# Presentation: 566167

## Slide 1

- Simon Capstick, Florida State University

## Nucleon Excited States-Theoretical Issues

- Overview: why study nucleon and meson excited states?
- Four QCD-based models of hadron structure
- How experiments can help resolve theoretical issues: salient examples
- Urgently needed theoretical developments

- Simon Capstick, Florida State University

## Why study nucleon and meson excited states?

- Uniqueness: bound states of strongly-interacting, relativistic confined systems
- Identification of important effective degrees of freedom in low-energy QCD
- Potential discovery of entirely new forms of matter: glueballs, hybrids

- Simon Capstick, Florida State University

## Uniqueness

- Unique?
- Nucleons interact strongly in nuclei...
- Can isolate relevant low-energy d.f. (nucleons)
- Can directly probe two-body potential in experiment
- Few body systems of most A exist to test model N-N, N-N-N,... potentials
- Can systematically expand around non-relativistic limit
- Heavy effective degrees of freedom
- Relatively large states

- Simon Capstick, Florida State University

## Uniqueness...

- Elementary d.f. are confined
- Can only indirectly infer low-energy interaction
- Only exist as bound states
- Not non-relativistic systems (unless **all** quarks heavy)

- Simon Capstick, Florida State University

## Effective degrees of freedom

- Low-energy QCD:
- Constituent quarks (CQs), confined by flux tubes?
- Confined CQs, elementary meson fields?
- Confined CQs, gas of instantons?

- D. Leinweber et al.
- QCD vacuum action
- density

- P.Page, S.C. Flux-tube
- model of baryons
- & hybrids

- Simon Capstick, Florida State University

## Entirely new forms of matter

- Gauge-field configurations provide confining potential
- States of pure glue exist
- Exotic states not light
- Others mix with
- Glue may not be in ground state
- Hybrid mesons: exotic quantum numbers
- Hybrid baryons: no exotics, mix with

- Simon Capstick, Florida State University

## Glueballs and hybrid mesons

- Colin Morningstar:
- Gluonic Excitations workshop, 2003 (Jlab)

- Simon Capstick, Florida State University

## Why do we need models?
Can solve for certain quantities in QCD using lattice gauge theory
Masses of lightest few states with given quantum numbers (especially pure glue)
Hadronic matrix elements of electro-weak operators
Especially heavy-quark hadrons:
Heavy-quark potentials

- Can solve for certain quantities in QCD using lattice gauge theory
- Masses of lightest few states with given quantum numbers (especially pure glue)
- Hadronic matrix elements of electro-weak operators
- Especially heavy-quark hadrons:
- Heavy-quark potentials

- QCD-based models of hadron structure

- Simon Capstick, Florida State University

## Why do we need models?

- Juge, Kuti, & Morningstar

- Heavy quark potentials in mesons
- Action density has flux-tube at large r
- Potentials deviate from flux-tube expectations at small r

- Bali et al.

- Simon Capstick, Florida State University

## Heavy quark potentials in baryons 

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

- Takahashi &Suganuma:
- Calculate Lmin=l1+l2+l3
- plot ground and first excited state energies of glue (VB and VH1) vs. Lmin

- Simon Capstick, Florida State University

## Why do we need models...?

- Description of full spectrum requires models based on QCD
- Quarks are confined
- pair-wise linear confinement
- string potential Lmin, scale set by meson string tension
- Spin and flavor-dependent “hyperfine” interactions are present between quarks
- Models differ in mechanism for short-distance, spin-dependent interactions
- Different pictures of the important physics!

- Simon Capstick, Florida State University

## Gluon-exchange models

- Emphasize:
- Connection to heavy-quark limit
- Universality of meson and baryon physics
- Quarks exchange gluons at short distance
- color-magnetic hyperfine interactions
- e.g. DeRujula, Georgi, Glashow (ground states)

- Simon Capstick, Florida State University

## Gluon-exchange models...

- Predict presence of additional tensor interactions
- Tensor
- mixes states split by contact interaction
- D-waves in the nucleon and ****
- Where are spin-orbit interactions?

- Simon Capstick, Florida State University

## One-boson exchange models

- Emphasize:
- aspects of QCD at low momenta imposed by chiral symmetry
- Goldstone-boson nature of ****, K, ****,... fields
- Bosons exchanged between quarks
- No spin-orbit from OBE (confinement?)

- Simon Capstick, Florida State University

## Instanton-based model

- 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
- Form chosen to reduce spin-orbit effects
- Reproduces correct “Regge trajectories”

- Simon Capstick, Florida State University

## Dynamical approaches

- Are **all** (or many) excited baryon states dynamically generated?
- States are poles in scattering matrix
- Potentials chosen to reproduce low-energy scattering data (chiral dynamics)
- Generate poles by iterating interaction based on potentials, coupled channels
- E. Oset et al., M. Lutz, S. Krewald et al.

- Simon Capstick, Florida State University

## Important required developments

- Experiment + theoretical analysis:
- Will ultimately sort out (or synthesize) these pictures
- Steer lattice groups toward important quantities to calculate

- Simon Capstick, Florida State University

## Important required developments

- Better determination of properties of states known to exist (say PDG 4*, 3*)
- Verification/removal of poorly determined states, discovery of “missing” resonances
- Evidence of overpopulation of states in some partial waves, decay signatures?
- Hybrids
- Possible **** partners of S=+1 pentaquarks
- Development of coupled-channel analysis (required for 1.-3.)

- Simon Capstick, Florida State University

## 1. Properties of existing states

- E.g.: some models predict (tensor) mixing between S11 and D13 (N*1/2-,N*3/2-) states
- Mixing angles differ in different approaches (no mixing at all with instantons)
- Theory: calculate mixing angles, effects on decays to:
-  ****K****...****
- Experiment + analysis: find accurate partial widths

- 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-
- Lattice QCD should also be able to determine ****S and ****D
- enough time (CPU and elapsed!)
- clever choice of correlators...

- Simon Capstick, Florida State University

## Properties of existing states...

- E.g. is the Roper resonance:
- A qqq (radial) excitation?
- Dynamically-generated bound state?
- S. Krewald et al., iterated ****interaction
-  no elementary excitation needed to fit data!
- Hybrid? Pentaquark?
- Bag/flux-tube models: lightest hybrids include P11 (N1/2+) states at 1500/1900 MeV
- Chiral-soliton picture anti-decuplet N(1647)
- More than one of the above?

- Simon Capstick, Florida State University

## Roper resonance

- Photo-couplings incompatible with (OGE) qqq interpretation
- Accurate determinations of photo-couplings (in coupled-channel analysis) required
- EM form factor from e-N
- Should fall off rapidly if state is predominantly a baryon-meson effect
- Focus on P11 partial wave (also other states)
- Lattice:
- Roper heavy in quenched calculations, lighter (threshold?) as pion mass is lowered: more development needed!

- Simon Capstick, Florida State University

## 2. Missing and 1*, 2* states

- Why bother finding new states or confirming/removing old ones?
- E.g.: current debate about chiral-symmetry restoration in spectrum
- Prediction of pairing of +ve/-ve parity states with same J higher in spectrum
- 1* states N1/2+(2100) & N1/2-(2090) identified as doublet (Cohen and Glozman)
- PDG: S11(2090) “any structure above 1800 MeV”
- 1885 +/- 30 MeV vs. 1928 +/- 59 (43 MeV)
- 2125 +/- 75 vs. 2180 +/- 80 (55 MeV)
- 2050 +/- 20 vs. 1880 +/- 20 (-165 MeV)

- Simon Capstick, Florida State University

## Missing resonances

- Symmetric (qqq) potential models:
- Agree on **number** of excited states of a given character
- Disagree on their **place** in spectrum, especially at higher energy
- many positive (and doubly-excited negative) parity states not seen in analyses of data: “missing” resonances
- Largest differences in predictions for (formation &) decay-channel couplings
- Model proponents **must** calculate baryon-meson (all open channels) and photo- couplings

- Simon Capstick, Florida State University

## Missing resonances

- Finding several missing (+ve parity) resonances:
- Would verify symmetric qqq correct picture
- PDG states established in analyses of N**** elastic scattering
- States which couple weakly to N****will 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 several final 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

## 3. Unconventional states

- All baryon JP quantum numbers possible with qqq: no exotic hybrids
- Light hybrid baryon states (flux-tube):
- Sqqq=1/2 states: N1/2+, N3/2+ at ~1870 +/- 100 MeV
- Sqqq=3/2 states: D1/2+, D3/2+, D5/2+ approx. 2075 +/- 100 MeV
- Theory needs to examine decays
- Easily identified decay signatures?
- Electromagnetic couplings? (Burkert and Li)

- Simon Capstick, Florida State University

## Unconventional states...

- Partners **** of ******** with JP=1/2+
- will mix with conventional states
- May have significant hidden strangeness:decays?
- Because of mixing, discovery may require overpopulation of states
- Another important reason to carefully study P11 (P13, P31, P33, F35) partial wave!

- Simon Capstick, Florida State University

## 4. Development of coupled-channel analysis

- Grand challenge for hadron structure physics:
- Extraction of model-independent information about overlapping, broad resonances from EM-production and hadron scattering data

- Simon Capstick, Florida State University

## Analysis of N* (and meson) data

- 	Masses, widths, decay branches, photocouplings, EM form factors
- from
- Partial wave data in many (all open) channels; multipoles in N
- from
- Scattering data

- Simon Capstick, Florida State University

## Analysis of N* (and meson) data...

- Necessary ingredients?
- Coupled-channel unitarity
- E.g. K-matrix approach: (D.M. Manley, KSU)
- K contains resonance information,  background terms
- CMB (Cutkosky; Vrana, Dytman and Lee) model:
- all channels re-scatter into all others via loops
- Effective Lagrangians: T. Sato and T.-S. H. Lee; GWU group: C. Bennhold, H. Haberzettl; Mainz group: L. Tiator, D. Drechsel,...

- Simon Capstick, Florida State University

## Analysis of N* (and meson) data...

- Fitting ambiguities can be lessened by imposing necessary analytic structure of amplitudes
- Resonances appear as poles
- Thresholds cause branch cuts, amplitudes on various sheets related
- Analytic structure can be made compatible with unitarity (CMB model)

- Simon Capstick, Florida State University

## Analysis of N* (and meson) data...

- Theory must provide:
- Strong form factors: e.g. N(1535) to N**** as a function of decay momentum (for loops)
- Open threshold causes cusp in N elastic scattering amplitude
- Amplitude is integral, involves form factor: not an observable!

- Simon Capstick, Florida State University

## Theoretical ingredients...

- Theory must provide:
- Technique for constraining background amplitudes
- Based on physics of competing processes
- 	e.g. t-channel (meson) exchange
- Consistent with unitarity, analyticity, gauge invariance

- Simon Capstick, Florida State University

- 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

## OBE spectrum...

- OBE Results for spectrum: Glozman, Plessas, Theussl, Wagenbrunn, & Varga

- Simon Capstick, Florida State University

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

## 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