physics from one year of qcdoc

ILFTnet IV Sokendai, Japan 8-11 March 2006 1

Physics from one year of QCDOC Physics from one year of QCDOC

Chris Maynard

epcc

University of Edinburgh

The Domain Wall fermion project

RBC and UKQCD

UK perspective


PeoplePeople Chris Allton, Dave Antonio, Tom Blum, Ken Bowler,

Peter Boyle, Michael Cheng, Norman Christ, Michael Clark, Saul Cohen, Chris Dawson, Luigi del Debbio, Takumi Doi, Michael Donellan, Jonathan Flynn, Alistair Hart, Koichi Hashimoto, Taku Izubuchi, Chulwoo Jung, Andreas Juttner, Tony Kennedy, Richard Kenway, Changhoan Kim, Sam Li, Huey Wen Lin, Meifeng Lin, Robert Mawhinney, Christopher Maynard, Jun Ichi Noaki, Shigemi Ohta, Brian Pendleton, Chris Sachrajda, Shoichi Sasaki, Amarjit Soni, Aurora Trivini, Robert Tweedie, Azusa Yamaguchi, Takeshi Yamazaki, James Zanotti


OutlineOutline

Brief overview of machine status– Ensembles past, present and future

Physics– Review of data– Preliminary results for data

ILDG– UKQCD status– QCDml1.3

Summary and outlook

8Sl16Sl


QCDOC (edinburgh)QCDOC (edinburgh)


QCDOC statusQCDOC status

UKQCD and RBC machines have been in operation for one year. (Mostly) jointly producing DWF ensembles

DOE and Regensburg machines both commisioned and running. Can’t comment, won’t comment


Current production runs Current production runs

Iwasaki gauge action Strange quark mass fixed up/down Two volumes

– Small ~4000 trajectories 1-2Knode• Gauge production complete• Measurement ongoing

– Large• 800-1500 trajectories. Ongoing. 3 4Knode

machines

16Sl

32163

64243

sud mm }{4

1,

2

1,

4

3

)20(O


Initial runsInitial runs

Parameter search– 2+1 flavours RHMC

• ams=0.04, amud={0.02,0.04}

– Effect on chiral symmetry breaking of• Gauge coupling and gauge action (IW vs DBW2)

Papers – PoS LAT2005

• 080, 093, 094. 095. 098, 135, 141, 346

– 3 papers in preparation

832163 Sl


IntroductionIntroduction

Chirally symmetric fermions– Domain Wall fermions (DWF)

Both chiral and flavour symmetry at finite a– Continuum-like chiral perturbation theory

– Baryon interpolating operators relate to spectrum in simple way

Kaplan 92, Shamir 93, Furman-Shamir 95

Computationally expensive Residual chiral symmetry breaking mres


Aoki phase – how coarse is coarse?Aoki phase – how coarse is coarse?

Schematic of phase diagramShaded region is super-critical

B is massless Aoki phase

Must be in C on the right to get to continuum QCD

Continuum-like symmetries at Coarse a large volumeMust be away from Aoki phase


Chiral symmetry breaking and mresChiral symmetry breaking and mres

4d quark field constructed from left (right) projections of on boundary

Quark mass is

LS not infinite L-R couplingDefine J5 current in terms of fields at LS/2 or mid-pointAxial Ward-Takahashi Identity and thus mres


Localisation and chiral symmetryLocalisation and chiral symmetry

P.A. Boyle PoS LAT2005:141,2005

Transfer matrix of 5d DWF operator, T

– Gap in spectrum of extended states local– Define mobility edge by critical eigen value

• for then is extended

What are the implications for chiral symmetry?

n )(xn

HT log


Chiral symmetryChiral symmetry

In correlations functions, volume suppression of localised states– Two leading contributions to mres

Volume enhanced states at mobility edge Low lying localised states

Valence LS study of LS(Sea)=8 data


DBW2 mres vs LSDBW2 mres vs LS


IW mres vs LSIW mres vs LS


Microscopic locality Microscopic locality

Negative mass operator– Gap in spectrum of extended states local– Define mobility edge by critical eigenvalue

• for then is extendedc

cn )(xn


Measuring localityMeasuring locality

Subset of configurations of LS=8 ensembles ~ 25

Measure 256 lowest eigen values and vectors

Determine smax for each

As c

– Smax↑– Eigen vectors become multi-peaked


Localisation of DBW2 Localisation of DBW2

smax


Localisation of IWLocalisation of IW

smax


Chiral symmetry and TopologyChiral symmetry and Topology

Chiral symmetry breaking effects greater for rougher gauge fields– mres smaller for smaller g2

– mres smaller for DBW2 than IW

• Smearing (smoothing) gauge fields reduces mres

Local topology variation greater for rougher gauge fields– Ultimately no tunnelling at zero quark mass

Chose IW as “optimal” solution


Topology on IW =2.13Topology on IW =2.13

QdV


Ls=8 DatasetsLs=8 Datasets

Action mud/ms Ntraj

0.72 DBW2 1 3395

0.72 DBW2 0.5 5000

0.72 DBW2 0.25 2240

0.764 DBW2 1 4000

0.764 DBW2 0.5 2500

0.78 DBW2 1 1620

0.78 DBW2 0.5 1505

2.13 Iwasaki 1 2380

2.13 Iwasaki 0.5 2450

2.2 Iwasaki 1 4565

2.2 Iwasaki 0.5 3175

163x32 Ls=8

RHMC

a-1 ~ 1.5 – 2.2 GeV

30K traj !

100K measurements

ams=0.04

Quark mass not constant


AutocorrelationsAutocorrelations

B=0.72 ms=0.04 mud=0.02

5000 trajectories

Independent cfgs = 2*


Pion dataPion data

Measure every 5

int = 12 x 5 ~ 60


Win when you binWin when you bin

=0.764 mR=0.5

4 time-planes

Local vector correlator

262 configurations separated every 10 trajectories

Bins size 5-10 int = 50-100


Meson SpectrumMeson Spectrum

Fit mres, mPS and mV

– Oversample and bin data– Multiple time planes– Multiple smearings– Multiple quark masses– Multiple gauge couplings– Multiple gauge actions

multiple effective mass plots


mres IW =2.2 {0.02,0.04}mres IW =2.2 {0.02,0.04}


mres DBW2 =0.72 {0.01,0.04}mres DBW2 =0.72 {0.01,0.04}


mPS IW =2.13mPS IW =2.13


mPS DBW2 =0.764mPS DBW2 =0.764


mV IW =2.13 {0.04,0.04}mV IW =2.13 {0.04,0.04}


mV IW =2.13 {0.02,0.04}mV IW =2.13 {0.02,0.04}


Chiral extrapolationChiral extrapolation

In general only two quark masses no extrapolation – Draw a straight line

Errors are (correctly) large for quantities evaluated at zero quark mass

Not much use for phenomenology– Map out parameter space– where to calculate 2+1 DWF


The static quark potential and r0The static quark potential and r0


Ensembles in physical unitsEnsembles in physical units

mres(mq0)

0.01077(9)

0.00529(5)

0.00430(4)

0.01050(10)

0.00656(6)


Setting strange quark massSetting strange quark mass

Lattice spacing from r0=0.5fm


DBW2 vectorsDBW2 vectors


Scaling of r0mK*Scaling of r0mK*


Axial current Axial current

Chiral symmetry ZA from two-point corrs

– CA(x) conserved current at LS/2 (a lá mres)

– LA(x) usual local current

– Correlate current with PS(x)

fPS from ratio of correlation functions


ZA =0.72 {0.02,0.04}ZA =0.72 {0.02,0.04}


=0.72 fPS=0.72 fPS


Scaling of fScaling of f

Suggestive of common continuum limit and better scaling


Scaling of fKScaling of fK

Again suggestive of good scaling


Scaling of f/fkScaling of f/fk

Flat!Ideal scaling!


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

local-wall correlator

N, N(T-t), N*


Scaling of nucleonsScaling of nucleons

Evidence of finite volume effect

N* and N become degenerate at sufficiently small volume

Seem to be coming together


Finite size effectsFinite size effects


Edinburgh PlotEdinburgh Plot

Data follows phenomenological curve

B=2.2 data anamolous, consistent with finite volume interpretation


LS=16 dataLS=16 data

Small volume 163x32, 4000 trajectories– Sample every 10 (one source)

– Trajectory length=1 int~25-50

– ~100 configurations– More sources and more sampling to be done

Spectrum results Matrix elements: BK

PRELIMINARYPRELIMINARY


Residual massResidual mass

Gauge fixed gaussian smearing


Ps mesonPs meson

Better statistical sampling should help with “wiggles”


BaryonsBaryons

M=0.03


Chiral ExtrapolationChiral Extrapolation


Finite size and mPLFinite size and mPL

Overlay mPL

Upper line finite size effects for N* (LS=8 data)?

Lower line finite size effects for N?


Edinburgh Plot againEdinburgh Plot again

This *is* QCD


BPS plateauxBPS plateaux

Gaussian sources


Chiral behaviour of unitary dataChiral behaviour of unitary data

Need to understand the chiral behaviour


SummarySummary

QCDOC excellent resource for QCD Ls=8 data

– Learned a lot about dynamical DWF– Can do interesting phenomenology– ILDG these ensembles are available

LS=16 163x32 initial measurements

– Preliminary: Promising phenomenology

243x64 in production (see Saul’s talk) LAT2006 Very interesting results

physics from one year of qcdoc

Documents

chiral symmetryp

flavour symmetry

aoki phasechiral symmetry

mobility edgelow

chris sachrajda

michael donellan

michael clark

michael cheng