Early experiences with DWF on QCDOC

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Early experiences with DWF on QCDOC
This is a physics talk
Only possible due to a huge amount of work from
all the people on the QCDOC project
Physics contributions from many RBC and UKQCD
people
All results are very preliminary

• Chris Maynard
• RBC-UKQCD

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Introduction

• Chirally symmetric fermions
• Domain Wall fermions (DWF)
• Both chiral and flavour symmetry at finite a
• Continuum-like chiral perturbation theory
• No flavour mixing, wrong chirality operating
  mixing small
• Dynamical DWF is QFT

Kaplan 92, Shamir 93, Furman-Shamir 95

• Computationally expensive
• Residual chiral symmetry breaking mres

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Outline

• Chiral symmetry breaking mres
• Preliminary results (statistics limited) for
• The effect of the gauge action on mres
• Valence M5 and LS. The potential
• The effect of the gauge coupling on mres
• The effect of the quark mass on mres
• The effect of LS on mres
• Other talks
• Algorithm (MAC) and Machine (PAB)
• Summary and outlook

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Chiral symmetry breaking and mres

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

Quark mass is
LS not infinite ? L-R coupling Define J5 current
in terms of fields at LS/2 - (1,LS) Axial
Ward-Takahashi Identity and thus mres
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Small is beautiful

• How to reduce chiral symmetry breaking
• Desire mres as small as possible
• LS ? infinity is expensive
• Overlap Ultimate operator. Expensive
• See BJ talk GWF and cost
• We are keen to adopt these improvements
• How do simulation parameters effect mres
• Gauge action, M5, LS, gauge coupling mf
• Inform decision on Big Run

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Gauge Action
Measure dependence of mres on rectangle
term Quenched studies show lines of constant a
approx quadratic in b,c1/1-8c1 plane Zoom in
to top left
Keep a constant vary c1 and b
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Ensembles RBC

• Nf3 amf0.04, t0.5 dt 0.01 aM51.8

b c1 Mud/ms LS Alg Traj/cfg
0.72 -1.4069 1 8 R 1500 / 96
0.48 -2.300 1 8 R 1605 / 101
0.32 -3.570 1 8 R 1600 / 101
0.16 -7.470 1 8 R 1520 / 102
0.80 -1.4069 1 8 R 1900 / 126
0.53 -2.300 1 8 R 1400 / 81
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Residual mass
Nf 3 amf 0.04 LS8 DBW2
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Mres versus rectangle
Increase rectange, decrease mres No dramatic
decrease in mres Lattice artefacts scaling
behaviour? Conservative opinion Maybe not worth
it
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The potential

• Compare lattice spacing from mr and r0
• Look for lattice artefacts

• ms0.04 mv-mres
• No sea extrapolation
• No strong sea quark mass dependence

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NF2 sea quark mass dependence
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Scaled potential

• Rescaled potential
• NF0,NF2 different short distance behaviour
• No obvious differences for c1

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Lattice artefacts

• Some variation with c1
• Approx 10
• This suggests it is not an extreme effect

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Valence LS

• LSsea8
• mres decreases as LS increases
• Not exponetial
• Not surprising as PQ
• Same as quenched

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Ensembles UKQCD

• RHMC

b c1 Mud/ms LS Alg Traj/cfg
0.72 -1.4069 1 8 R 1500 / 70
0.72 -1.4069 0.5 8 R 1345 / 51
0.72 -1.4069 1 8 RHMC 1200
0.72 -1.4069 1 12 RHMC lt500
0.72 -1.4069 0.5 12 RHMC 1200
0.72 -1.4069 0.3 12 RHMC lt500
0.88 -1.4069 1 8 R 1500 / 75
0.88 -1.4069 0.5 12 RHMC lt500
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mres vs mf
b 0.72 LS 8 R algorithm mval msea No
strong mq dependence No fit. Straight line
through two points
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(amPS)2 vs amq

• Intercept not equal to mres
• Straight line through two points
• Autocorrelation?
• Statistics (50)

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amr vs amq

• msea mval
• Straight line through two points
• amr at mq - mres
• a-1 1.4(3) GeV

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amr vs amf valence

• Valence only extrapolation
• a-1 1.45 GeV

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mres vs a2

• Lattice spacing PQ r mass
• mres PQ extrapolation
• Sea quark mass not same
• Approx exponential behaviour

Preliminary
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Summary and Outlook

• First physics from QCDOC!
• Very preliminary
• We are exploring the effects of simulation
  parameters on residual chiral symmetry breaking
• Accumulating more data
• Some conclusions soon!