# Presentation: 470016

## Slide 1

- Simon Capstick, Florida State University

## Theory of the hadron (baryon) spectrum

- Missing resonances, N* program at Jlab
- Unitary, multi-channel analysis
- Competing models of the short-distance qq interaction
- Can this issue be resolved by examining mixing angles in S11 and D13 states?
- New insights from lattice QCD calculations
- Flux tube potential picture of QQ, QQQ
- String breaking
- Dramatic behavior of baryon masses in low m**** limit

- Simon Capstick, Florida State University

## Missing resonances

- Symmetric quark models predict many positive (and doubly-excited negative) parity states not seen in analyses of data
- PDG states were based on analyses of N**** elastic scattering
- Are there states which couple weakly to N****
- These can be expected to be “missing”
**Evidence** for them should show up in other (N****, ****K,...) final states, excited with EM probes from nucleon targets (make N* or *****)
- Their existence will be **established** in multi-channel analyses of many different final states

- Simon Capstick, Florida State University

## Missing resonances...

- R. Koniuk and N. Isgur
- Elementary-meson emission decay model (quarks directly emit mesons)
- Baryon structure from Isgur-Karl model
**** Showed missing states correspond in number and energy to those predicted to decouple from N****
- 3P0 : quark-pair creation decay model
- Hadrons decay by creation of quark pair with quantum numbers of the vacuum
- String breaking has same structure
- Emitted mesons have structure
- Baryons wave functions from structure model
****Can correlate many decays with a couple of parameters, predict which final states will show evidence of new states

- Simon Capstick, Florida State University

## Nucleon model states and N couplings

- SC and N. Isgur,
-   PRD**34** (1986) 2809;
- SC and W. Roberts,
-   PRD**47** (1993) 2004

- Nucleon model states and N couplings

- Simon Capstick, Florida State University

## model states and N couplings

- Simon Capstick, Florida State University

## Predictions for branching fractions

- Can calculate decay branching fractions if calculate enough decay channels!
- Have looked at decays of N*, ***** states to N, , N(1440), (1600)... and ’
- Also decays to strange final states, including *, (1405),... and K, K* (not shown below)

- Simon Capstick, Florida State University

## Predictions for branching fractions...

- Simon Capstick, Florida State University

## Have we seen new resonances?

- Effect seen in ****p to ****K+ at W ~1900 MeV at SAPHIR; C. Bennhold et al.
- Could be D13 predicted by model (has sizeable ****N and ****K coupling)
- Or the effectof more than one state
- Need coupledchannels to confirm

- Simon Capstick, Florida State University

## Have we seen new resonances?...

- Possible third S11 resonance at ~1.8 GeV
- Rapidly rising cross section for ****N to N**** above existing S11 states at GRAAL
- Similar rise seen in CLAS in ****photoproduction experiments
- Very interesting possibility for quark models!
- Evidence from N****, **** electroproduction in CLAS that P13(1720) region not understood
- Two states? Hard to fit in models...
- Huge potential for interesting new results from Jlab experiments!
- Need multi-channel analysis to firmly establish new states

- Simon Capstick, Florida State University

## Unitary multi-channel analysis

- Based on K-matrix: KSU group, D.M. Manley and collaborators
- Effective Lagrangians: T. Sato and T.-S. H. Lee; GWU group: C. Bennhold, H. Haberzettl,...
- CMU-LBL (Cutkosky) method: Vrana, Dytman and Lee, Phys. Rept. **328**, (200), 181 (Pitt-ANL)
- Extend **************analysis******to many other channels
- N****, N****, N****, N****, ****, N****, ****K, ****K,...
- Incorporate constraints from analyticity
- Impose multi-channel unitarity
****Resonance parameters are extracted from analysis of partial-wave amplitudes in all open channels simultaneously

- Simon Capstick, Florida State University

## Slide 12

- Simon Capstick, Florida State University

## Results of Pitt-ANL analysis

| state | Mass
(MeV) | Width
(MeV) | BN | BN |
| --- | --- | --- | --- | --- |
| S11(1535)
(PDG) | 1545(3)
1520-1555 | 127(19)
100-250 | 35(4)
35-55 | 55(5)
30-55 |
| S11(1650)
(PDG) | 1693(12)
1640-1680 | 225(40)
145-190 | 73(2)
55-90 | -2(1)
3-10 |
| D13(1520)
(PDG) | 1520(3)
1515-1530 | 118(4)
110-135 | 61(2)
50-60 | 0(1) |
| D13(1700)
(PDG) | 1729(33)
1650-1750 | 178(133)
50-150 | 4(1)
5-15 | 7(1) |

- Simon Capstick, Florida State University

## QCD-inspired models of baryons

- Work in adiabatic (Born-Oppenheimer) approximation
- Effect of glue is to generate qq potentials
- Confining potential:
- flux-tube?
- Dirac structure in relativistic treatments?
- Short-distance (residual) interactions
- OGE model: link to meson and heavy-quark physics
- OBE model: chiral symmetry dominates soft QCD spectrum
- Instanton-induced model: QCD vacuum structure implies ‘t Hooft’s instanton-induced interaction

- Simon Capstick, Florida State University

## Constituent quarks:
Dynamically generated constituent masses, which run with Q2 : mu,d  Ku,d  QCD  200 MeV 
Effective sizes, form factors

- Dynamically generated constituent masses, which run with Q2 : mu,d  Ku,d  ****QCD  200 MeV
- Effective sizes, form factors

- Effective degrees of freedom

- One popular picture:
- Constituent quarks
- Glue in flux tubes (confinement)

- Simon Capstick, Florida State University

## Ground-state spectrum suggests flavor-dependent short-range (contact) interactions
One-gluon exchange: good fit to ground states with (color-magnetic dipole-dipole), e.g. -DeRujula,Georgi,Glashow

Explains regularities in meson spectrum (e.g. evolution of vector-pseudoscalar splitting with quark mass)
Unclear why this should work for light quarks...
Taken at face value predicts tensor interaction

And spin-orbit interactions, at a level not present in spectrum

- One-gluon exchange: good fit to ground states with (color-magnetic dipole-dipole), e.g. ****-********DeRujula,Georgi,Glashow
- Explains regularities in meson spectrum (e.g. evolution of vector-pseudoscalar splitting with quark mass)
- Unclear why this should work for light quarks...
- Taken at face value predicts tensor interaction
- And spin-orbit interactions, at a level not present in spectrum

- What are their residual interactions?

- Simon Capstick, Florida State University

## Residual interactions...

- Isgur and Karl PRD**20**, (1979) 768
- Contact splitting active in L=1 excited states
- Characteristic splitting is (m****-mN)/2

- Add consistent tensor interaction
- No strong evidence for tensor from spectrum
- Best evidence from decays, S11(1535)N****

- PDG quoted range of central values

- Isgur and Karl
- PRD**20**, (1979) 768

- Simon Capstick, Florida State University

## Residual interactions...

- Variational calculation in large HO basis (SC, N. Isgur)
- String confinement, plus associated spin-orbit
- Include OGE Coulomb, contact, tensor, spin-orbit
- Relativistic KE, extended constituent quarks
- parameterize momentum dependence, running coupling...
- Photocouplings calculated with Hint expanded to O(p2/m2)
- Strong decays calculated in pair creation (3P0) model (with W. Roberts)
- Reasonable agreement; allows prediction of favorable channels to find ‘missing’ baryons
- Puzzles: Roper mass; ****3/2**-**(1520)-****1/2**-**(1405); L=1 too light by 50 MeV, positive parity too massive by 50 MeV,...

- Simon Capstick, Florida State University

## Another possibility: should light quarks exchange pions? Robson; Buchmann, Faessler,...
Claim gluons not active in light-quark hadrons: flavor dependence through exchange of octet of pseudoscalars (GBE)
Contact interaction:

Order of states inverted? Natural with GBE              
         Glozman & Riska (GR)

- Claim gluons not active in light-quark hadrons: flavor dependence through exchange of octet of pseudoscalars (GBE)
- Contact interaction:
- Order of states inverted? Natural with GBE
-         **** Glozman & Riska (GR)

- Residual interactions...

- PDG 1550-1700

- PDG 1560-1700

- Simon Capstick, Florida State University

## Residual interactions...

- GR fit radial matrix elements of V(rij) to spectrum
**Calculated** in variational H.O. basis with consistent tensor Glozman, Plessas, Theussl, Wagenbrunn, & Varga
- Add nonets of exchange vector mesons and scalars
- Relativistic K.E., string confinement; calculate decays
- Problems can arise in some of these models with decays (poor results with OBE)
- E.g. N**** decay of S11(1535) not possible without vector exchange added to GBE

- Simon Capstick, Florida State University

**Notes:**
Low mass states only
Vectors and scalars required for tensor mixings in strong decays, nucleon form factors

## Residual interactions...

- Results for spectrum:

- Simon Capstick, Florida State University

**Notes:**
Low mass states only
Vectors and scalars required for tensor mixings in strong decays, nucleon form factors

## Residual interactions...

- Another flavor–dependent possibility: instanton-induced interactions
- Present if qq in S-wave, I=0, S=0 state
- W is a contact interaction (has range ****)
- causes no shifts in ***** masses
- No tensor interaction, or spin-orbit forces
- Applied to excited states Blask, Bohn, Huber, Metsch & Petry
- solve Bethe-Salpeter equation

- Simon Capstick, Florida State University

## Instanton-induced interactions

- 		V(**r**1,**r**2,**r**3) = A3 + B3 i<j |**r**i - **r**j|
- Relativistic treatment, so need to choose Dirac structure of potential
- Chosen to reduce spin-orbit effects
- Produces correct Regge trajectories
- For N*,D* only five parameters: 	mn , gnn, a, b, ****

- Simon Capstick, Florida State University

## Instanton-induced interactions...

- spectrum of ***** only from confiningpotential
- Blask, Bohn, Huber, Metsch & Petry

- Simon Capstick, Florida State University

## N* spectrum from ‘t Hooft’s force

- Simon Capstick, Florida State University

## Nature of short-range qq interactions

- Spectrum alone cannot distinguish models
- Wave functions much more sensitive
- Baryons have near degenerate excited states
- two orbital spaces in 3q system, degenerate l=1 orbital excitations
- two possible total quark spins
- Degeneracy broken by spin-spin interactions (L=0 x S=0 operator)
- Large mixing caused by tensor, spin-orbit,... interactions which must be present (relativity)

- Simon Capstick, Florida State University

## Why are mixing angles important?...

- Chizma and Karl, hep-ph/0210126
- Different effective interactions, adjusted to contact splittings, have very different tensor (and spin-orbit) interactions
- Cause different mixing angles in low-lying S11 & D13 states
****A determination of mixing angles can establish nature of effective interactions between quarks

- Simon Capstick, Florida State University

## Low lying excited baryons

- LP=1- + Sqqq(1/2) = 1/2-, 3/2-
- LP=1- + Sqqq(3/2) = 1/2-, 3/2-, 5/2-
- Orbital excitations in **** or ****
- 2(N1/2-,N3/2-), N5/2-, D1/2-, D3/2-
- Two N1/2- model states, S=1/2 or S=3/2,
- are S11 in ****N********N
- resonances N(1535) and N(1650) in analyses
- Two N3/2- states are D13 **** N(1520), N(1700)

- Simon Capstick, Florida State University

## Low lying excited baryons...

- Without spin-dependent interactions between the quarks
- Two degenerate S11 states (S=1/2 and S=3/2) and two degenerate D13 states
- Contact interactions breaks degeneracy
- Proportional to ****i<j **S**i . **S**j f(rij)
- Tensor and spin-orbit interactions **mix** two S=1/2 and S=3/2 states with same JP

- Simon Capstick, Florida State University

## Mixing angles

- Physical states are admixtures of two possible L,S combinations
- 		N(1535)1/2- = cos(****S) N2P1/2- - sin(****S) N4P1/2-
- 		N(1650)1/2- = sin(****S) N2P1/2- + cos(****S) N4P1/2-
- 		N(1520)3/2- = cos(****D) N2P3/2- - sin(****D) N4P3/2-
- 		N(1700)3/2- = sin(****D) N2P3/2- + cos(****D) N4P3/2-
- How can ****S and ****D be determined?
- Lattice QCD, with enough time (CPU and elapsed!) and clever choice of correlators... or model of baryon structure and strong decays

- Simon Capstick, Florida State University

## Unmixed model states

- Work done with W. Roberts (Jlab/ODU)
- Variational calculation in large HO basis
- Unmixed states are orthogonal eigenstates of H, with definite L(=1) and Sqqq (1/2 or 3/2)
- OGE contact and color-Coulomb interactions
- Turn off any interactions which are not simultaneous spin and spatial scalars
- No tensor, spin-orbit (from confinement, OGE)

- Simon Capstick, Florida State University

## Decay model

- Use 3P0, phenomenological decay model
- Calculate decay amplitudes of unmixed states to N****, N****, ****K
- Find decay amplitudes as a function of ****S and ****D
- Compare to Pitt-ANL analysis results

- Simon Capstick, Florida State University

## Slide 33

- Simon Capstick, Florida State University

## Slide 34

- Simon Capstick, Florida State University

## Extracted mixing angles

- Model does not fully describe S11(1535) ********
- Mixing angles ****S~35-40o, ****D ~10-20o
- Other determinations: ****S~32o, ****D ~-10o
- B. Saghai and Z. Li
- Hey, Litchfield and Cashmore (’75)

|  | [ ]1 | [ ]2 | [ ]1 | [ ]2 | [ ]2 |
| --- | --- | --- | --- | --- | --- |
| S | 41o | 33o | -8o | 39o | ~20o |
| D | 9o | 21o |  | >11o |  |

- Simon Capstick, Florida State University

## New insights from lattice QCD

- Is the potential model picture reasonable, at least for heavy-quark systems?
- Can lattice calculations explain the position of the light positive-parity states (like the Roper)?

- Simon Capstick, Florida State University

## Confinement in heavy quark mesons

- Bali et al.
- Static quark and antiquark separated by 2 fm
- Gluonic flux shows tube structure between quarks

- Simon Capstick, Florida State University

## How should we treat confinement?

- Quenched lattice measurement of QQQ potential
- Takahashi, Matsufuru, Nemoto and Suganuma, PRL**86** (2001) 18.
- Measure potential with 3Q-Wilson loop (static quarks) for 0<t<T
- Also fit QQ potential to compare  and Coulomb terms

- Simon Capstick, Florida State University

## Confinement

- Quenched lattice calculation of QQQ static potential
- Takahashi, Matsufuru, Nemoto and & Suganuma, PRL**86** (2001) 18, **hep-lat/0210024**
- Plot vs.* L*min = min. length
- 	Y-shaped string for 24 configurations
- String-like flux-tube potential in QQQ baryons

*V*B(***r***1,***r***2,***r***3)=****(*l*1+*l*2+*l*3)=*****L*min

- Simon Capstick, Florida State University

## Flux tube in QQQ baryons

- Abelian action distribution of gluons and light quarks nr. QQQ
- Ichie, Bornyakov, Struer & Schierholz, hep-lat/0212024

- Simon Capstick, Florida State University

## Leading Born-Oppenheimer approximation

- Juge, Kuti, Morningstar PRL82, 4400 (’99)
- Born Oppenheimer approximation for heavy-quark mesons
- Use heavy-quark adiabatic potentials from lattice, including excited glue states
- No light-quarks, no quark spin or retardation effects
- Compared to NRQCD results (Morningstar)
- Retardation effects and mixing between states in different adiabatic potentials allowed

- Simon Capstick, Florida State University

## LBO approximation...

- Good agreement (10%) for level splittings of 4 conventional and 2 hybrid heavy-quark mesons
- Partially explains success of constituent quark model
- Allows inclusion of gluon dynamics
- Current LQCD studies:
- Does LBO survive inclusion of quark spin?
- OK, but worse in charmonium than upsilon
- Drummond et al PLB478, 151 (’00)
- Burch and Toussaint, hep-lat/0305008
- Do light dynamical quarks spoil this picture?

- Simon Capstick, Florida State University

## Light quark effects on potential?

- Explore string breaking using two-body operators
- Allow two flavors of dynamical staggered quarks

- Simon Capstick, Florida State University

## Baryon spectroscopy in lattice QCD

- Recent progress in understanding first excited states (J****=1/2+, 1/2-)
- If pion masses ~500 MeV, calculated masses N1/2+ < N1/2- < N*1/2+  with roughly equal spacing
- Physical state at (940/1535/1440)
- Problem with quenched approximation?
- Problem with m**** (light quark masses) being too large?

- Simon Capstick, Florida State University

## Baryon spectroscopy in LQCD...

- C. Maynard, D.G. Richards (LHPC/UKQCD)
- Show that this remains true in full (un-quenched) QCD at m**** ~ 500 MeV
- Light quarks (m********
- Wilson fermions: m**** ~ 400 MeV
- Smoothed actions (FLIC) m**** ~ 300 MeV
- Have chiral symmetry only in a****0 limit
- Overlap/domain wall fermions
- Have exact analog of ****-symm. at finite a
- Other physics and calculational advantages
- But cost a factor of 30 in CPU time!

- Simon Capstick, Florida State University

## Light m baryon masses in LQCD

- F. Lee et al. (Kentucky collaboration)
- hep-lat/0208070
- Use overlap fermions and simple qqq operators
- Levels cross at low m****

- Simon Capstick, Florida State University

## Light m baryon masses in LQCD...

- Same level crossing observed in light ****1/2+ and ****1/2-  states

- Simon Capstick, Florida State University

## Light m baryon masses in LQCD...

- Also shows approximate degeneracy of *****3/2+ and ****3/2-

- Simon Capstick, Florida State University

## Baryon spectroscopy in LQCD...

- Chiral behavior is important!
- Non-analytic terms present in low m**** limit give rapidly varying behavior
- Need to make (quenched) ****-PT extrapolations of lattice data to low m****
- Roper likely a qqq state
- Bare quark model qqq state should be too massive!
- Couples strongly to N**** decay channel
- Model with baryon-meson loops?
- Constituent quark model without loop effects will miss this important physics

- Simon Capstick, Florida State University

## Loop effects in baryon spectrum

- Two approaches:
- Include elementary (bare) qqq excitations in careful calculation of reaction observables
- Include rescattering into open B’M channels
- S. Krewald, et al. (Juelich), T. Sato & H. Lee, C. Bennhold & GWU group
- Explicitly evaluate hadron loop corrections to masses and decays
- Mesons (******-******): P. Geiger and N. Isgur

- Simon Capstick, Florida State University

## Unquenching the quark model

- In QCD qqq(qq) configurations possible in baryons: effect on CQM?
- Model with baryon-meson intermediate states, loops  self energies: Danielle Morel & SC
- High-momentum part of loops contains OBE

-          (k)

- Simon Capstick, Florida State University

## Unquenching the quark model...

- Hecht, Roberts, Tandy, Thomas,...
- Schwinger-Dyson Bethe-Salpeter study
- examine m**** dependence of N**** loop contribution to nucleon mass
- D. Morel and A.Thomas
- Studying m**** dependence of contributions to resonance masses from N**** & ****... loops
- Non-analytic behavior in extrapolation of lattice data for baryon masses to light quark (pion) masses

- Simon Capstick, Florida State University

## Summary

- New data from JLab and elsewhere
- Contains evidence for new (missing) baryon states
- Refines our knowledge of existing states
- Unitary multi-channel analysis of this data
- Will establish new states
- Can distinguish between QCD-inspired models
- Dramatic new lattice calculations
- Support flux-tube potential model picture, at least for heavy-quark hadrons
- Point to importance of decay-channel couplings with light quarks

- Simon Capstick, Florida State University

## Summary...

- Challenges to theory:
- Analysis of data in many channels:
- Reduce ambiguities in analysis by incorporating constraints from:
- Multi-channel unitarity, analyticity, gauge invariance,...
- Efficient treatment of ‘background’ consistent with these constraints
- Include effects of open channels in:
- Lattice QCD calculations
- Reaction models
- QCD-inspired models

- Simon Capstick, Florida State University

## Slide 55

- Simon Capstick, Florida State University