19

20 But: P 31 - Where is the ground state? MeV? 1750 MeV? 1750? 1910? - Recalculate with overlapping fermions close to chiral limit D. Leinweber et al. Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 20

21 The theorist s way to finding N*s Step 1: Measure all observables for all channels at all energies and all angles! Step 2: Perform perfect partial wave analysis Step 3: Construct dynamical model with baryons and mesons Step 4: Fit model parameters to extracted partial waves Step 5: Separate background from resonance contributions Step 6: Extract resonance properties and done? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 21

22 We cannot directly compare experiment to QCD therefore, we must use an intermediary : QCD Lattice, Quark models, M N*, Γ pn, A 1/2 Dynamical Models: mesons + Baryons Multipoles Phase shifts Experiments: gnfi pn, ppn hn, KL, pnfi pn, ppn hn, KL, Theoretical challenge: Resolution of broad, overlapping resonances in a strongly-coupled, multi-channel system Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 22

23 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, π π = + π K Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 23

24 What channels? Depends on W For W 2 GeV and Strangeness S=0: Two-body: πn, γn, ηn, ω N, ΚΛ, Κ Σ Three-body: ππn, πηn, πκλ, πκσ Quasi 2-body: π ρn σn η πs 11 Κ Λ Κ Σ π Ν What about 4-body: π π π N ρ? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 24

25 Coupled-channels picture of resonance excitation Missing N*: pn p D gn fi N* fi rn hn KL T πν πν T ην πν T γν πν T ρν πν T σν πν T ΚΛ πν T ΚΣ πν T πν ην T ην ην T γν >ην T ρν ην T σν ην T ΚΛ ην T ΚΣ ην T= 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 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 Find the same N* in different reaction channels! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 25

26 What have we found in the past 7 years? New Topic Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 26

27 Back to 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 2004 Jlab User s Meeting: The Next 7 Years, page 27

28 The P 13 partial wave: N(1720)*** and N( 1900)** - No clean 1 st tier N* in this partial wave! - Broad resonance signals on large background - Very inelastic pn fi pn partial wave gn fi pn multipole Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 28

29 γp π 0 p Graal data New SAID analysis shows larger P 13 signal Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 29

30 look at gn fi ppn New Topic Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 30

31 Another signal for a new P 13 around 1700? 1900 Too low for quark model? 1720 Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 31

32 Caution: from coupled channels to single channel: Scattering amplitude: M = V + V G 0 T T πν πν T ην πν T γν πν T ρν πν T σν πν T ΚΛ πν T ΚΣ πν T πν ην T ην ην T γν >ην T ρν ην T σν ην T ΚΛ ην T ΚΣ ην T= T πν γν T ην γν T γν γν T ρν γν T σν γν T ΚΛ γν T ΚΣ >γν T gn T πν ρν T ην ρν T gnfi γν ρν rn 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 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 2004 Jlab User s Meeting: The Next 7 Years, page 32

33 Resonances in g p fi p p + p -? g p??? fi D ++ p - RPI 2003 RPI 2003 Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 33

34 Quark model Capstick et.al. Dominant decay for P 13 (1720) state: πn, ηn, but not % ρn! Cannot use predictions as guidance! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 34

35 γp π 0 π 0 p W 1700MeV 2-pion production N* around 1700 MeV D 13 (1700) D 33 (1700) P 11 (1710) P 13 (1720) πn πn D 13 πn π DS 13 W (GeV) W (GeV) Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 35

36 looking in places: gn fi KL(S) New Topic Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 36

37 Threshold Region: S 11 (1650), P 11 (1710), P 13 (1720) What does the quark model predict? (Capstick, Roberts) 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 gpfik + L Onset of p- wave New results (prelim): S 11 (1650) MeV P 11 (1710) 1650 or 1730 MeV possibly 2 different N*? P 13 (1720) but total width is MeV! Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 37

38 looking at gn fi w N New Topic Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 38

39 Resonance Contributions to γ*p pω? g w above resonance region σ p p g p N * p w in resonance region -1 cos θ ω +1 Difficult to disentangle N* in differential cross section, but Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 39

40 γ p ωp t-channel exchange only without P 13 (1720) including P 13 (1720) Quark model calculations by Zhao, Li, C.B. Clear evidence for P 13 strength in γp ωp, possibly several N* Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 40

41 Let s summarize: N* in partial wave P 13 For the established states P 13 (1720), P 13 (1900) : Better visible in γ N π N multipoles P 13 (1720) seen in γn ρn partial wave? Evidence for new states: Narrow state seen in γ N ππn? In γp Κ + Λ? Possibly several states in γn ωn? Similar arguments can be made for a 3 rd state in the S 11 and D 13 partial waves Are missing N* finally appearing? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 41

42 The next 7 years New Topic Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 42

43 Baryon Resonance Widths quark flavor up, down strange charm bottom n(udu) G~200 MeV L(uds) G~30 MeV L c (udc) G~3 MeV L b (udb) E (MeV) Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 43

44 Until now, N* production in intermediate states: N*, * N* πn ηn KΛ ΚΣ At higher W, produce N*,Y* in final states: K + Y* Note: no electromagnetic form factors or helicity amplitudes! Observe number of states and their strong decays Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 44

45 Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 45

46 K + K + How about Ξ* spectroscopy? M a sgs ) e V Lots and lots of missing states X* Ξ * /2 + 3/2 + 5/2 + 7/2 + 1/2-3/2-5/2 - Capstick and Isgur, PRD, 1986 Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 46

47 Conclusions:What do we want? We don t want to study 500 N* on the lattice! Study a few low-lying states in great detail P 33 (1232), D 13 (1520), S 11 (1535) Masses, branching fractions, el.magn. form factors Study a few partial waves in great detail: S 11, P 11, P 13, D 13, Find all Resonances: Anyone missing? Exotic Resonances: Hybids and pentaquarks? Cornelius Bennhold, George Washington University 2004 Jlab User s Meeting: The Next 7 Years, page 47