January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration 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

January 2006UKQCD meeting - Edinburgh Contents  Actions  Datasets from QCDOC  Residual mass  Pseudoscalar and vector masses  Decay constants  Nucleons  Scaling  Summary and conclusions

January 2006UKQCD meeting - Edinburgh Actions

January 2006UKQCD meeting - Edinburgh Actions

January 2006UKQCD meeting - Edinburgh Actions

January 2006UKQCD meeting - Edinburgh Actions Domain wall height = M 5 = 1.8

January 2006UKQCD meeting - Edinburgh Actions

January 2006UKQCD meeting - Edinburgh Actions m f = 4 dimensional bare quark mass Explicitly couples the s=0 and s=L s -1 walls mixing the two chiralities

January 2006UKQCD meeting - Edinburgh Actions

January 2006UKQCD meeting - Edinburgh Actions

January 2006UKQCD meeting - Edinburgh Actions DBW2 c 1 = Iwasaki c 1 =-0.331

January 2006UKQCD meeting - Edinburgh QCDOC 16 3 x32x8 2+1f datasets  Actionm ud /m s VN traj #meas 0.72DBW x32x DBW2½16 3 x32x DBW2¼16 3 x32x DBW2½16 3 x32x DBW x32x DBW2½16 3 x32x DBW x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x

January 2006UKQCD meeting - Edinburgh QCDOC 16 3 x32x8 2+1f datasets  Actionm ud /m s VN traj #meas 0.72DBW x32x DBW2½16 3 x32x DBW2¼16 3 x32x DBW2½16 3 x32x DBW x32x DBW2½16 3 x32x DBW x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x

January 2006UKQCD meeting - Edinburgh QCDOC 16 3 x32x8 2+1f datasets  Actionm ud /m s VN traj #meas 0.72DBW x32x DBW2½16 3 x32x DBW2¼16 3 x32x DBW2½16 3 x32x82940* DBW x32x85320* DBW2½16 3 x32x DBW x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x Iwasaki½16 3 x32x85900* Iwasaki116 3 x32x85800*1004

January 2006UKQCD meeting - Edinburgh 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  = /0.04  = /0.04

January 2006UKQCD meeting - Edinburgh QCDOC 16 3 x32x8 2+1f datasets  Actionm ud /m s VN traj #meas 0.72DBW x32x DBW2½16 3 x32x DBW2¼16 3 x32x DBW2½16 3 x32x DBW x32x DBW2½16 3 x32x DBW x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x

January 2006UKQCD meeting - Edinburgh QCDOC 16 3 x32x8 2+1f datasets  Actionm ud /m s VN traj #meas 0.72DBW x32x DBW2½16 3 x32x DBW2¼16 3 x32x DBW2½16 3 x32x DBW x32x DBW2½16 3 x32x DBW x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x Iwasaki½16 3 x32x Iwasaki116 3 x32x

January 2006UKQCD meeting - Edinburgh Datasets  First dynamical DWF 2+1 quark flavour ensembles  All ensembles generated with the RHMC algorithm  Volume = 16 3 x32 with L s =8  Ensembles are am ud =0.01/0.02/0.04, am s =0.04 and aM 5 =1.8  Up to four valence quark masses on each ensemble –am f = 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

January 2006UKQCD meeting - Edinburgh Binning Local vector correlator  =0.764 m R =0.5  Over sample & average into bins  4 time-planes, 215 configs separated by 10 trajectories  Choose bin size 5-10 since  int ~ 100 trajectories  Full correlated analysis with binned data as input  Errors stabilise as bin size >  int as expected  Get independent data with low variance

January 2006UKQCD meeting - Edinburgh Residual Mass m res  m res measures violation of chiral symmetry  L s not infinite  L-R coupling between quark fields on walls  Define J 5 in terms of fields at L s /2  m res follows from Axial Ward- Takahashi Identity  Simultaneously fit to both point- point and smeared/wall-point Iwasaki  = f

January 2006UKQCD meeting - Edinburgh Chiral Extrapolation of m res  Actionm res 0.72DBW (1) 0.764DBW (1) 0.78DBW (1) 2.13Iwasaki0.0105(1) 2.2Iwasaki0.0066(1) Iwasaki  = 2.13 Shift quark mass am q = a( m f + m res (m f ) )

January 2006UKQCD meeting - Edinburgh Chiral Extrapolation of m res  Actionm res 0.72DBW (1) 0.764DBW (1) 0.78DBW (1) 2.13Iwasaki0.0105(1) 2.2Iwasaki0.0066(1) Iwasaki  = 2.13 Shift quark mass am q = a( m f + m res (m f ) ) Perform unitary extrapolation am q  0

January 2006UKQCD meeting - Edinburgh Chiral Extrapolation of m res  Actionm res 0.72DBW (1) 0.764DBW (1) 0.78DBW (1) 2.13Iwasaki0.0105(1) 2.2Iwasaki0.0066(1) Iwasaki  = 2.13 Shift quark mass am q = a( m f + m res (m f ) ) Perform unitary extrapolation am q  0 Do fit for DBW2  = 0.72 or draw straight lines

January 2006UKQCD meeting - Edinburgh 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 DBW2  = 0.72 m ud /m s =0.5  Simultaneously fit point-point and smeared-point correlators

January 2006UKQCD meeting - Edinburgh m PS chiral extrapolation and am s  Shift input quark masses am f  am q =a( m f + m res (m f ) )  unitary extrapolation  Deviation from origin acceptable given low stats  Use Kaon mass in limit m ud  0 to give degenerate am s /2  Action(am Ps ) DBW (2) 0.764DBW (2) 0.78DBW (10) 2.13Iwasaki-0.002(4) 2.2Iwasaki-0.008(3) DBW2  = 0.72

January 2006UKQCD meeting - Edinburgh m PS chiral extrapolation and am s  Shift input quark masses am f  am q =a( m f + m res (m f ) )  unitary extrapolation  Miss the origin in some cases  Use Kaon mass in limit m ud  0 to give degenerate am s /2 DBW2  = 0.72  Actionam s 0.72DBW20.039(2) 0.764DBW20.032(3) 0.78DBW20.036(5) 2.13Iwasaki0.036(4) 2.2Iwasaki0.032(2)

January 2006UKQCD meeting - Edinburgh Vector mass and lattice spacing DBW2  = 0.78  Lattice spacing from  mass in chiral limit (1.4  2.2 GeV -1 )  K. Hashimoto, J. Noaki, T. Izubuchi - hep-lat/ lattice spacing calculation from static potential  Only have degenerate quarks  am K* = A + B( m s /2 + m s /2 )  Strange quark mass from previous slide

January 2006UKQCD meeting - Edinburgh Volumes and lattice spacing  mRmR a -1 (GeV)L(fm)mLmLm  / m V (1) ½1.7(1) (1) ½2.0(1) (1) ½1.8(1) (1) ½2.1(1) DBW2 IW

January 2006UKQCD meeting - Edinburgh Vector mass and lattice spacing DBW2  = 0.78  Lattice spacing from  mass in chiral limit (1.4  2.2 GeV -1 )  K. Hashimoto, J. Noaki, Taku Izubuchi - hep-lat/ lattice spacing calculation from static potential  Only have degenerate quarks  am K* = A + B( m s /2 + m s /2 )  Strange quark mass from previous slide

January 2006UKQCD meeting - Edinburgh Vector mass and lattice spacing DBW2  = 0.78  Lattice spacing from  mass in chiral limit (1.4  2.2 GeV -1 )  K. Hashimoto, J. Noaki, Taku Izubuchi - hep-lat/ lattice spacing calculation from static potential  Only have degenerate quarks  am K* = A + B( m s /2 + m s /2 )  Strange quark mass from previous slide

January 2006UKQCD meeting - Edinburgh  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 Z A first  Both methods give equivalent results within errors Pseudoscalar decay constant Iwasaki  = 2.13

January 2006UKQCD meeting - Edinburgh Z A calculation  Calculate Z A from the conserved and local axial current  Simultaneously fit both point-point and smeared/wall-point data Iwasaki  = 2.13

January 2006UKQCD meeting - Edinburgh  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 Z A first  Both methods give equivalent results within errors  f K using lattice spacing from am  and r 0 Pseudoscalar decay constant Iwasaki  = 2.13

January 2006UKQCD meeting - Edinburgh J parameter  Data from different actions and lattice spacings  J parameter defined by  Determined at experimental ratio

January 2006UKQCD meeting - Edinburgh J parameter  Data from different actions and lattice spacings  J parameter defined by  Determined at experimental ratio

January 2006UKQCD meeting - Edinburgh Scaling  Set the lattice spacing from r 0  Expect discretisation errors to be O(a 2 )  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 f K /f PS

January 2006UKQCD meeting - Edinburgh Scaling  Set the lattice spacing from r 0  Expect discretisation errors to be O(a 2 )  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 f K /m 

January 2006UKQCD meeting - Edinburgh Scaling  Set the lattice spacing from r 0  Expect discretisation errors to be O(a 2 )  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 f  /m 

January 2006UKQCD meeting - Edinburgh Scaling  Set the lattice spacing from r 0  Expect discretisation errors to be O(a 2 )  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 m K* /m 

January 2006UKQCD meeting - Edinburgh Nucleon operators  Standard Nucleon operator  Operator for negative parity partner  In finite box, backward propagating state has opposite parity

January 2006UKQCD meeting - Edinburgh Nucleon Effective mass plots DBW2  =0.72 m R =½ Closed symbols: WL-WL-WL Open symbols: SL-SL-LL  N,  N (T-t),  N*

January 2006UKQCD meeting - Edinburgh Chiral Extrapolation Only two sea quark masses Draw a straight line N, N*  =0.72,  =0.764

January 2006UKQCD meeting - Edinburgh Edinburgh plot  No extrapolations  Data follows phenomenological curve for both actions  Possible finite size effect for the lightest nucleon at IW  =2.2 (open square)

January 2006UKQCD meeting - Edinburgh Nucleon scaling  Expect discretisation errors of O(a 2 )  Use r 0 to set the scale  Plot dimensionless quantities  Moderate scaling observed

January 2006UKQCD meeting - Edinburgh Summary and conclusions  Many ensembles created on QCDOC – some with limited statistics/small volumes  Only two quark masses for most  values – need third point to improve error estimates  Finite size effects  L s = 8 too small – need increased L s to decrease m res –Analysising 16 3 x32 with L s =16 (Dave Antonio’s talk)  Scaling unclear as errors are large  In production: Iwasaki  = 2.13, 24 3 x64, L s = 16 ensembles with 2+1 quark flavours and three quark mass values: 0.01/0.02/0.03 –Finite volume effects ?