physical point simulation in 2+1 flavor lattice qcd · physics plan aim: 2+1 flavor qcd simulation...
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Physical Point Simulation in 2+1 Flavor
Lattice QCD
Y.Kuramashi for PACS-CS Collaboration
(Univ. of Tsukuba)
July 29, 2009
1
Plan of talk
§1. The PACS-CS project
§2. Reweighting method
§3. Parameters
§4. Preliminary Results
§5. Summary
2
§1. The PACS-CS projectParallel Array Computer System for Computational Sciences
operation started on 1 July 2006 at CCS in U.Tsukuba
3
collaboration membersphysicists:S.Aoki, N.Ishizuka, D. Kadoh, K.Kanaya, TsukubaY.Kuramashi, Y.Namekawa, Y.Taniguchi, A.Ukawa,N.Ukita, T.YoshieK.-I.Ishikawa, M.Okawa HiroshimaT.Izubuchi BNL
computer scientists:T.Boku, M.Sato, D.Takahashi, O.Tatebe TsukubaT.Sakurai, H.Tadano
4
Physics plan
aim: 2+1 flavor QCD simulation at the physical point
PACS-CS CP-PACS/JLQCDgauge action Iwasaki Iwasakiquark action clover with cNP
SW clover with cNPSW
a[fm] 0.07,0.1,0.122 0.07,0.1,0.122volume ∼> (3fm)3 ∼ (2fm)3
mAWIud physical point 64MeV
algorithm for ud DDHMC with improvements HMCalgorithm for s UV-filtered exact PHMC exact PHMC
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Why is physical point simulation necessary?
• difficult to trace chiral logs for chiral extrapolation
• ChPT is not always a good guiding principle
• need a proper treatment of resonances
• simulations with different up and down quark masses
⇒ there are two types of problems
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(1) Computaional cost
0 0.2 0.4 0.6 0.8 1mπ/mρ
0.0
2.0
4.0
6.0
8.0
10.0
Tfl
ops
year
s
HMCDDHMCMPDDHMC
Nf=2+1
10000 MDa=0.1fmL=3fm
pysi
cal p
t
successfully solved by (Mass-Preconditioned) DDHMC
PRD79(2009)034503
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(2) Fine tuning on physical point
need 3 simulation points within a few MeV differenes around the
physical point in 2+1 flavor case
⇒ demanding computational cost
try reweighting method both for ud and s quarks
8
§2. Reweighting method
original:(κud, κs) ⇒ target:(κ′ud, κ′
s) assuming ρq ≡ κ′q/κq ≈ 1
⟨O[U ](κ′ud, κ′
s)⟩(κ′ud,κ′
s)=
⟨O[U ](κ′ud, κ′
s)Rud[U ]Rs[U ]⟩(κud,κs)
⟨Rud[U ]Rs[U ]⟩(κud,κs)
reweighting factors
Rud[U ] = |det [W [U ](ρud)]|2 , Rs[U ] = det [W [U ](ρs)]
where W [U ](ρq) ≡Dκ′q
[U ]
Dκq[U ]
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Evaluation of Rud[U ]
introduce a complex bosonic field η
Rud[U ] = |det [W [U ](ρud)]|2
= ⟨e−|W−1[U ](ρud)η|2+|η|2⟩η
given a set of η(i) (i = 1, . . . , Nη) with the Gaussian distribution
Rud[U ] = limNη→∞
1
Nη
Nη∑i=1
e−|W−1[U ](ρud)η|2+|η|2
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Evaluation of Rs[U ]
assume detW [U ](ρs) is positive
Rs[U ] = det [W [U ](ρs)]
= ⟨e−|W−1/2[U ](ρs)η|2+|η|2⟩ηTaylor expansion for W−1/2[U ](ρs)η
W−1[U ](ρs) =Dκs[U ]
Dκ′s[U ]
= 1 − (1 − ρs)(1 − (Dκ′
s[U ])−1
)= 1 − X[U ](ρs)
where |1 − ρs| ≪ 1
⇒ expansion of W−1/2[U ](ρs)η in terms of X[U ](ρs)
11
Additional technique Hasenfratz-Hoffmann-Schaefer
determinant breakup: divide (κ′q − κq) into NB subintervals
κq ⇒ κq + ∆q ⇒. . . ⇒ κq + (NB − 1)∆q ⇒ κ′q
with ∆q = (κ′q − κq)/NB
det[W−1[U ](ρq)
]= det
[W−1[U ]
(κq + ∆q
κq
)]× det
[W−1[U ]
(κq + 2∆q
κq + ∆q
)]
× . . . × det
[W−1[U ]
(κ′
q
κq + (NB − 1)∆q
)],
reduce fluctuations of the reweighting factors
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§3. Parameters
simulation parameters
– original: (κud,κs)=(0.137785,0.136600)– 1000 MD time, still increasing– MP2DDHMC for ud quark with 84 block, ρ1 = 0.9995, ρ2 = 0.99– UV-filtered PHMC for s quark with Npoly = 220
reweighting parameters
– target: (κ′ud,κ
′s)=(0.137800,0.136645), (0.137800,0.136690)
– breakup intervals: ∆ud = (0.137800 − 0.137785)/2,– breakup intervals: ∆s = (0.136690 − 0.136600)/4– Nη = 10 for stochastic estimation of Rud,s
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§4. Preliminary Results
concentrate on (κ′ud, κ′
s) = (0.137800,0.136645)
• results for Rud,s
• Reweighting for plaquette
• Reweighting for mπ, mK, mΩ
(physical inputs for mud, ms, a−1)
• hadron spectrum
• locate the physical point
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Reweighting factors on each configuration
0 50 100 150 200
Conf.
0.01
0.1
1
10
100
Rud
Rs
Rud
Rs
Reweighting factors
normalized with ⟨Rud,s⟩ = 1
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Reweighting factors vs. plaquette value
0.5708 0.5709 0.571 0.5711 0.5712 0.5713
PLQ
0.01
0.1
1
10
100
Rud
Rs
Rud
Rs
Reweighting factors
clear dependence
16
Plaquette histgram w/ and w/o Rud
-0.0002 -0.0001 0 0.0001 0.0002PLQ − <PLQ>
0
5
10
15
20
25 originalreweighted w/ R
ud
distribution is slightly moved toward larger values
17
Plaquette histgram w/ and w/o Rs
-0.0002 -0.0001 0 0.0001 0.0002PLQ − <PLQ>
0
5
10
15
20
25 originalreweighted w/ R
s
distribution is slightly moved toward larger values
18
π effective mass
0 10 20 30
t0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
originalPQPQ+RW
π effective mass
reweighting effects are observed
19
K effective mass
0 10 20 30
t0.22
0.23
0.24
0.25
originalPQPQ+RW
K effective mass
similar to π case
20
Ω effective mass
0 5 10 15 20
t0.72
0.74
0.76
0.78
0.80
0.82
0.84
originalPQPQ+RW
Ω effective mass
mΩ is slightly decreased
21
Hadron spectrum in comparison with experiment
0
-0.2
-0.1
0.0
0.1
0.2
0.3
π K ρ K* φ N Λ Σ Ξ ∆ Σ* Ξ* Ωη
ss
originaltarget
(mh/mΩ)
lat / (m
h/mΩ)
exp - 1
mπ/mΩ, mK/mΩ are properly tuned
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Locate the physical point
7.256 7.257 7.258 7.2581/κ
ud
7.3150
7.3175
7.3200
7.3225
1/κ s
originaltarget (0.137800,0.136645)target (0.137800,0.136690)estimated physical point
physical point
confirmed with three data point analysis
∆mud ∼ 1MeV, ∆ms∼<3MeV
23
§5. Summary
– Chiral extrapolation is not necessary anymore
– (6fm)3 box simulation is under way
– starting point for precision measurements
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