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
March 2005
ILFT2 Edinburgh
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Introduction
 Chirally symmetric fermions
– Domain Wall fermions (DWF)
Kaplan 92, Shamir 93,
Furman-Shamir 95
 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
 Computationally expensive
 Residual chiral symmetry breaking mres
March 2005
ILFT2 Edinburgh
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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
March 2005
ILFT2 Edinburgh
3
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
March 2005
ILFT2 Edinburgh
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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”
March 2005
ILFT2 Edinburgh
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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
March 2005
ILFT2 Edinburgh
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Ensembles RBC
 Nf=3 amf=0.04, t=0.5 dt =0.01 aM5=1.8
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
March 2005
ILFT2 Edinburgh
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Residual mass
Nf = 3 amf = 0.04
LS=8 DBW2
March 2005
ILFT2 Edinburgh
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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
March 2005
ILFT2 Edinburgh
9
The potential
 Compare lattice spacing from mr and r0
– Look for lattice artefacts
 ms=0.04 mv=-mres
 No sea extrapolation
 No strong sea quark mass dependence
March 2005
ILFT2 Edinburgh
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NF=2 sea quark mass dependence
March 2005
ILFT2 Edinburgh
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Scaled potential
 Rescaled
potential
 NF=0,NF=2
different short
distance
behaviour
 No obvious
differences for c1
March 2005
ILFT2 Edinburgh
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Lattice artefacts
 Some
variation with
c1
 Approx 10%
 This suggests
it is not an
extreme effect
March 2005
ILFT2 Edinburgh
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Valence LS
 LSsea=8
 mres decreases
as LS increases
 Not exponetial
 Not surprising as
PQ
 Same as
quenched
March 2005
ILFT2 Edinburgh
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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
0.72
0.72
0.72
-1.4069
-1.4069
-1.4069
-1.4069
0.5
1
1
0.5
8
8
12
12
R
RHMC
RHMC
RHMC
1345 / 51
1200
<500
1200
0.72
0.88
0.88
-1.4069
-1.4069
-1.4069
0.3
1
0.5
12
8
12
RHMC
R
RHMC
<500
1500 / 75
<500
March 2005
ILFT2 Edinburgh
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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
March 2005
ILFT2 Edinburgh
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(amPS)2 vs amq
 Intercept not
equal to mres
 Straight line
through two
points
 Autocorrelation?
 Statistics (50)
March 2005
ILFT2 Edinburgh
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amr vs amq
 msea = mval
 Straight line
through two
points
 amr at
mq = - mres
 a-1 = 1.4(3) GeV
March 2005
ILFT2 Edinburgh
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amr vs amf valence
 Valence only
extrapolation
 a-1 ~ 1.45 GeV
March 2005
ILFT2 Edinburgh
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mres vs a2
 Lattice spacing
PQ r mass
 mres PQ
extrapolation
 Sea quark mass
not same
 Approx
exponential
behaviour
March 2005
ILFT2 Edinburgh
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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!
March 2005
ILFT2 Edinburgh
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