1. DWF@10 : BNL, NY : 15-17 March 20071 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

2. DWF@10 : BNL, NY : 15-17 March 20072 Outline  Motivation –Why baryons  Ensemble details –What has been measured  Baryon spectrum (degenerate) –Nucleons –Decuplet baryons  Outlook and conclusions

3. DWF@10 : BNL, NY : 15-17 March 20073 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

4. DWF@10 : BNL, NY : 15-17 March 20074 Roper Resonance QM HO potential Spectrum not completely understood Excited states do not fit “naturally” in Quark Model e.g. the Roper resonance N(1440) J P =1/2 + Lattice QCD can give definitive answer Excited states are hard Is Roper radial excitation of nucleon, or something else

5. DWF@10 : BNL, NY : 15-17 March 20075 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

6. DWF@10 : BNL, NY : 15-17 March 20076 Ensembles mumu volumeN traj N tp N ind 0.0316 3 x324000270 0.0216 3 x324000470 0.0116 3 x324000470 0.0324 3 x643000250 0.0224 3 x643600250 0.0124 3 x644000280 0.00524 3 x644500180 Iwasaki gauge action  =2.13, 2+1 flavours (m s =0.04) L S =16 m res =0.003 a -1 =1.60(3) (rho,r0, method of planes) L= 2fm L= 3fm 24 3 is still running and more measurements to come Results are preliminary Not complete

7. DWF@10 : BNL, NY : 15-17 March 20077 Nucleons  RBC and UKQCD separate measurement datasets for matrix elements  Combined analysis for m=0.01 V=24 3 –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)

8. DWF@10 : BNL, NY : 15-17 March 20078 Nucleon mass  Fit effective mass  1 fit parameter  No fit-range systematic error  Only for m=0.01

9. DWF@10 : BNL, NY : 15-17 March 20079 Nstar mass  3-6 timeslices per correlator  Result is fit-range sensitive for individual correlators  Uber-fit is fit- range insensitive

10. DWF@10 : BNL, NY : 15-17 March 200710 Finite size effects

11. DWF@10 : BNL, NY : 15-17 March 200711 Nucleon FSE  No obvious FSE for Nucleon –2 and 3 fm box –m P ~ 390Mev –m P L ~ 3.9 and 5.8 –m P /m V ~ 0.45  No FSE expected –m=0.005 m P L ~ 4.6

12. DWF@10 : BNL, NY : 15-17 March 200712 Nstar FSE  No obvious FSE for Nstar –No expectation –N* Uber fit for 24 3 –N* noisey for 16 3  No FSE –Statistics limited

13. DWF@10 : BNL, NY : 15-17 March 200713 Edinburgh plot  Displays all 2+1 flavour DWF data  Apparently lies on universal curve –L S, gauge coupling, volume  Lightest data noisy due to vector correlator

14. DWF@10 : BNL, NY : 15-17 March 200714 Chiral extrapolation  Linear extrap. vs m P 2  m=0.01 uberfit –No fit systematic  m=0.005 datum low? –Chiral effect? –m P ~ 310MeV

15. DWF@10 : BNL, NY : 15-17 March 200715 Chiral extrapolation II  NLO  PT term –m P 3  Radius of convergence?  Maybe lightest –Definitely not heaviest  Just for fun!

16. DWF@10 : BNL, NY : 15-17 March 200716 Decuplet baryons  Valence degenerate   m V =m u =m Sea   m V =m strange  Effective mass plot for  m=0.01 –Not fitting M eff

17. DWF@10 : BNL, NY : 15-17 March 200717 Chiral extrapolation  Data consistent with linear extrapolation

18. DWF@10 : BNL, NY : 15-17 March 200718 Baryon Spectrum  Three lowest lying valence degenerate states –Negative parity partners  Reasonable agreement with experiment –a -1 =1.60(3) GeV

19. DWF@10 : BNL, NY : 15-17 March 200719 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

20. DWF@10 : BNL, NY : 15-17 March 200720 Conclusions  Preliminary results for Baryon spectrum –Broadly agrees with experiment –starting to reach interesting regime –m u /m s < 1/5, m P /m V ~ 0.38, m P ~ 310 MeV –Measurements still running  Complex chiral behaviour must be explored to get spectrum right  Finer lattice spacing simulation under way –control lattice artefacts