January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with...

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


ContentsContents

Actions Datasets from QCDOC Residual mass Pseudoscalar and vector masses Decay constants Nucleons Scaling Summary and conclusions


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Domain wall height = M5 = 1.8


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mf = 4 dimensional bare quark mass

Explicitly couples the s=0 and s=Ls-1 walls mixing the

two chiralities


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DBW2 c1=-1.4069 Iwasaki c1=-0.331


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




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


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




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


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


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


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


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) )



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


Perform unitary extrapolation

amq 0



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


Perform unitary extrapolation

amq 0

Do fit for DBW2 = 0.72

or draw straight lines


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


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


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)


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


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


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


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


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


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


J parameterJ parameter

Data from different actions and lattice spacings

J parameter defined by

Determined at experimental ratio


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


ScalingScaling






fK/m


ScalingScaling






f/m


ScalingScaling






mK*/m


Nucleon operatorsNucleon operators

Standard Nucleon operator

Operator for negative parity partner

In finite box, backward propagating state has opposite parity


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*


Chiral ExtrapolationChiral Extrapolation

Only two sea quark masses

Draw a straight line

N, N*

=0.72, =0.764


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)


Nucleon scalingNucleon scaling

Expect discretisation errors of O(a2)

Use r0 to set the

scale Plot dimensionless

quantities Moderate scaling

observed


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 ?

January 2006UKQCD meeting - Edinburgh Light Hadron Spectrum and Pseudoscalar Decay Constants with...

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