january 2006ukqcd meeting - edinburgh light hadron spectrum and pseudoscalar decay constants with...
TRANSCRIPT
![Page 1: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/1.jpg)
January 2006 UKQCD meeting - Edinburgh
Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at Ls = 8 Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at Ls = 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
![Page 2: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/2.jpg)
January 2006 UKQCD meeting - Edinburgh
ContentsContents
Actions Datasets from QCDOC Residual mass Pseudoscalar and vector masses Decay constants Nucleons Scaling Summary and conclusions
![Page 3: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/3.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
![Page 4: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/4.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
![Page 5: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/5.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
![Page 6: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/6.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
Domain wall height = M5 = 1.8
![Page 7: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/7.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
![Page 8: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/8.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
mf = 4 dimensional bare quark mass
Explicitly couples the s=0 and s=Ls-1 walls mixing the
two chiralities
![Page 9: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/9.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
![Page 10: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/10.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
![Page 11: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/11.jpg)
January 2006 UKQCD meeting - Edinburgh
ActionsActions
DBW2 c1=-1.4069 Iwasaki c1=-0.331
![Page 12: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/12.jpg)
January 2006 UKQCD meeting - Edinburgh
QCDOC 163x32x8 2+1f datasetsQCDOC 163x32x8 2+1f datasets
Action mud/ms V Ntraj #meas
0.72 DBW2 1 163x32x8 3395 479
0.72 DBW2 ½ 163x32x8 6000 1000
0.72 DBW2 ¼ 163x32x8 6000 1000
0.764 DBW2 ½ 163x32x8 2940 215
0.764 DBW2 1 163x32x8 5320 541
0.78 DBW2 ½ 163x32x8 1505 142
0.78 DBW2 1 163x32x8 1620 165
2.13 Iwasaki ½ 163x32x8 3590 520
2.13 Iwasaki 1 163x32x8 3590 520
2.2 Iwasaki ½ 163x32x8 5900 1026
2.2 Iwasaki 1 163x32x8 5800 1004
![Page 13: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/13.jpg)
January 2006 UKQCD meeting - Edinburgh
QCDOC 163x32x8 2+1f datasetsQCDOC 163x32x8 2+1f datasets
Action mud/ms V Ntraj #meas
0.72 DBW2 1 163x32x8 3395 479
0.72 DBW2 ½ 163x32x8 6000 1000
0.72 DBW2 ¼ 163x32x8 6000 1000
0.764 DBW2 ½ 163x32x8 2940 215
0.764 DBW2 1 163x32x8 5320 541
0.78 DBW2 ½ 163x32x8 1505 142
0.78 DBW2 1 163x32x8 1620 165
2.13 Iwasaki ½ 163x32x8 3590 520
2.13 Iwasaki 1 163x32x8 3590 520
2.2 Iwasaki ½ 163x32x8 5900 1026
2.2 Iwasaki 1 163x32x8 5800 1004
![Page 14: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/14.jpg)
January 2006 UKQCD meeting - Edinburgh
QCDOC 163x32x8 2+1f datasetsQCDOC 163x32x8 2+1f datasets
Action mud/ms V Ntraj #meas
0.72 DBW2 1 163x32x8 3395 479
0.72 DBW2 ½ 163x32x8 6000 1000
0.72 DBW2 ¼ 163x32x8 6000 1000
0.764 DBW2 ½ 163x32x8 2940* 215
0.764 DBW2 1 163x32x8 5320* 541
0.78 DBW2 ½ 163x32x8 1505 142
0.78 DBW2 1 163x32x8 1620 165
2.13 Iwasaki ½ 163x32x8 3590 520
2.13 Iwasaki 1 163x32x8 3590 520
2.2 Iwasaki ½ 163x32x8 5900* 1026
2.2 Iwasaki 1 163x32x8 5800* 1004
![Page 15: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/15.jpg)
January 2006 UKQCD meeting - Edinburgh
Farmin’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
=0.764 0.04/0.04
=0.764 0.02/0.04
![Page 16: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/16.jpg)
January 2006 UKQCD meeting - Edinburgh
QCDOC 163x32x8 2+1f datasetsQCDOC 163x32x8 2+1f datasets
Action mud/ms V Ntraj #meas
0.72 DBW2 1 163x32x8 3395 479
0.72 DBW2 ½ 163x32x8 6000 1000
0.72 DBW2 ¼ 163x32x8 6000 1000
0.764 DBW2 ½ 163x32x8 2940 215
0.764 DBW2 1 163x32x8 5320 541
0.78 DBW2 ½ 163x32x8 1505 142
0.78 DBW2 1 163x32x8 1620 165
2.13 Iwasaki ½ 163x32x8 3590 520
2.13 Iwasaki 1 163x32x8 3590 520
2.2 Iwasaki ½ 163x32x8 5900 1026
2.2 Iwasaki 1 163x32x8 5800 1004
![Page 17: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/17.jpg)
January 2006 UKQCD meeting - Edinburgh
QCDOC 163x32x8 2+1f datasetsQCDOC 163x32x8 2+1f datasets
Action mud/ms V Ntraj #meas
0.72 DBW2 1 163x32x8 3395 479
0.72 DBW2 ½ 163x32x8 6000 1000
0.72 DBW2 ¼ 163x32x8 6000 1000
0.764 DBW2 ½ 163x32x8 2940 215
0.764 DBW2 1 163x32x8 5320 541
0.78 DBW2 ½ 163x32x8 1505 142
0.78 DBW2 1 163x32x8 1620 165
2.13 Iwasaki ½ 163x32x8 3590 520
2.13 Iwasaki 1 163x32x8 3590 520
2.2 Iwasaki ½ 163x32x8 5900 1026
2.2 Iwasaki 1 163x32x8 5800 1004
![Page 18: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/18.jpg)
January 2006 UKQCD meeting - Edinburgh
DatasetsDatasets
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
![Page 19: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/19.jpg)
January 2006 UKQCD meeting - Edinburgh
BinningBinning
Local vector correlator
=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 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
![Page 20: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/20.jpg)
January 2006 UKQCD meeting - Edinburgh
Residual Mass mresResidual 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 mres follows from Axial Ward-
Takahashi Identity
Simultaneously fit to both point-point and smeared/wall-point
Iwasaki =2.13 2+1f
![Page 21: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/21.jpg)
January 2006 UKQCD meeting - Edinburgh
Chiral Extrapolation of mresChiral Extrapolation of mres
Action mres
0.72 DBW2 0.0108(1)
0.764 DBW2 0.0053(1)
0.78 DBW2 0.0043(1)
2.13 Iwasaki 0.0105(1)
2.2 Iwasaki 0.0066(1)
Iwasaki = 2.13
Shift quark mass
amq = a( mf + mres(mf) )
![Page 22: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/22.jpg)
January 2006 UKQCD meeting - Edinburgh
Chiral Extrapolation of mresChiral Extrapolation of mres
Action mres
0.72 DBW2 0.0108(1)
0.764 DBW2 0.0053(1)
0.78 DBW2 0.0043(1)
2.13 Iwasaki 0.0105(1)
2.2 Iwasaki 0.0066(1)
Iwasaki = 2.13
Shift quark mass
amq = a( mf + mres(mf) )
Perform unitary extrapolation
amq 0
![Page 23: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/23.jpg)
January 2006 UKQCD meeting - Edinburgh
Chiral Extrapolation of mresChiral Extrapolation of mres
Action mres
0.72 DBW2 0.0108(1)
0.764 DBW2 0.0053(1)
0.78 DBW2 0.0043(1)
2.13 Iwasaki 0.0105(1)
2.2 Iwasaki 0.0066(1)
Iwasaki = 2.13
Shift quark mass
amq = a( mf + mres(mf) )
Perform unitary extrapolation
amq 0
Do fit for DBW2 = 0.72
or draw straight lines
![Page 24: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/24.jpg)
January 2006 UKQCD meeting - Edinburgh
Pseudoscalar and Vector mass fitsPseudoscalar 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 mud/ms=0.5 Simultaneously fit point-point
and smeared-point correlators
![Page 25: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/25.jpg)
January 2006 UKQCD meeting - Edinburgh
mPS chiral extrapolation and amsmPS chiral extrapolation and ams
Shift input quark masses
amfamq=a( mf + mres(mf) )
unitary extrapolation Deviation from origin
acceptable given low stats Use Kaon mass in limit mud0
to give degenerate ams/2
Action (amPs)2
0.72 DBW2 -0.008(2)
0.764 DBW2 -0.004(2)
0.78 DBW2 -0.011(10)
2.13 Iwasaki -0.002(4)
2.2 Iwasaki -0.008(3)
DBW2 = 0.72
![Page 26: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/26.jpg)
January 2006 UKQCD meeting - Edinburgh
mPS chiral extrapolation and amsmPS chiral extrapolation and ams
Shift input quark masses
amfamq=a( mf + mres(mf) )
unitary extrapolation Miss the origin in some cases Use Kaon mass in limit mud0
to give degenerate ams/2
DBW2 = 0.72
Action ams
0.72 DBW2 0.039(2)
0.764 DBW2 0.032(3)
0.78 DBW2 0.036(5)
2.13 Iwasaki 0.036(4)
2.2 Iwasaki 0.032(2)
![Page 27: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/27.jpg)
January 2006 UKQCD meeting - Edinburgh
Vector mass and lattice spacingVector 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/0510079 lattice spacing calculation from static potential
Only have degenerate quarks amK* = A + B( ms/2 + ms/2 )
Strange quark mass from previous slide
![Page 28: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/28.jpg)
January 2006 UKQCD meeting - Edinburgh
Volumes and lattice spacingVolumes and lattice spacing
mR a-1 (GeV) L(fm) mL m/ mV
0.72 1 1.7(1) 1.9 7.8 0.69
0.72 ½ 1.7(1) 1.9 6.0 0.59
0.764 1 2.0(1) 1.6 6.7 0.70
0.764 ½ 2.0(1) 1.6 5.1 0.62
2.13 1 1.8(1) 1.8 7.5 0.70
2.13 ½ 1.8(1) 1.8 5.8 0.62
2.2 1 2.1(1) 1.5 6.8 0.73
2.2 ½ 2.1(1) 1.5 5.1 0.68
DBW2
IW
![Page 29: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/29.jpg)
January 2006 UKQCD meeting - Edinburgh
Vector mass and lattice spacingVector 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/0510079 lattice spacing calculation from static potential
Only have degenerate quarks amK* = A + B( ms/2 + ms/2 )
Strange quark mass from previous slide
![Page 30: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/30.jpg)
January 2006 UKQCD meeting - Edinburgh
Vector mass and lattice spacingVector 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/0510079 lattice spacing calculation from static potential
Only have degenerate quarks amK* = A + B( ms/2 + ms/2 )
Strange quark mass from previous slide
![Page 31: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/31.jpg)
January 2006 UKQCD 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 ZA first
Both methods give equivalent results within errors
Pseudoscalar decay constantPseudoscalar decay constant
Iwasaki = 2.13
![Page 32: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/32.jpg)
January 2006 UKQCD meeting - Edinburgh
ZA calculationZA calculation
Calculate ZA from the conserved and local axial current
Simultaneously fit both point-point and smeared/wall-point data
Iwasaki = 2.13
![Page 33: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/33.jpg)
January 2006 UKQCD 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 ZA first
Both methods give equivalent results within errors
fK using lattice spacing from amand r0
Pseudoscalar decay constantPseudoscalar decay constant
Iwasaki = 2.13
![Page 34: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/34.jpg)
January 2006 UKQCD meeting - Edinburgh
J parameterJ parameter
Data from different actions and lattice spacings
J parameter defined by
Determined at experimental ratio
![Page 35: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/35.jpg)
January 2006 UKQCD meeting - Edinburgh
J parameterJ parameter
Data from different actions and lattice spacings
J parameter defined by
Determined at experimental ratio
![Page 36: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/36.jpg)
January 2006 UKQCD meeting - Edinburgh
ScalingScaling
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
![Page 37: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/37.jpg)
January 2006 UKQCD meeting - Edinburgh
ScalingScaling
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/m
![Page 38: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/38.jpg)
January 2006 UKQCD meeting - Edinburgh
ScalingScaling
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
f/m
![Page 39: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/39.jpg)
January 2006 UKQCD meeting - Edinburgh
ScalingScaling
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*/m
![Page 40: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/40.jpg)
January 2006 UKQCD meeting - Edinburgh
Nucleon operatorsNucleon operators
Standard Nucleon operator
Operator for negative parity partner
In finite box, backward propagating state has opposite parity
![Page 41: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/41.jpg)
January 2006 UKQCD meeting - Edinburgh
Nucleon Effective mass plotsNucleon Effective mass plots
DBW2 =0.72
mR=½
Closed symbols:
WL-WL-WL
Open symbols:
SL-SL-LL
N, N(T-t), N*
![Page 42: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/42.jpg)
January 2006 UKQCD meeting - Edinburgh
Chiral ExtrapolationChiral Extrapolation
Only two sea quark masses
Draw a straight line
N, N*
=0.72, =0.764
![Page 43: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/43.jpg)
January 2006 UKQCD meeting - Edinburgh
Edinburgh plotEdinburgh plot
No extrapolations Data follows
phenomenological curve for both actions
Possible finite size effect for the lightest nucleon at IW =2.2 (open square)
![Page 44: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/44.jpg)
January 2006 UKQCD meeting - Edinburgh
Nucleon scalingNucleon scaling
Expect discretisation errors of O(a2)
Use r0 to set the
scale Plot dimensionless
quantities Moderate scaling
observed
![Page 45: January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with 2+1f DWF at L s = 8 Robert Tweedie RBC-UKQCD Collaboration](https://reader033.vdocument.in/reader033/viewer/2022051517/5697bf721a28abf838c7ec37/html5/thumbnails/45.jpg)
January 2006 UKQCD meeting - Edinburgh
Summary and conclusionsSummary 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 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 = 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 ?