# Presentation: 695496

## Baryon spectrum from 2+1 flavours of DWF QCD

- Chris Maynard

- RBC and UKQCD collaborations

- Chris Allton, Tom Blum, Paul Cooney, Luigi del Debbio, Meifeng Lin, Aurora Trivini, Takeshi Yamazaki, James Zanotti

## Outline

- Motivation
- Why baryons
- Ensemble details
- What has been measured
- Baryon spectrum (degenerate)
- Nucleons
- Decuplet baryons
- Outlook and conclusions

## Why baryons are important

- N. Isgur *1947-2001* **nucl-th/0007008**
*Why N*'s are Important"*
*Nucleons **are** the stuff of which world is made*
*Simplest system** in which the quintessentially **nonabelian** character of QCD is **manifest*
*N**c** quarks** in proton because there are **N**c** colours*
*Baryons are sufficiently complex to reveal physics hidden from us in Mesons*
*Non-analytic** chiral behaviour*

## Spectrum not completely understood

- Roper Resonance

- QM HO potential

- Excited states do not fit “*naturally*” in Quark Model *e.g.* the Roper resonance
- N(1440) JP=1/2+
- Lattice QCD can give definitive answer
- Excited states are hard
- Is Roper radial excitation of nucleon, or something else

## Matrix elements

- Diverse phenomenology
- Structure functions
- Collider physics
- Strangeness content of nucleon
- Cold Dark Matter
- Neutron electro-dipole moment
- SUSY phenomenology
- Proton decay
- GUT and SUSY GUT models

## Ensembles

| mu | volume | Ntraj | Ntp | Nind |
| --- | --- | --- | --- | --- |
| 0.03 | 163x32 | 4000 | 2 | 70 |
| 0.02 | 163x32 | 4000 | 4 | 70 |
| 0.01 | 163x32 | 4000 | 4 | 70 |
| 0.03 | 243x64 | 3000 | 2 | 50 |
| 0.02 | 243x64 | 3600 | 2 | 50 |
| 0.01 | 243x64 | 4000 | 2 | 80 |
| 0.005  | 243x64 | 4500 | 1 | 80 |

- Iwasaki gauge action =2.13, 2+1 flavours (ms=0.04) LS=16 mres=0.003 a-1=1.60(3) (rho,r0, method of planes)

- L= 2fm

- L= 3fm

- 243 is still running and more measurements to come
- Results are preliminary

- Not complete

## Nucleons

- RBC and UKQCD separate measurement datasets for matrix elements
- Combined analysis for m=0.01 V=243
- 60 configurations
- 5 Smearing combinations (6 for N*)
- Local-local **LL**
- Gaussian-local (R=4)  **GL**
- Gaussian-Gaussian **GG**
- Box (L=16) (extra N* operator) **BL **
- Gaussian-local (R=7) **G2L **(4 tps)

## Nucleon mass

- Fit effective mass
- 1 fit parameter
- No fit-range systematic error
- Only for m=0.01

## Nstar mass

- 3-6 timeslices per correlator
- Result is fit-range sensitive for individual correlators
- Uber-fit is fit-range insensitive

## Finite size effects

## Nucleon FSE

- No obvious FSE for Nucleon
- 2 and 3 fm box
- mP ~ 390Mev
- mPL ~ 3.9 and 5.8
- mP/mV ~ 0.45
- No FSE expected
- m=0.005 mPL ~ 4.6

## Nstar FSE

- No obvious FSE for Nstar
- No expectation
- N* Uber fit for 243
- N* noisey for 163
- No FSE
- Statistics limited

## Edinburgh plot

- Displays all 2+1 flavour DWF data
- Apparently lies on universal curve
- LS, gauge coupling, volume
- Lightest data noisy due to vector correlator

## Chiral extrapolation

- Linear extrap. vs mP2

- m=0.01 uberfit
- No fit systematic

- m=0.005 datum low?
- Chiral effect?
- mP ~ 310MeV

## Chiral extrapolation II

- NLO PT term
- mP3
- Radius of convergence?
*Maybe* lightest
- Definitely not heaviest
- Just for fun!

## Decuplet baryons

- Valence degenerate
-  mV=mu=mSea
-  mV=mstrange
- Effective mass plot for  m=0.01
- Not fitting Meff

## Chiral extrapolation

- Data consistent with linear extrapolation

## Baryon Spectrum

- Three lowest lying valence degenerate states
- Negative parity partners
- Reasonable agreement with experiment
- a-1=1.60(3) GeV

## Baryon spectrum

- Ultimately expect non-linear chiral behaviour
- Can’t get spectrum right with linear
- NLO PT fit not realistic
- goes in right direction
- maybe just statistics
- Require lighter quarks and better statistics

## Conclusions

- Preliminary results for Baryon spectrum
- Broadly agrees with experiment
- starting to reach interesting regime
- mu/ms < 1/5, mP/mV ~ 0.38, mP ~ 310 MeV
- Measurements still running
- Complex chiral behaviour must be explored to get spectrum right
- Finer lattice spacing simulation under way
- control lattice artefacts