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Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8

Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8. D.J. Antonio, K.C. Bowler, P.A. Boyle, M.A. Clark, B. Joo, A.D. Kennedy, R.D. Kenway, R.J. Tweedie, A. Yamaguchi. Robert Tweedie RBC-UKQCD Collaboration. Contents. Actions Datasets from QCDOC Residual mass

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Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8

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  1. Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at Ls = 8 D.J. Antonio, K.C. Bowler, P.A. Boyle, M.A. Clark, B. Joo, A.D. Kennedy, R.D. Kenway, R.J. Tweedie, A. Yamaguchi Robert Tweedie RBC-UKQCD Collaboration UKQCD meeting - Edinburgh

  2. Contents • Actions • Datasets from QCDOC • Residual mass • Pseudoscalar and vector masses • Decay constants • Nucleons • Scaling • Summary and conclusions UKQCD meeting - Edinburgh

  3. Actions UKQCD meeting - Edinburgh

  4. Actions UKQCD meeting - Edinburgh

  5. Actions UKQCD meeting - Edinburgh

  6. Actions Domain wall height = M5 = 1.8 UKQCD meeting - Edinburgh

  7. Actions UKQCD meeting - Edinburgh

  8. Actions mf = 4 dimensional bare quark mass Explicitly couples the s=0 and s=Ls-1 walls mixing the two chiralities UKQCD meeting - Edinburgh

  9. Actions UKQCD meeting - Edinburgh

  10. Actions UKQCD meeting - Edinburgh

  11. Actions DBW2 c1=-1.4069 Iwasaki c1=-0.331 UKQCD meeting - Edinburgh

  12. QCDOC 163x32x8 2+1f datasets UKQCD meeting - Edinburgh

  13. QCDOC 163x32x8 2+1f datasets UKQCD meeting - Edinburgh

  14. QCDOC 163x32x8 2+1f datasets UKQCD meeting - Edinburgh

  15. Farmin’ • Search parameter space • Optimise physics output in shortest time scale • Thermalisation from start or existing R-algorithm ensemble • Datasets have 4 time planes per configuration • O(~4000) measurements for some quantities b=0.764 0.04/0.04 b=0.764 0.02/0.04 UKQCD meeting - Edinburgh

  16. QCDOC 163x32x8 2+1f datasets UKQCD meeting - Edinburgh

  17. QCDOC 163x32x8 2+1f datasets UKQCD meeting - Edinburgh

  18. Datasets • First dynamical DWF 2+1 quark flavour ensembles • All ensembles generated with the RHMC algorithm • Volume = 163x32 with Ls=8 • Ensembles are amud=0.01/0.02/0.04, ams=0.04 and aM5=1.8 • Up to four valence quark masses on each ensemble • amf = 0.01,0.02,0.03,0.04 • Multiple time planes on several of the ensembles • Multiple smearings • point-point, wall-point, hydrogen-like wavefunction, doubly smeared at source • Integrated autocorrelation time for pseudoscalar meson measured to be ~100 trajectories • O(40K) trajectories and O(100K) measurements UKQCD meeting - Edinburgh

  19. Binning Local vector correlator b=0.764 mR=0.5 • Over sample & average into bins • 4 time-planes, 215 configs separated by 10 trajectories • Choose bin size 5-10 since tint ~ 100 trajectories • Full correlated analysis with binned data as input • Errors stabilise as bin size > tint as expected • Get independent data with low variance UKQCD meeting - Edinburgh

  20. Residual Mass mres • mres measures violation of chiral symmetry • Ls not infinite  L-R coupling between quark fields on walls • Define J5 in terms of fields at Ls/2 • mresfollows from Axial Ward-Takahashi Identity • Simultaneously fit to both point-point and smeared/wall-point Iwasaki b=2.13 2+1f UKQCD meeting - Edinburgh

  21. Chiral Extrapolation of mres Iwasaki b = 2.13 Shift quark mass amq = a( mf + mres(mf) ) UKQCD meeting - Edinburgh

  22. Chiral Extrapolation of mres Iwasaki b = 2.13 Shift quark mass amq = a( mf + mres(mf) ) Perform unitary extrapolation amq 0 UKQCD meeting - Edinburgh

  23. Chiral Extrapolation of mres Iwasaki b = 2.13 Shift quark mass amq = a( mf + mres(mf) ) Perform unitary extrapolation amq 0 Do fit for DBW2 b = 0.72 or draw straight lines UKQCD meeting - Edinburgh

  24. Pseudoscalar and Vector mass fits • Perform a double cosh fit to both the excited and ground states where statistics allow • Removes systematic error in choice of fit range due to excited state • Simultaneously fit point-point and smeared-point correlators DBW2 b = 0.72 mud/ms=0.5 UKQCD meeting - Edinburgh

  25. mPS chiral extrapolation and ams • Shift input quark masses amfamq=a( mf + mres(mf) ) • unitary extrapolation • Deviation from origin acceptable given low stats • Use Kaon mass in limit mud0 to give degenerate ams/2 DBW2 b = 0.72 UKQCD meeting - Edinburgh

  26. mPS chiral extrapolation and ams • Shift input quark masses amfamq=a( mf + mres(mf) ) • unitary extrapolation • Miss the origin in some cases • Use Kaon mass in limit mud0 to give degenerate ams/2 DBW2 b = 0.72 UKQCD meeting - Edinburgh

  27. Vector mass and lattice spacing DBW2 b = 0.78 • Lattice spacing from r mass in chiral limit (1.4  2.2 GeV-1 ) • K. Hashimoto, J. Noaki, T. Izubuchi - hep-lat/0510079 lattice spacing calculation from static potential • Only have degenerate quarks • amK* = A + B( ms/2 + ms/2 ) • Strange quark mass from previous slide UKQCD meeting - Edinburgh

  28. Volumes and lattice spacing DBW2 IW UKQCD meeting - Edinburgh

  29. Vector mass and lattice spacing DBW2 b = 0.78 • Lattice spacing from r mass in chiral limit (1.4  2.2 GeV-1 ) • K. Hashimoto, J. Noaki, Taku Izubuchi - hep-lat/0510079 lattice spacing calculation from static potential • Only have degenerate quarks • amK* = A + B( ms/2 + ms/2 ) • Strange quark mass from previous slide UKQCD meeting - Edinburgh

  30. Vector mass and lattice spacing DBW2 b = 0.78 • Lattice spacing from r mass in chiral limit (1.4  2.2 GeV-1 ) • K. Hashimoto, J. Noaki, Taku Izubuchi - hep-lat/0510079 lattice spacing calculation from static potential • Only have degenerate quarks • amK* = A + B( ms/2 + ms/2 ) • Strange quark mass from previous slide UKQCD meeting - Edinburgh

  31. Pseudoscalar decay constant • Calculate the pseudoscalar decay constant in two ways • Define as: • Using axial Ward-Takahashi identity • Require only the pseudoscalar correlator and mres • From the axial-axial correlator • Require calculation of ZA first • Both methods give equivalent results within errors Iwasaki b = 2.13 UKQCD meeting - Edinburgh

  32. ZA calculation • Calculate ZA from the conserved and local axial current • Simultaneously fit both point-point and smeared/wall-point data Iwasaki b = 2.13 UKQCD meeting - Edinburgh

  33. Pseudoscalar decay constant • Calculate the pseudoscalar decay constant in two ways • Define as: • Using axial Ward-Takahashi identity • Require only the pseudoscalar correlator and mres • From the axial-axial correlator • Require calculation of ZA first • Both methods give equivalent results within errors • fK using lattice spacing from amr and r0 Iwasaki b = 2.13 UKQCD meeting - Edinburgh

  34. J parameter • Data from different actions and lattice spacings • J parameter defined by • Determined at experimental ratio UKQCD meeting - Edinburgh

  35. J parameter • Data from different actions and lattice spacings • J parameter defined by • Determined at experimental ratio UKQCD meeting - Edinburgh

  36. Scaling • Set the lattice spacing from r0 • Expect discretisation errors to be O(a2) • Errors will decrease with additional datasets allowing improved fitting to chiral extrapolations (rather than drawing straight lines) • Errors should decrease with increased statistics • Hint of scaling for two different gauge actions – looks better for Iwasaki than DBW2 fK/fPS UKQCD meeting - Edinburgh

  37. Scaling • Set the lattice spacing from r0 • Expect discretisation errors to be O(a2) • Errors will decrease with additional datasets allowing improved fitting to chiral extrapolations (rather than drawing straight lines) • Errors should decrease with increased statistics • Hint of scaling for two different gauge actions – looks better for Iwasaki than DBW2 fK/mr UKQCD meeting - Edinburgh

  38. Scaling • Set the lattice spacing from r0 • Expect discretisation errors to be O(a2) • Errors will decrease with additional datasets allowing improved fitting to chiral extrapolations (rather than drawing straight lines) • Errors should decrease with increased statistics • Hint of scaling for two different gauge actions – looks better for Iwasaki than DBW2 fp/mr UKQCD meeting - Edinburgh

  39. Scaling • Set the lattice spacing from r0 • Expect discretisation errors to be O(a2) • Errors will decrease with additional datasets allowing improved fitting to chiral extrapolations (rather than drawing straight lines) • Errors should decrease with increased statistics • Hint of scaling for two different gauge actions – looks better for Iwasaki than DBW2 mK*/mr UKQCD meeting - Edinburgh

  40. Nucleon operators • Standard Nucleon operator • Operator for negative parity partner • In finite box, backward propagating statehasopposite parity UKQCD meeting - Edinburgh

  41. Nucleon Effective mass plots DBW2 b=0.72 mR=½ Closed symbols: WL-WL-WL Open symbols: SL-SL-LL WN, WN(T-t),WN* UKQCD meeting - Edinburgh

  42. Chiral Extrapolation Only two sea quark masses Draw a straight line N, N* b=0.72, b=0.764 UKQCD meeting - Edinburgh

  43. Edinburgh plot • No extrapolations • Data follows phenomenological curve for both actions • Possible finite size effect for the lightest nucleon at IW b=2.2 (open square) UKQCD meeting - Edinburgh

  44. Nucleon scaling • Expect discretisation errors of O(a2) • Use r0to set the scale • Plot dimensionless quantities • Moderate scaling observed UKQCD meeting - Edinburgh

  45. Summary and conclusions • Many ensembles created on QCDOC – some with limited statistics/small volumes • Only two quark masses for most b values – need third point to improve error estimates • Finite size effects • Ls = 8 too small – need increased Ls to decrease mres • Analysising 163x32 with Ls=16 (Dave Antonio’s talk) • Scaling unclear as errors are large • In production: Iwasaki b = 2.13, 243x64, Ls = 16 ensembles with 2+1 quark flavours and three quark mass values: 0.01/0.02/0.03 • Finite volume effects ? UKQCD meeting - Edinburgh

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