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
What do we want? New Topic Cornelius Bennhold, George Washington University HYP2003, page 2
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 2 010001-56 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 *
Comparison with lattice results What is the nature of the Roper (P 11 (1440) 1/2 + ) resonance? Mass (GeV) 2.5 2.0 1.5 1.0 0.5 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 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. Lee et al., 2003 Cross over occurs very close to chiral limit! Cornelius Bennhold, George Washington University HYP2003, page 6
What about Hyperons? The Λ(1405)? 2.5 Λ(1600) 1/2 + Mass (GeV) 2.0 1.5 1.0 0.5 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
How do we find the resonances? New Topic Cornelius Bennhold, George Washington University HYP2003, page 8
N* spectral lines don t quite look like this: but more like this: 70 60 σ (µb) 50 40 30 Nucleon resonances are broad and overlapping! 20 10 0 200 400 600 800 1000 1200 1400 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 1.5 2 Intermediate W High W W (GeV) Cornelius Bennhold, George Washington University HYP2003, page 10
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
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
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) ~ ~ -20 100 200 300 400 500 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
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
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
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
What are missing Resonances? New Topic Cornelius Bennhold, George Washington University HYP2003, page 17
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 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
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
Nucleon flux-tube hybrids: SCapstick and P. Page, PRD60 (1999) 111501 Even more missing states!!! Cornelius Bennhold, George Washington University HYP2003, page 21
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* 1900 1720 Cornelius Bennhold, George Washington University HYP2003, page 22
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
looking in places: γn ΚΛ(Σ) New Topic Cornelius Bennhold, George Washington University HYP2003, page 24
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
Background: tree level with SU(3) couplings Hadronic form factors: Vertex F(s,t,u) Meson Baryon Baryon 40 20 0 resonance background -20 100 200 300 400 500 ω(mev) Cornelius Bennhold, George Washington University HYP2003, page 26
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 30-40 parameters χ 2 1.1 Cornelius Bennhold, George Washington University HYP2003, page 27
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 2.4 GeV): G 17 (2190), γn ΚΛ σtotal S 11 (1650), P 11 (1710), P 13 (1720) Missing N* Region High-spin N* and Regge 1.61 1.75 2.1 W (GeV) Threshold Intermediate W High W Cornelius Bennhold, George Washington University HYP2003, page 29
Threshold Region New Topic Cornelius Bennhold, George Washington University HYP2003, page 30
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) 1610 1650 MeV P 11 (1710) P (1720) 1650 or 1730 MeV possibly 2 different N*? 1660 1720 but total width is 40-70 MeV! Cornelius Bennhold, George Washington University HYP2003, page 31
Another signal for a new P 13 around 1700? Cornelius Bennhold, George Washington University HYP2003, page 32
Missing N* region New Topic Cornelius Bennhold, George Washington University HYP2003, page 33
Before 2003: suggestion for a new resonance, D 13 (1900). No sign of any other states. Cornelius Bennhold, George Washington University HYP2003, page 34
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
New resonances in γn ΚΛ in the region 1.75 < W < 2.1 GeV (preliminary) N* State Mass range (MeV) P 13 1880 1930 D 13 1820 1880 D 13 2000 2080 D 15 1970 2030 F 17 1890 1950 Particle Data Group P 13 (1900)**? D 13 --- D 13 (2080)**? D 15 --- F 17 (1900)**? Cornelius Bennhold, George Washington University HYP2003, page 36
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 (1880-1930) [P 13 ] 5 (2030±100) missing small - [D 13 ] 3 (1960±50) missing very large D 13 (1820-1880) [D 13 ] 4 (2055±100) missing large D 13 (2000-2080) [D 13 ] 5 (2095±100) D 13 (2080)** zero - [D 15 ] 2 (2080±50) missing large D 13 (1970-2030) [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 (1890-1950) Cornelius Bennhold, George Washington University HYP2003, page 37
High energy (Regge) region New Topic Cornelius Bennhold, George Washington University HYP2003, page 38
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
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
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