Recent results
from
unquenched light quark simulations
Taku Izubuchi
RIKEN BNL Reserch Center
Taku Izubuchi, Dublin, 25/July/2005
Kanazawa University
1
Contents
• Introduction
• Performance
• Nf=2, 3 Dynamical simulations
• Quark mass
• Conclusions
Taku Izubuchi, Dublin, 25/July/2005
2
Introduction
• In quenched simulations ( NF = 0, no sea quark in QCD vacuume ), Hadron spectrum found to be 5-10% different from experiments (CP-PACS, JLQCD, UKQCD)
linear fit
NLO fit
experiment
0.5
• (RBC) NF = 0, 2 DWF
˛
2 ˛
dmps ˛
J = mV
˛
dmV ˛
J
0.4
mV /mps =1.8
0.3
0.2
quenched
0
0.01
0.02
0.03
msea
0.04
0.05
• Is it only 5-10% ?
Taku Izubuchi, Dublin, 25/July/2005
3
• More obious quenched pathology was found in NS scalar meson
G
a0
I (J)
PC
+
= 1 (0
++
)
(Bardeen et.al.)
0
a0 → η (quenched) + π → a0
As η 0(quenched) failed to get heavy having double pole, this contribution was
argued to make a0 propagator to be negative using QChPT in finite volume.
• quenched theory is not unitary nor local field theory.
Taku Izubuchi, Dublin, 25/July/2005
4
Introduction...
Dynamical simulation is difficult not only it's computationally demanding, but also gauge filed tend to be more fructuating at short distance
than quenched simulation (fixing scale at Hadronic scale).
⇐⇒ milder running αS (µ) for NF > 0 (asymptotic freedom).
t=4,5, R=1.2−7.5
0
−1
r0 × [V (r) − V (r0)] vs r/r0 for
DFW NF = 0, 2.
dynamical mf=0.02
quenched DBW2 beta=1.04
−2
−3
0
0.2
0.4
0.6
0.8
1
This makes dynamical simulation even more difficult.
Taku Izubuchi, Dublin, 25/July/2005
5
Dynamical simulation for DWF (GW)
• Such short distance fructuation has an impact on DWF (GW) fermion simulations.
• Axial Ward-Takahashi identity,
a
∂µAµ(x)
=
≈2
a
a
2mf J5 (x) + 2J5q (x)
a
(mf + mres)J5 (x)
J5a(x) : non-singlet pseudoscalar,
a
J5q
(x) : explicit breaking term
consists of field at s = Ls/2 −
1, Ls/2.
A measure of the residual chiral symmetry breaking,
E
P D a
a
x,y J5q (y, t)J5 (x, 0)
−λLs
∼
e
, λ ∼ HW = γ5DW
mres = P
a (y, t)J a (x, 0)i
hJ
5
5
x,y
1e+05
DBW2 0.764
10000
Leff
1000
100
10
1
0.1
0
0.1
0.2
Lambda
Taku Izubuchi, Dublin, 25/July/2005
0.3
0.4
• Sudden growth of eigenmode size at λ = λc.
Roughly consistent with mres(Ls) behaviors.
DWF NF = 3 (P.Boyle, N.Christ @ chiral
)
Mobility edge
(M.Golterman, Y.Shamir)
(S.Aoki, Y.Taniguchi)
6
mres in dynamical simulations
• In practice Ls <
∼ a few 10 is preferable. At the same time amres must be small,
less than a few MeV, to realize the advantages of DWF.
• In NF = 0 DWF QCD (RBC) tuning RG action, the negative coefficients to
the rectangular plaquette, suppresses small dislocations drastically, but the parity
broken phase, still exists for small enough β (S. Aoki) .
• In NF = 2 , mres ∼ O(1) MeV, for Ls = 12, a−1 = 1.7 GeV using DBW2 gauge
action.
• In NF = 3, Ls = 8, an order of magnitude larger mres than NF = 2, Ls = 12.
Tuning of recutangular actions (R.Mawhiney @ spectrum 11) .
• Fructuations at short distance might cause bad things (taste breaking, exceptional
configuration) for other fermions as well.
Taku Izubuchi, Dublin, 25/July/2005
7
Sincere apologies
I apologise sincerely to those whom I won't cite. There are also many
interesting and important works and talks I should have covered, but it
was totally beyond my capability.
Let me try to understand and mention in the proceedings.
If you could drop an email to taku@bnl.gov to call my attention , I
will highly appreciate that.
Taku Izubuchi, Dublin, 25/July/2005
8
1. Performance
Taku Izubuchi, Dublin, 25/July/2005
9
Simulation for Dynamical Fermion
It is important to improve the performance of dynamical simulation to reduce the statistical error on physical output.
s
statistical error ∝
1
Nconf
Hybrid Monte Carlo ( Exact algorithm)
Prob(Uµ(x)) ∝ e
−S(Uµ )
[dUµ] =⇒ e
−H
[dUµ][dΠµ],
1 2
H = Π + S(U )
2
Conjugate momentum Πµ(x)
• 1. Refresh momentum Π, (Φ, ΦP V ).
• 2. Approximately solve Hamilton's equation (H preserved, reversible, areapreserving) :1 trajectory.
• 3. correct the approximation by a Metropolis reject/accept test :acceptance.
Taku Izubuchi, Dublin, 25/July/2005
10
Factors of Simulation Performance
Three factors that have impact on the performance of dynamical
simulations
1. Speed of integrator for Hamilton's equation
(many Matrix inversions)
2. Acceptance
3. Autocorrelation, τint, between consecutive trajectories
In this conference:
• Schwartz-preconditioned HMC (domain decomposition) (M.Lüscher @ plenary)
• mass preconditioning (Hasenbusch trick) & multiple time scale integration
(M.Hasenbusch, C.Urbach @ algorithm 2)
• Twisted mass (A.Shindler @ plenary, and therein)
• Ginsparg-Wilson fermions (M.Clark, P.Hasenfratz @ algorithm 2)
(B.Joo, R. Edwards @ chiral 4)
(A.Borici, S.Krieg @ algorithm poster )
Taku Izubuchi, Dublin, 25/July/2005
11
DWF (R)HMC experiences
• started by Columbia Univ. (G. Fleming, P. Vranas,et.al.)
• Force term modification (P.Vranas, C.Dawson)
• Chronological inverter (Brower, Ivanenko, Levi, Orginos)
• Acceptance, autocorrelation, τint, was insensitive to quark mass.
• On Nf = 2 + 1 DWF RHMC (double precision), acceptance is almost flat in light
quark mass with multiple gauge steps (∼ 4 per a fermion step) in the integrator.
0.6085
R algorithm
RHMC result
2
aδτ + b
3
2
aδτ + bδτ + c
0.60845
0.6084
0.60835
Plaquette
0.6083
• R algorithm (inexact) vs RHMC (exact)
( M.Clark @ algorithm 2)
=⇒ Use exact algorithm, unless the performance is away worse.
0.60825
0.6082
0.60815
0.6081
0.60805
0.608
• NF = 3 DWF, Plaquette
0
0.002
Taku Izubuchi, Dublin, 25/July/2005
0.004
δτ
0.006
0.008
0.01
12
Cost estimation
• Panel discussion @ Berlin Lattice conference.
• Assuming ((mπ /mρ)2 ∝ mq )
• τint ∝ 1/mq ,
• (inversion cost) ∝ 1/mq ,
• ∆t ∝ mq
• TFLOPS× Year to generate 1,000 independent configuration
(Thanks to K.Jansen, A.Ukawa, T.Yoshie) :
TflopsY = C
»
#conf
1, 000
–»
(mπ /mρ)
+S
0.6
–−6 »
L
2.12fm
–5 "
−1
a
2.60GeV
#7
S : cost for strange quark. C ≈ 0.312 (Ukawa) .
Taku Izubuchi, Dublin, 25/July/2005
13
• MILC points are from Urbach et.al
3
1k configs, a=0.08 fm, Vol=24 40
TFlops Year
2
1.5
• Scaled for a = 0.08fm, 243×40 lattice
using the formula.
Ukawa’s formula
MILC asqtad Nf=3
CP-PACS JLQCD, clover, ms(heavy)
CP-PACS JLQCD, clover, ms(light)
Urbach et. al. Wilson Nf=2
extrapolation power = -6
extrapolation power= -4
• CP-PACS JLQCD NF = 3 clover on Earth
simulator τint = 0.6/(amq )
• Urbach et.al
multiple time scale
τint(plaq)
(Sexton, Weingarten)
+
Hasenbusch accel.
1
0.5
0
0
0.2
0.4
0.6
mπ/mρ
Taku Izubuchi, Dublin, 25/July/2005
0.8
1
• Note the formula's assumptions are not
totally confirmed: try lighter quark mass
to see if τint, C∆H change.
•
fixing a−1 has no absolute meaning.
c.f. O(a) vs O(a2) discretization.
14
2. Dynamical Simulations
Taku Izubuchi, Dublin, 25/July/2005
15
Dynamical simulations
Dynamical Wilson fermions
(M.Lüscher @ plenary)
Dynamical twisted mass Wilson
Rossi) (A.Shindler @ plenary)
(R. Frezzotti and G.C.
parameters of dynamical simulations
• Gauge action
• Fermion action
• NF : number of dynamical light quarks
• a−1
• msea ( mπ /mρ)
• renormalization
Taku Izubuchi, Dublin, 25/July/2005
16
MILC collaboration
RG(Symanzik) + Improved staggered( Asqtad ) NF = 2 + 1
R algorithm
300-700 configurations, (2.4 fm)3
( (2.9fm)3 / (3.4fm)3 for coarse/fine lightest mass)
• coarse lattice a−1 = 1.6 GeV mq = 10 − 50 MeV 5 points (mπ /mρ = 0.3 − 0.6)
Added second (40% lighter) strange quark points (2 mass points).
• fine lattice a−1= 2.3 GeV mq = 10 − 30 MeV 3 points mπ /mρ = 0.3 − 0.5)
Added lightest quark mass points (now 170 confs)
• Also quenched simulations on similar lattice spacing/size to study quenched staggered chiral perturbation theory.
perturbative renormalization
(C.Bernard @ spectrum poster, also thanks to D. Toussaint)
Taku Izubuchi, Dublin, 25/July/2005
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MILC collaboration
• The new lightest quark points doesn't change mass results much, so doesn't quark
masses.
• Including new data, decay constants shifted by a significant amount.
• new (preliminary) results of decay constants.
Taku Izubuchi, Dublin, 25/July/2005
18
MILC collaboration
• only analytic terms in NNLO, (and NNNLO) are included in the fits.
• R algorithm.
• electromagnetic effects is the biggest error on mu/md.
(N.Yamada, Y.Namekawa @ spectrum 10)
• Quenched fπ is larger than experimental value by 28%.
(Setting scale by r0, σ , 21%, 14% larger respectively).
consistent with other quenched simulations ?
(A.Mason @ plenary )
(C. McNeile @ spectrum 1)
(J. Bailey @ spectrum 2)
(C.Aubin @ spectrum 10 )
Taku Izubuchi, Dublin, 25/July/2005
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(J.Shigemitsu @ heavy 2)
Coarse lattice, Partially Quenched
Coarse lattice, Full QCD
Fine lattice, Full QCD
Full QCD Stagg. ChPT
Physical Quark Mass
Φ(Bs ) / Φ(Bq )
1.3
1.2
Previous calculations
1.1
1
0.9
0
0.1
0.2
0.3
0.4
0.5
mq / ms
0.6
0.7
0.8
0.9
1
• Bq : b (NRQCD) + light quark (staggered) meson
• Φ q = fB q
p
M Bq
Taku Izubuchi, Dublin, 25/July/2005
20
staggered a0 on staggered sea
(A.Irving @ spectrum poster)
2
ground
next
pi+eta
KKbar
phys a_0
am(scalar_NS)
1.5
• flavour nonsinglet scalar
• Spin × Taste = 1 ⊗ 1
• excited state is compatible to
a0(980)
1
• ground state : partially quenched effect ?
0.5
• (S.Dürr @ plenary)
0
0
C(t) =
1
X
2
3
t_min
(n) −m(n) t
A
e
4
+
5
6
(n)
+m∗ t
A(n)
∗ e
n
m∗ : γ4γ5 ⊗ γ4γ5
Taku Izubuchi, Dublin, 25/July/2005
(taste-split pion)
21
DWF a0 on staggered sea
(S.Prelovsek @ spectrum 8)
tuning 1: Mπ
DWF
8e-04
=Mπ5 (LHPC); tuning 2: Mπ
DWF
a0 correlator for mq=0.01/0.05
=MπI
2
tuning 1 (a ∆Mix=0)
2
tuning 1 (a ∆Mix=0.01)
4e-04
tuning 1 (a ∆Mix=-0.01)
2
tuning 1 (a ∆Mix=-0.02)
2
tuning 2 (a ∆Mix=-0.01)
2
tuning 2 (a ∆Mix=-0.02)
0e+00
2
tuning 2 (a ∆Mix=0)
2
tuning 2 (a ∆Mix=0.01)
• For DWF-valence + DWF-sea, C(t) <
0 for mπ (sea) > mπ (val), vice versa.
(S. Prelovsek,et.al.)
• DWF a0 could be a ``detector'' of
mπ (sea).
-4e-04
-8e-04
• Partially quenched ChPT.
2
0
2
4
6
8
10
12
14
16
• For GW-valence pion on staggered sea: mπ (val)=mπ,I (sea) leads ``continuum like''
NLO pion mass formula (O.Baer et.al.) .
• For DWF-valence + staggered-sea mixed action , a0's C(t) is still negative for
mπ,5(sea) = mπ (val) for a range of unknown parameter ∆mix.
• DWF a0 feels staggered mπ (sea) is heavier than NG pion mπ,5 ?
Taku Izubuchi, Dublin, 25/July/2005
22
CP-PACS and JLQCD collaboration
• RG improved gauge action + nonperturbatively O(a) improved Wilson NF = 2 + 1,
• 3k-10k trajectories,(2fm)3 box.
• a−1 = 1.6, 2.0, 2.6 GeV (mπ /mρ = 0.60 − 0.78)
• measure on dynamical (unitary, msea = mval ) points.
• Exact NF =2+1, PHMC (K.Ishikawa)
• perturbative renormalization
• AWI quark masses
AW I
mq
=
∆4A4(t)J5(0)
2(J5(t)J5(0))
• r0 = 0.5fm is consistent with mρ input.
(T. Ishikawa’s talk @ spectrum 3, S.Takeda @ spectrum 2)
Taku Izubuchi, Dublin, 25/July/2005
23
ms
MS
(µ=2GeV) [MeV]
120
K-input
110
Nf=0,VWI
Nf=2,VWI
100
Nf=0,AWI
90
Nf=2,AWI
80
Nf=2+1,AWI
ms
MS
(µ=2GeV) [MeV]
Nf=2+1,VWI
• polynomial chiral extrapolations.
φ-input
140
130
Nf=0,VWI
Nf=2,VWI
120
Nf=0,AWI
110
Nf=2,AWI
100
90
Nf=2+1,AWI
80
Nf=2+1,VWI
70
• perturbative renormalization.
0
0.01
0.02 0.03
2
2
a [fm ]
Taku Izubuchi, Dublin, 25/July/2005
0.04
0.05
24
NF = 2 Dynamical Wilson simulations
• ALPHA
Wilson + nonperturbatively O(a) improved Wilson NF = 2,
a−1 = 2.1 , 2.4, 2.8 GeV (mps = 495 MeV)
nonperturbative renormalization (Schrodinger functional)
(M.D.Morte’s talk @ improvement 1, also thanks to F.Knechtli)
• QCDSF-UKQCD
Wilson + nonperturbatively O(a) improved Wilson NF = 2,
a−1 = 2.1, 2.4, 2.8 GeV ( mπ /mρ ≥ 0.6)
NLO
nonperturbative renormalization (RI-MOM)
(R.Horsley’s talk @ spectrum 8, D.Pleiter @ spectrum 4,
also thanks to G.Schierholz)
• SPQcdR
Wilson + Wilson NF = 2,
a−1 = 3.2 GeV (mπ /mρ = 0.63 − 0.75)
nonperturbative renormalization (RI-MOM)
Also quenched simulation at similar at a
(C.Tarantino’s talk @ spectrum 8)
Taku Izubuchi, Dublin, 25/July/2005
25
SPQcdR
2.09
0.075
2.08
(aMP(κs,κv1,κv2) −aR0(κs))/(amv
0.055
0.045
2
(aMP(κs,κv1,κv2))
2
AWI
)
0.065
κs=0.1535
κs=0.1538
κs=0.1540
κs=0.1541
0.035
0.025
0.015
0.02
AWI
am
0.025
(κs,κv1,κv2)
0.03
0.035
2.07
2.06
2.05
2.04
κs=0.1535
κs=0.1538
κs=0.1540
κs=0.1541
2.03
2.02
2.01
0.015
0.02
0.025
AWI
ams
0.03
0.035
• mπ /mρ ≥ 0.6, too heavy ?
• Chiral extrapolation, Wilson ChPTs (O.Baer et.al., S. Aoki) .
• Perturbative renormalizations tend to underestimate quark mass ?
Taku Izubuchi, Dublin, 25/July/2005
26
RBC collaboration
• RG(DBW2) + Domain Wall Fermions, NF = 2
• a−1 = 1.7 GeV (mπ /mρ = 0.54 − 0.65), (1.9fm)3 box.
6k trajectories, 94 confs.
• non-perturbative renormalization (RI-MOM)
• LO and NLO ChPT fit.
• Ls = 12, mres = 0.001372(44) ∼ 0.1msea ∼ a few MeV.
( C.Dawson, T.Blum’s talk @ plenary)
( S.Prelovsek @ spectrum 8, N.Yamada @ spectrum 10)
Taku Izubuchi, Dublin, 25/July/2005
27
Pseudoscalar decay constant
0.115
0.11
• NLO fits are also examined.
0.105
0.1
• mval , msea ∈ [0.01, 0.03]
• 30% smaller f than linear fit.
• Larger mass points are missed
badly.
=⇒ LO (linear) extrapolation.
0.095
0.09
0.085
0.08
mdyn=0.02
0.075
mdyn=0.03
0.07
mdyn=0.04
mdyn=m
0.065
0.06
0.055
-0.01
Taku Izubuchi, Dublin, 25/July/2005
0
0.01
0.02
0.03
mvalence
0.04
0.05
0.06
28
Pseudoscalar Meson mass
Fit using msea,val < 0.03 only
msea=0.02
msea=0.03
( msea=0.04 )
4.5
• NLO fit using msea,val ≤ 0.03
not inconsistent.
4
• constraints:
• m2ps = 0 at mval,sea = −mres,
• f = 0.0781 from linear fit of fps.
m
2
ps
/ ( mval + mres )
5
3.5
3
0
0.01
0.02
Taku Izubuchi, Dublin, 25/July/2005
0.03
0.04
0.05
29
Physical Results
(max)
• NLO fits results using m2ps at mf = msea,val ≤ mf
. Pseudo-scalar wall-point
(upper two column), and axial-vector wall point. uncorrelated χ2. GasserLeutwyler low energy constants Li multiplied by 104 at Λχ = 1 GeV.
(max)
mf
0.03
0.04
0.03
0.04
χ2/dof
0.1(1)
2(1)
0.3(2)
1.9(9)
2 B0
4.0(3)
4.2(1)
4.0(3)
4.2(1)
L4 − 2L6
−1.5(7)
−0.2(4)
−1.9(8)
−0.4(4)
L5 − 2L8
−2(1)
−1.1(4)
−1(1)
−0.8(3)
• By linear extrapolations/interpolations for fps to m̄ and ms,
fπ
fK
fK /fπ
NF = 2
134(4)
157(4)
1.18(1)
experiment
130.7
160
1.224
NF = 0
129.0(50)
149.7(36)
1.118(25)
better agreement with experiment than quenched DWF simulations.
Taku Izubuchi, Dublin, 25/July/2005
30
RBC and UKQCD collaboration
• RG(Iwasaki, DBW2) + Domain Wall Fermions NF = 2 + 1
• Ls = 8 parameter search runs. amres <
∼ O(0.01)
• a−1 = 1.7-2.0 GeV
• QCDOC, QCDOC collaboration (T.Wettig @ plenary)
• R algorithm and Exact RHMC algorithm (M. Clark @ algorithm 2)
in CPS++ (maintainer: C.Jung)
• 1.5-6 k trajectories.
• 243 × 64, Ls = 16 started.
preliminary investigations
Taku Izubuchi, Dublin, 25/July/2005
31
(K.Hashimoto @ spectrum 11)
(J.Noaki) (L.Shu)
Nf=3, DWF (DBW2)
5.4
5.2
• Static quark potential
(preliminary)
β=0.72
β=0.764
β=0.78
5
• r0 = 0.5 fm
β
DBW2
0.764
0.72
Iwasaki 2.2
2.13
4.8
r0
4.6
4.4
4.2
4
3.8
3.6
0
0.01
0.02
0.03
mu,d + mres
Taku Izubuchi, Dublin, 25/July/2005
0.04
0.05
a−1
2.0 GeV
1.7 GeV
2.1 GeV
1.8 GeV
• consistent with fπ , mρ inputs
within ∼ 10%.
32
Spectrum
(C.Maynard @ spectrum 11)
(S. Cohen @ weak 2)
DBW2 β=0.72
IW β=2.2
DBW2 β=0.764
IW β=2.13
1.6
Meson Spectrum on ms =0.04, ml =0.02
f2 1.6
a1
1.4
a0
1.2
Ρ
1. GeV
Π 0.8
1
0.8
1.4
M
mN / mV
1.5
0.6
f2
a1
a0
Ρ
0.6
0.4
1.3
K
0.2
0.4
0.2
Π
1.2
0.2
0.4
0.6
mP / mV
0.8
1
0
0.02
mav
0.04
0.06
0
roughly consistent with experimental value
Taku Izubuchi, Dublin, 25/July/2005
33
(A.Yamaguchi @ chiral 2)
topology, hq̄qi, ...
(R. Tweedie @ spectrum 8)
Scaling study of decay constants, ....
(M.Lin @ spectrum 11)
evolution details, decay constants....
0.8
0.14
sea
= 0.01, degenerate
sea
mu
sea
mu
sea
mu
sea
mu
= 0.02, degenerate
mu
0.12
0.75
= 0.04, degenerate
0.7
= 0.01, nondegenerate
0.65
fπ
mρ
AV
= 0.02, nondegenerate
dynamical extrapolation
ml = 0.01, mh = 0.04
ml = 0.02, mh = 0.04
ml = 0.04, mh = 0.04
dynamical points
Linear extrapolation
0.6
0.1
0.55
0.5
0.08
-0.02
-0.01
0
0.01
0.02
(m1 + m2) / 2
Taku Izubuchi, Dublin, 25/July/2005
0.03
0.04
0.05
0.45
-0.02
-0.01
0
0.01
mval
0.02
0.03
0.04
0.05
34
GW/overlap/chirally improved dynamical simulations
(P.Majumdar @ chiral 2)
(D.Kadoh @ chiral 2)
(T.DeGrand @chiral 3)
(B.Joo @chiral 4)
(W.Ortner @ chiral poster)
(Y.Kikukawa @ chiral poster)
(S.Schaefer @chiral 3)
(R.Edwards @chiral 4)
(W. Kamleh @ algorithms poster)
Taku Izubuchi, Dublin, 25/July/2005
(S. Kreig @ algorithms poster)
35
3. quark masses
Taku Izubuchi, Dublin, 25/July/2005
36
Light quark masses
Quark mass is a fundamental parameter of the standard model Lagrangian, which is not directly accessible from experiments due to confinement.
• Lattice QCD : map between hadronic observables (hadron mass, decay constant)
and quark mass,
(exp)
Mhad(mq ) = Mhad
• fix lattice scale, a−1 (Sommer scale r0, mρ, fπ )
• Extrapolate to chiral regime (mu,d ∼ O(1) MeV).
• mass renormalization, Z factors, for non-lattice community.
• Extrapolate to continuum (a → 0).
Taku Izubuchi, Dublin, 25/July/2005
37
map between hadronic mass and quark mass on
lattice
• Set lattice scale, a−1, from mρ,
r0, or fπ .
• quark mass at physical Kaon mass
(horizontal line)
mdyn=0.02
0.15
mdyn=0.03
mdyn=0.04
2
(aM)K
mdyn, mval 1 = mud
0.1
• By using non-degenerate ChPT
formula (red dots), amstrange =
0.0446(29) is extracted.
0.05
0
0
0.01
0.02
mvalence
Taku Izubuchi, Dublin, 25/July/2005
0.03
0.04
0.05
• If one uses dynamical, msea =
mval , points instead of NF =
2
sea
quarks,
one
finds
amstrange = 0.04177(64), 7%
smaller than partially quenched
analysis.
38
Operator Renormalization on lattice
Lattice perturbative calculation (improved)
RI-MOM (Rome/Southhampton)
Schrodinger Functional (ALPHA)
Real-space NPR (Giménez et.al.) (V.Porretti @ spectrum 8)
Taku Izubuchi, Dublin, 25/July/2005
39
NPR(RI-MOM) on dynamical lattice
• measure quark propagator,SF (q), on Landau gauge fixed gauge configuration.
• calculate amputated green function of bilinear operators, Γ = 1, γ5, γ5γµ, ...
˙
¸
¯
ΠΓ = u(−p)[ūΓd]d(q) AM P
˛
Tr (ΓΠΓ) ˛˛
ΛΓ =
Tr(ΓΓ) ˛p2,q2=µ2
on lattice ensemble.
• Subtract mass pole to avoid non-perturbative effects (hq̄qi) by fitting
Λγ5
Zq
c1
=
+
+ c3mq + · · ·
mq
ZP
at ΛQCD |p| a−1 on each sea quark ensemble.
(Zq quark field normalization, ZP,S,A pseudoscalar, scalar, axial current)
Taku Izubuchi, Dublin, 25/July/2005
40
NPR(RI-MOM) on dynamical lattice...
3
2.5
ΛP (1/m pole subtracted)
2
ΛS (1/m pole subtracted)
• ΛP ≈ ΛS ≈ ∂S −1/∂m →
-1
mass slope of Tr S
2
• convert from RI to M S with c(pa)2
subtraction.
1.5
• constant fit all msea (mild dependency).
1
0.5
0
0
Zq
ZP
• ZP = 0.62(5)
(250 MeV ≤ ΛQCD ≤ 300 MeV)
0.5
1
1.5
2
(pa)
Taku Izubuchi, Dublin, 25/July/2005
2
2.5
3
41
recent dynamical strange quark masses
based on ALPHA's compilation (Thanks to F.Knechtli) + new results.
Preliminary
140
mS (MS µ=2GeV) [MeV]
120
100
80
60
ALPHA Nf=2 NPR
ALPHA Nf=2 NPR
CP-PACS Nf=2 pert
CP-PACS/JLQCD, Nf=3, pert.
JLQCD Nf=2 pert
HPQCD, MILC, UKQCD Nf=3, pert
QCDSF UKQCD, Nf=2, VWI, NPR
QCDSF UKQCD, Nf=2, AWI, NPR
RBC Nf=2 NPR
SPQcdR Nf=2 NPR
40
20
0
0
0.02
Taku Izubuchi, Dublin, 25/July/2005
0.04
0.06
2
(a/r0)
0.08
0.1
42
NF = 2, 3 (difference is small in CP-PACS/JLQCD)
scale is r0 = 0.5 fm. (MILC corresponds to r0 = 0.467 fm, not
corrected)
chiral extrapolation ?
perturbation tends to give smaller Zm ?
(QCDSF-UKQCD, SPQcdR, ALPHA)
DWF
NPR
Pert (Kc)
ZV,A 0.7574(1) 0.770
ZS,P 0.62(5)
0.847
Taku Izubuchi, Dublin, 25/July/2005
43
Conclusions
• Performance of Dynamical simulation is updated.
• We need ``fair'' way to compare different simulations other than fixing a.
• Seemingly promising {new,improved} algorithms.
• Now three NF = 2 + 1 dynamical simulations.
• New dynamical Wilson fermion simulations with NPR.
• New strange quark mass results (4 Wilson, 1 DWF).
• Systematic error (chiral extrapolation, perturbative Z )
Taku Izubuchi, Dublin, 25/July/2005
44