Nucleon Resonances in the Quark Model

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(No Transcript)
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NSTAR 2007 Summary

• Experiment/analysis
• Facilities/new results
• Upcoming developments
• Theory
• Baryons
• Dynamics of reactions involving baryons

3
BRAG pre-meeting

• L. Tiator, A. Svarc problem relating
  experimental results to theoretical predictions
• Partial wave analysis and amplitude analysis give
  reliable results for dressed scattering matrix
  singularities
• Quark model calculations give information on bare
  resonant quantities
• Does not apply to those states seen in chiral
  unitary modelssee talks by A. Ramos, E. Oset,
  A. Martinez Torres, and M. Doering at this
  meeting
• Dressing (un-quenching) the quark model is tough,
  but solvable in principle
• See talks by E. Santopinto, R. Bijker, and B.
  Pasquini at this meeting S.C. and M. Giannini in
  BRAG pre-meeting
• Undressing dressed scattering matrix
  singularities in coupled-channel models is in
  principle a model-dependent procedure because of
  presence of model-dependent hadronic mass shifts
• From unmeasurability of off-shell effects
  accompanying any dressing procedure.
• BRAG pre-meeting talks by Ch. Hanhart, S.
  Scherer, J. Gegelia

4
BRAG pre-meeting

• Conclusions
• (1) Bare quantities in coupled-channel models are
  legitimate quantities to be extracted
• Only within a framework of a well defined model
• To interpret, keep track of the existence of the
  hadronic mass shifts produced by
  off-shell-ambiguities
• (2) Dressed scattering matrix singularities are
  best meeting point between quark model
  predictions and experiments
• Recommendation put a lot of effort into defining
  and thoroughly checking the pole extraction
  procedures
• starting either from energy dependent partial
  waves or from partial wave data directly

5
Experimental programs for N

• Common developments
• Precision data on host of final states
• Emphasis on ?N, ?N, 2?N, ??N, K?, K?,
• Polarization (beam, target, double planned or
  underway)
• Aim is to measure as many observables as possible
  for a subset of these reactions (complete
  experiments)
• Reduce (not eliminate) model dependence of
  analysis
• Challenge for models to fit polarization
  observables
• Strong sensitivity to resonance properties
• This is how physics progresses!

6
CLAS_at_Jefferson Lab
Expt.

• V. Burkert CLAS collaboration
• Major focus is N physics
• the search for new baryon states and
  determination of baryon resonance properties
• resonance transition form factors
• Nucleon spin structure in the transition region
• polarized proton structure function g1(x,Q2)
• Bjorken Sum ?1p-n(Q2)
• Deeply exclusive processes and generalized parton
  distributions (GPDs)
• DVCS/Bethe-Heitler beam spin asymmetry sensitive
  to H

7
CLAS_at_Jefferson Lab
Expt.

• Search for new baryon states
• Aim for complete or nearly complete
  measurements
• ?p?pN, ?N, KY and ?n?pN, K0Y
• Combinations of beam, target (new FROST target),
  and recoil polarizations
• differential cross sections with unpolarized,
  circularly polarized, and linearly polarized
  photon beams
• recoil polarizations for hyperons
• longitudinally or transversely polarized proton
  and neutron (deuteron) targets
• Other reactions
• ?p ? ?N, ?p, ppN
• linearly polarized beams, polarized beam and
  polarized targets

8
CLAS_at_Jefferson Lab
Expt.

• R. Schumacher polarization transfer in K?
  photo and electro-production
• Polarized beam, ? (recoil) polarization through
  its weak decay asymmetry
• New GRAAL results for recoil polarization P agree
  with CLAS results
• Large polarization transfer Cz along circularly
  polarized photon beam direction
• Find P2 Cx2 Cz2 ' 1
• Models did not predict this
• Bonn, Giessen, Gatchina (Sarantsev, Nikonov,
  Anisovich, Klempt, Thoma ) fit with additional
  resonance P13(1860)
• See talks by A. Sarantsev, V. Nikonov this
  meeting
• Beam asymmetry ? featureless (GRAAL, LEPS)

9
CLAS_at_Jefferson Lab
Expt.
10
CLAS_at_Jefferson Lab
Expt.
11
CLAS_at_Jefferson Lab
Expt.

• V. Burkert, V. Mokeev
• Q2 dependence of EM transition form factors (0-6
  GeV2) using CLAS_at_Jefferson Lab
• Probes evolution of relevant degrees of freedom
  in baryons
• e-N ! ? ! N?
• Dominant M1 contains non-resonant effects
  involving ?, at level of 30
• Ratios of electric and scalar (quadrupole)
  multipoles to M1 measured to 0.5-2 over entire
  range of Q2
• Do not tend to pQCD limits
• e-N ! N½(1440) ! N?, N??
• Changes sign at Q2 0.5 GeV2 (seen in
  relativistic models based on light-cone dynamics)
• Consistent results using different analysis
  methods, different final states

12
Electron scattering labs
Expt.
Np, ppp-
np
DR
UIM
pp0
np
pp0

• CLAS_at_Jefferson Lab

13
Electron scattering labs
Expt.
D13(1520)
P11(1440)
from analysis of 1p CLAS data
from analysis of CLAS 2p data within the
framework of JM06
combined analysis of 1p/2p CLAS data
14
Electron scattering labs
Expt.

• N3/2-(1520)D13

A3/2
Previous pp0 based data
preliminary
preliminary
A1/2
Q2, GeV2
Q2, GeV2
15
CLAS_at_Jefferson Lab
Expt.

• Cascade (?0 ssu, ?- ssd) baryon program
• Advantage that low-lying states are likely narrow
• ?p?gtKK?-
  ?p?gtp-KK?0

16
BaBar
Expt.

• Veronique Ziegler ee- annihilation at BaBar
  (results preliminary, under BaBar internal
  review)
• Study ?0(1530) in ?c ! (?-?) K
• Indication is J3/2 (confirms decuplet
  expectation)
• Study ?0(1690) in ?c ! (LK 0) K
• Preferred spin is J1/2, some indication of
  negative parity
• If negative parity, not Roper equivalent as some
  of us (!) thought
• Much too light for quark model expectations of
  L1 excited states N 2(ms-mu,d) !
• Calculable on the lattice (D. Richards)

17
Crystal Barrel/TAPS_at_ELSA
Expt.

• H. Schmieden Physics at ELSA
• Photoproduction of baryon resonances
• ELSA
• photon beam energy (to 2.5 GeV)
• Linear and circular polarization
• CB/TAPS
• provides 4? detection
• Best for neutral final states (missing mass for
  a charged particle) through their photon decays

18
Crystal Barrel/TAPS_at_ELSA
Expt.

• Goal complete experiments on ? and ?
  photoproduction
• Analysis simplified because only make N (no D)
• Recent results
• Unpolarized photoproduction of ?
• Differential cross sections
• From ?? and 3?0! 6? decays of ?
• Linearly polarized photoproduction of ? (D.
  Elsner talk)

19
Crystal Barrel/TAPS_at_ELSA
Expt.

• D. Elsner linearly polarized photoproduction of
  ?
• Targetpolarization ?
• Consistent withGRAAL results

20
Crystal Barrel/TAPS_at_ELSA
Expt.

• Photoproduction of ? off deuteron

21
Crystal Barrel/TAPS_at_ELSA
Expt.

• Data analysed to d?/d?
• 
  Bonn-Gatchina PWA
  see P11(1840)
• Polarization asymmetries R, ?

22
Crystal Barrel/TAPS_at_ELSA
Expt.

• Talk by E. Gutz polarization asymmetry ? in
• Bonn-Gatchina PWA ?(1940)D33

23
Crystal Barrel/TAPS_at_ELSA
Expt.

• Polarized photoproduction of ?
• Penner et al. and Shkylar (Giessen) analyses
  disagree

24
ANKE, TOF_at_COSY
Expt.

• W. Schroeder
• ANKE can see Y states up to 1540 MeV, TOF is
  best for threshold region
• pp! pKY0! pK? X
• Select events where X- ?-, plot vs. MM(pK)
• Effect in X-?at 1480 MeV,?60 MeV
• Also in X?-

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ANKE, TOF_at_COSY
Expt.

• ANKE line shape of ?(1405)
• Not Breit-Wigner, see talk by E. Oset this meeting

L.S. Geng, E. Oset, arXiv 0707.3343
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ANKE, TOF_at_COSY
Expt.

• TOF
• See no ? pentaquark in pp! (pK0)? or in
  (pK0)??
• Need polarized beam, target and detector
  improvements to continue program of examining N!
  YK in 1.6-1.9 GeV region
• New detector WASA (? and neutrals) will allow
  study of excited hyperons
• pp! pK?(1405)! pK?0?0! pK(??)?0

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Crystal Ball/TAPS_at_MAMI
Expt.

• M. Kotulla
• Determination of magnetic moment of ?(1232)
• Use ? p! ?0 ?0 p

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Crystal Ball/TAPS_at_MAMI
Expt.

• Analysis effort underway
• Pascalutsa and Vanderhaeghen, chiral effective
  theory (good to E? 100 MeV)
• Sensitivity 0.2 ?N

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BESII_at_IHEP
Expt.

• W. Li light hadron spectroscopy in J/? decays
• New states
• ?, ? (masses and widths determined)
• X(1835) in J/?? ??????
• X(1580) in J/?? KK?
• Enhancement in J/?? ???
• ?(1760) in J/?? ???
• N observed in
• J/?? pn?? J/?? pp?0 J/?? nKS? Compared with
  ?(2S) decay
• Some N, e.g. N(1535), N(2065) better measured
• Some branching fractions involving baryons are
  measured
• Analysis of existing data ongoing
• BEPCII/BESIII should collect data in 2008

30
LNS_at_Sendai
Expt.

• H. Shimizu observation of N(1670)
• Have 300 MeV e- linac coupled to a 1 GeV
  synchroton
• Use ?d ! ?X
• Also ?p ! ?X to subtract proton contribution
• Use ?-MAID analysis to understand ?p ! ?p
• Interpret as new S11 at 1670 MeV, width below 50
  MeV, strong in ?n ! ?n
• Not seen in proton channel
• Could this be an antidecuplet pentaquark?

31
LEGS_at_BNL
Expt.

• A. Sandorfi Physics at LEGS
• LEGS-Spin collaboration
• LEGS 2.8 GeV e- beam, backscattered laser beam,
  maximum photon energy 430 MeV
• High circular polarization
• HD frozen spin
• Hydrogen polarized or D polarized or both
• Mostly HD and a little H2 and D2 which feed HD
  polarized state (then decay away themselves, so
  HD spin frozen)
• Spin relaxation times 1 year
• Can transfer polarization from H to D
• Polarized photon HD double-polarization physics
• Measure various polarization asymmetries in
  inclusive and exclusive ? HD ! ? X reactions on
  neutron
• Use Lee Sato Matsuyama ? N! ? N amplitudes and
  fold into D structure

32
LEGS_at_BNL
Expt.

• Analysis
• Not a free neutron! Only half of the events are
  quasi-free
• Analysis of data on-going separate ? using
  momentum analysis
• Targets and some of staff migrating from BNL to
  JLab
• E06-101 ?(pol) HD ! K0?(pol), K0?(pol), i.e. ?n
• Electron experiments on transversely polarized
  target
• GPDs, N form factors, Collins/Sivers functions

33
MAMI_at_Mainz
Expt.

• A. Thomas Physics at MAMI
• Virtual and real photons, linear and circular
  polarization
• Three detectors Kaos,,Crystal Ball/TAPS
• MAMI
• Harmonic double-sided microtron (electron
  accelerator)
• four bending magnets and two linacs
• Energy 0.855-1.5 GeV
• Tagged photon and electron scattering experiments
• Experiments
• Target asymmetry puzzle in ? and ?0 production
  off proton
• Isobar models and Giessen models fail to describe
• Electroproduction of ? at low Q2
• Cross section and recoil polarization
• Single and double pion production
• Helicity asymmetry in double-pion production
• Discrepancies with models

34
MAMI_at_Mainz
Expt.

• Physics at MAMI
• ?, ?0 physics
• ? mass, rare ? decays (C,CP violation)
• Quark mass different mu-md in ? ! 3?0
• ?0 ! ??0?0 decays
• GDH experiment _at_ MAMI-B with DAPHNE detector
  (charged particle tracking)
• Polarized butanol target with high deuteron
  polarization
• MAMI/ELSA GDH sum rule ?3/2-?1/2
• Verified at 10 level
• Also in exclusive reactions, important for PWAs
• Have for ? production
• Photoproduction of p??-
• Helicity-dependent invariant mass distributions
• The future
• Frozen spin target for Crystal Ballbuilt this
  year
• Recoil polarization of proton
• Kaoskaon electroproduction

35
Theory developments

• Both lattice QCD and quark model calculations
  must face reality of light quark pairs
• Un-quenching either is hard work
• Requires calculation of couplings to continuum
  states
• Coupled-channel analyses are becoming
  increasingly sophisticated
• Need to preserve unitarity, gauge invariance, and
  analytic structure, but remain manageable

36
Lattice QCD
Theory

• The nucleon and baryon resonances on the lattice
  C. Gattringer (Graz-Regensburg), D. Richards
  (LHPC collaboration), A. Rusetsky
• Recent important developments
• Basic quantities are Euclidean two and
  three-point functions
• Time dependence of two-point functions gives
  masses
• Matrix elements in three-point functions give
  properties
• Extraction of excited state masses using
  carefully chosen basis of interpolators Oi
• Use these to construct a matrix of correlators
• Solve eigenvalue problem to get accurate signal
  for mass of excited states

37
Lattice QCD
Theory

• Eigenvalues ??(t) vs. Euclidean time

38
Lattice QCD
Theory

• Recent important developments
• Hadron interpolators distributed over spatial
  lattice points
• LHPC collaboration, Graz-Regensburg
• classify into irreducible representations of
  lattice rotation group
• Allows nodes in radial wave function
• Can avoid chiral extrapolations by using chiral
  perturbation theory in a finite volume
  (small-scale expansion) See talk by A. Rusetsky,
  this meeting
• Luscher formalism developed for ?N scattering
• Use statistical method to extract resonance mass
  and width from lattice results
• Demonstrated for ?(1232) mass and width

39
Lattice QCD
Theory

• Spatially distributed interpolators
• Much better overlap with excited states

40
Lattice QCD
Theory

• Baryon spectrum, quenched calculations

41
Lattice QCD
Theory
42
Lattice QCD
Theory

• Proton structure from three-point functions,
  chiral extrapolation to physical pion masses
• Different treatment of valence and sea quarks
  allows first look at chiral regime (un-quenched)
• Isovector charge form factor (p-n)
• Isovector charge radius
• Axial charge gA
• Moments of quark momentum fraction hxiu-d and
  helicity fraction hxi?u -?d
• Study of GPDs
• Calculation of quark orbital angular momentum
• Nucleon transverse size

43
Lattice QCD
Theory

• Lu and Ld substantial, total small

44
Lattice QCD
Theory

• Un-quenched calculations in development
• Need clean separation of scattering states once
  decays possible
• Use different volume dependence of masses of
  resonances and continuum states, large lattices
• Working on evaluating transition matrix elements
  (decay constants) for resonances
• Need contribution of disconnected diagrams
  (loops, gluons) to hadron structure
• Currently sensitive to statistical fluctuations

45
Models
Theory

• B. Borasoy chiral corrections to the Roper
  resonance mass
• Lighter than its parity partner S11(1535)
• 30-40 branch into N??
• Parity order not settled in lattice QCD
• Need reliable chiral extrapolation techniques
• Use effective Lagrangian (N, Roper, ?), calculate
  mR(m?2) to full 1-loop order (no explicit ?p)
• Have R? coupling gA ' 1.26, RN? coupling
  (0.3-0.4), 4 chiral parameters
• Infrared regularization scheme extended to one
  light scale (m?) and two heavy (MN2 ltlt MR2)
• No strong m? dependence near physical point

46
Models
Theory

• Constituent Quark Model E. Santopinto, R.
  Bijker
• See also talk by Qiang Zhao, this meeting, on
  selection rules and quark correlations in the N
  spectrum
• See also talk by A. Buchmann, this meeting, on
  calculation of higher (octupole) moments of
  baryons in pion-cloud quark model
• Tackle difficult problem of inclusion of next
  Fock space component in quark model
• Use large baryon-meson basis to expand qqq
  qq(bar)
• Flux-tube breaking model gives overlap between
  qqq and qqq qq(bar)
• Checked that calculation returns usual CQM in
  closure limit
• Evaluate flavor asymmetry of nucleon sea

47
Models
Theory

• Results significant difference from naïve
  nonrelativistic CQM results and relativistic CQM
  results
• Closer to experiment and lattice QCD

?u 1.00 ?uexp 0.82(5) ?uLQCD
0.79(11) ?uNRM 4/3 ?uRQM 1.01 ?d
-0.43 ?dexp -0.44(5) ?dLQCD -0.42(11)
?dNRM -1/3 ?dRQM -0.251 ?s -0.06
?sexp -0.10(5) ?sLQCD -0.12(11) ?sNRM
0 ?sRQM 0

48
Models
Theory

• B. Metsch Covariant constituent quark model
• Based on instantaneous approximation to
  Bether-Salpeter equation
• Relativistic form of confining potential, chosen
  to minimize spin-orbit effects
• Instanton-based spin-spin interaction between
  quarks
• Model parameters fit to spectrum
• Calculate a host of other properties
• Magnetic moments and charge radii
• Including magnetic moments of excited states
• Resonance photocouplings and semi-leptonic decays
• Strong two-body decay amplitudes
• Verifies pattern of decoupling of states not seen
  in analyses

49
Models
Theory

• B. Metsch Covariant constituent quark model
• Provides useful background against which to
  search for unconventional states
• Roper resonance EM couplings anomalous
• Everything (mass, EM and strong couplings) about
  the ?(1405) is anomalous
• Hard to understand why the second band of
  negative parity ? states D35 and its partners
  can be as low as 1900 MeV

50
Models
Theory

• Chiral Unitary Approach A. Ramos, E. Oset
• KN I0 JP1/2- (S01) scattering state ?(1405) is
  27 MeV below threshold
• Looks like quasi-bound state
• Use chiral meson-baryon Lagrangian to generate an
  S-wave potential
• Need KN, ??, ??, and K? channels to fit decay
  branching ratios of this and nearby states
• Get two poles in T matrix approaching 1400 MeV
  when break SU(3)f gradually
• Explains why properties of ?(1405) depend on
  channel in which it is observed

51
Models
Theory

• ?(1405) in chiral unitary approach pole
  positions move as break SU(3)f gradually

52
Models
Theory

• ?-p! K0??N mass 1385 ? 50 MeV
• K-p! ?0?0?0 mass 1420 ? 38 MeV
• Other baryons in the chiral unitary approach
• JP1/2- N(1535), ?(1620), ?(1690)
• JP3/2- ?(1700), ?(1520), ?(1670), ?(1820)
• From baryon decuplet interacting with meson 0-
  octet
• ?(1620) bump seen at Jefferson Lab in ?p!
  ?-KK-(??)
• Width is larger than width of ?? invariant mass
  distribution (near threshold)
• No claim for this state made in JLab
  experimental paperV. Burkert

53
Models
Theory

• Chiral Unitary Approaches A. Ramos
• Heavy flavored baryons udc ?c(2593)
• DN s-wave molecule
• Predicts another ?c(2800), similar to
  experimental state
• Interaction of charmed mesons in hadronic medium
  DD-
• Important for explaining J/? suppression in
  heavy-ion collisions
• Related to nucleon-antinucleon interactions

54
Models
Theory

• Chiral Unitary Approaches E. Oset
• ?(1405) is an interesting state
• See two poles in many models, one couples
  strongly to ??, the other to KN
• Experimental tests of ?(1405) structure
• K-p ! ??(1405)
• K-p ! ?0?(1405)
• Radiative decay of two ?(1405) states
• Different shapes and rates for two states
  depending on reaction used
• K-p! ?0??, ?0??0
• pp ! Kp?(1405) measured by ANKE_at_COSY
• Fit with kaon, pion and rho exchange diagrams

55
Models
Theory

• Excited baryons in 1/Nc expansion C. Schat
• How do we match quark models to 1/N_c?
• Useful perturbative expansion
• Baryons fall into irreducible representations in
  large N_c limit
• N_c counting rules
• Quark operator expansion Hmass? ciOi and fit
  constants to baryon masses
• Detailed calculations for L1 baryons
• To leading order write down all operators with
  correct properties
• Have explicit flavor dependence (different from
  OGE)
• Fit to 5 N1 excited states degenerate S11/D13
  D13/D15 pairs in large Nc limit
• Orderings of singlet and two doublets not
  specified by 1/Nc

56
Models
Theory

• Excited baryons in 1/Nc expansion
• Extend using 1/Nc corrections and SU(3)f
• ?(1405) and ?(1520) split by spin-orbit operator
• What order is spin-orbit interaction?
• Is core - exited quark separation necessary?
• How match to quark model?
• Consider
• One gluon exchange (general spatial dependence)
• OPE (now explicit flavor dependence)

57
Models
Theory

• Shows using exchange symmetry that can calculate
  orbitally excited states using CCGL states
• Expression for most general OGE and OPE mass
  operators (different)
• Constants written to leading order in overlap
  integrals
• Match forms to general form in 1/Nc
• OGE has c30 but fits in literature show not zero
• Conclusion
• SN analysis shows core and excited core basis
  necessary
• Matching to quark models reproduces 1/Nc operator
  expansion
• Spin orbit is leading order, partial cancellation
  between LS coming from OGE and OPE flavor
  dependent interactions
• Matching method very general

58
SAID/MAID analyses
Expt.

• B. Briscoe, George Washington University Data
  Analysis Center (SAID) L. Tiator, S. Kamalov
  Mainz (MAID)
• Maintain important database for most reactions
  including N
• On-line analysis tools important for single and
  coupled-channel analysis of data
• New analysis of ?N! ?N, photo and
  electro-production of p0n, ?p by GWDAC
• 4-channel K-matrix ?N, ?N, ??, ?N up to 2.5 GeV
• CLAS, CB-ELSA and GRAAL data
• A1/2 from Np analysis for S11(1535) now agrees
  with N? results
• Agrees with previous result from
  electro-production
• P13(1720) has large Ap1/2
• consistent with earlier analysis of ppp- in low
  Q2 electro-couplings

59
Coupled-channel analysis
Theory

• A. Sibirtsev Resonances in hadron-induced
  interactions
• See also talk by S. Krewald, this meeting, for a
  description of the Juelich coupled-channels
  approach to resonance analysis
• Need to match to Regge theory (pQCD) at very high
  energy
• Matches down to 3 GeV, PWA stops at 2.4 GeV
• Evidence of resonances in 2.43 GeV region?
• Through optical theorem find forward-pion
  charge-exchange indicates structures up to 3 or 4
  GeV
• Also ?-p! ?0n data show traces of high-mass
  baryons
• Dont neglect single-pion photoproduction for
  high mass Ns (dont stop calculating in models
  at 2 GeV)

60
Coupled-channel analysis
Theory

• Giessen V. Shklyar (G. Penner, U. Mosel, H.
  Lenske)
• Data on
• Unitarity optical theorem relates forward part
  of elastic scattering T matrix to inelastic c.s.
  to various channels (NEXT SLIDE)
• NOT UNRELATED!
• Solve D-S eqn in ladder approximation
• V has s, u and t-channel diagrams (matrix in
  channel space)
• Use effective Lagrangian approach (relativistic)
• Solve Bethe-Salpeter equation by putting
  intermediate particles on mass shell
• Allows PW decomposition, equations become
  algebraic
• Compare to SAID analysis PWs
• Works well for ?N but misses some PWs in ?N
• Focus on ?p! ?p (and on neutron)

61
?N, ?N total cross sections
62
Coupled-channel analysis
Theory

• ?p! ?p (and on neutron)
• S11(1535) properties not well known, complicates
  analysis in this region
• Ratio of helicity amplitudes in ?N! ?N differs
  from ! ?N
• Fit GRAAL beam asymmetry ? data well, target
  asymmetry not so well
• Fit d?/d? for ?p ! ?p well, with S11(1650) giving
  structure at 1670 MeV
• No need for new resonance in ?N
• Destructive interference effect in ?-N! ?N from
  S11(1650) and P11(1710) at higher mass explains
  bump

63
Coupled-channel analysis
Theory

• Giessen V. Shklyar
• Narrow bump in differential c.s. ?n at 1670, is
  this a new state?
• GRAAL also see this bump (see talk by V.
  Kuznetzov)
• Non-strange partner of ? ?
• Exotic state?
• Could S11(1650) and P11(1710) explain this effect
  at 1670 MeV?
• Look at all reactions simultaneously to make sure
  have treated these resonances properly
• Can fit with existing resonances, what price do
  you pay?
• Need larger neutron photocoupling for S11
• S11(1650) properties agree with PDG P11(1710) is
  not as well known as implies!
• Change slightly size of 1650 An1/2, up comes bump
  in ? for ?n! ?n SHOW GRAPH
• Shape of differential c.s. not changed
• Cannot rule out narrow P11(1675), data not yet
  good enough
• Be careful about Fermi motion in neutron state
• Beam asymmetry ? may help

64
Coupled-channel analysis
Theory

• MAID analysis S. Kamalov (D. Drechsel, L.
  Tiator, S.N. Yang)
• MAID 2007, recent results for pion photo and
  electroproduction
• Two-step process
• Extract partial waves
• Model dependence because of lack of data
• Extract resonance parameters from partial waves
• Background and resonance T matrices
• Background contains pion loop SHOW DIAGRAMS
  defined by K-matrix theory from background
  T-matrix
• Resonances dressed by pi N rescattering
• Phase put into resonance piece to allow unitarity
  (Watsons theorem)

65
Coupled-channel analysis
Theory

• MAID analysis S. Kamalov
• Pion/photoproduction data set now includes
  GWU/SAID, Mainz, Bonn, GRAAL, LEGS
• Results
• S11(1535) photocouplings differ from SAID by a
  factor of 2, smaller than PDG
• P13(1720) shows up here, not in SAID
• See bump in P11 partial wave
• Fit an additional P11 at 1700 MeV, ?30 MeV
• Electroproduction
• Better data has improved situation

66
Coupled-channel analysis
Theory

• MAID analysis S. Kamalov
• ? electroproduction
• A. Buchmann has parameterized E/M, S/M, and MAID
  fit to this form
• RSM(Q2) related to neutron EM form factors
• Quite different S1/M1 than CLAS analysis
• Q2 dependence of A1/2 and A3/2 for first
  resonances in P11, S11, D13, and F15
• Helicity asymmetry changes sign in case of F15
  also

67
Coupled-channel analysis
Theory

• Bonn/Gatchina analysis A. Sarantsev
• Need polarization to sort out photoproduction
• Technique
• Relativistically invariant
• Simultaneously analysis single and multiple-meson
  production
• Specify energy dependence due to unitarity and
  analyticity
• Unitarize using K-matrix approach, has poles for
  resonances
• Doesnt use real part of loops (real part smooth
  in physical region.)
• Use dispersion relations to put in below
  threshold (but not everywhere)
• Regge-ized t- and u-channel exchange amplitudes
  for background
• Use maximum likelihood method for three-particle
  final states N?? and N??
• s-channel a product of two isobar terms

68
Coupled-channel analysis
Theory

• Bonn/Gatchina analysis results
• Need ?-p! n?0?0 at higher energy, fit well ? p!
  p?0?0
• Find helicity 1/2 and 3/2 amplitudes
• Help to establish properties of existing states
• S11(1650) Ap1/2 significantly larger than PDG
• D13(1520) lower photocouplings than PDG and agree
  with SAID 07
• Roper has largest coupling to ? N
• A1/2 has phase of residue of almost 90deg, sign
  different than PDG
• Eta photoproduction data from GRAAL stops at 1933
  MEVclaim of new state N(2070)D15 requires double
  polarization data
• K? CLAS/CB-ELSA (see Nikonov talk)
• need P11(1860) and P13(1900)
• Fit to pi0 eta photoproduction total c.s. (Horn
  et al)
• Need second D33(1940) at high energy
• Need polarization data

69
Analysis
Theory/Expt

• Matt Bellis CMU analysis technique
• Event-based energy independent amplitude analysis
• Describe the events in a small energy bin with
  some set of processes
• Take out acceptance, get d\sigma/d\Omega
• Get resonance terms, NR term, phase difference
  between resonant terms
• Use Rarita-Schwinger formalism (used by
  Bonn-Gatchina group)
• Dont need energy dependence in s-channel
  propagator since bin in W
• Need to put in t and u-dependence into
  non-resonant terms
• Find minimum set of diagrams which preserves
  gauge invariance and describes data
• See set of channels included (high statistics
  data sets) from CLAS
• Show ?K, p? results, unpolarized photon beam

70
Analysis
Theory/Expt

• Matt Bellis CMU analysis technique
• Close to finishing ?, K? and ?/?0
• Maintaining this as an active database
• Requests from theorists to try out models
• Gauge invariance-have to put in complete set of
  diagrams
• Thresholds opening can change amplitudes within
  10 MeV

71
Coupled-channel analysis
Theory

• T.-S.H. Lee Dynamical Coupled-channel Analysis
  by EBAC at Jefferson Lab
• Structure of N coupled to reaction channels
• Need to account for coupled-channel unitarity
  conditions
• Need reactions mechanism at short range
• Coupled-channel analysis based on effective
  Hamiltonian
• Re-examined ?N! ?N
• Doing ?N!?N, ?N!?pN, ?N !?pN, electroproduction

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