Field Theory Simulation towards
FugakuYasumichi Aoki (Field Theory Research Team)17, February 2020
2nd R-CCS Inernational SymposiumQuantum Field Theory• Quantum mechanics: physics framework for microscopic world• Special Relativity:
physics framework of fast moving particle• Quantum Field Theory (QFT)• Standard Model of Particle Physics : most successful application of QFT

2

Quantum Field Theory• Quantum mechanics: physics framework for microscopic world• Special Relativity:
physics framework of fast moving particle• Quantum Field Theory (QFT)• Standard Model of Particle Physics : most successful application of QFT
Standard Model• Electromagnetism• Weak Interaction• QCD

StandardModel

2

Quantum Field Theory• Quantum mechanics: physics framework for microscopic world• Special Relativity:
physics framework of fast moving particle• Quantum Field Theory (QFT)• Standard Model of Particle Physics : most successful application of QFT
Standard Model• Electromagnetism• Weak Interaction• QCD• Test of the Standard Model• Seeking physics beyond the Standard Model for “New” Physics
are central targets of particle physics

Standard
Model
New Physics

2

Quantum Field Theory• Quantum mechanics: physics framework for microscopic world• Special Relativity:
physics framework of fast moving particle• Quantum Field Theory (QFT)• Standard Model of Particle Physics : most successful application of QFT
Standard Model• Electromagnetism• Weak Interaction• QCD• Test of the Standard Model• Seeking physics beyond the Standard Model for “New” Physics
are central targets of particle physics

QCD
Standard
Model
New Physics• QCD has most complex dynamics → numerical simulation is most powerful tool2

Fermilab/ J-Parc(g-2)μheavy flavor KEK
QCDStandardModel

3

Fermilab/ J-Parc(g-2)μheavy flavor KEK
QCDStandard
Model
New Physics

3

heavy flavor

Compute=?
≠MeasureKEK
QCD
StandardModel

4

heavy flavor

Compute (Vij) =reality is much complicatedMeasureConstrains parameters in Standard Model
KEK

Kobayashi-Maskawa matrix elements Vij

QCDStandardModel

Q: consistency btw
many different
processes ?

5

Fermilab/ J-Parc(g-2)μheavy flavor KEK
QCDStandard
Model
New Physics

proton decay

Kamioka6

THOMAS BLUM, TAKU IZUBUCHI, AND EIGO SHINTANIREVIEW D 88, 094503 (2013)
Kamioka PHYSICAL
protondecay

holds:forOðappxÞ
covarianton eachnew
configuration,rather
QCD
theistooltobridgephysicsðappxÞ
gðappxÞ;g3α [GeV ]error from OðrestÞ is below, say, one-half of the desired final
precision. Too accurate an approximation wastes
resour½U $ ¼ O½U$).
than on average, O
QCD
ces. In OðimpÞ , most of the statistical fluctuation is carried
Note that OðappxÞ and OðappxÞ;g refer to the approximations
proton decay matrix element as an example
before and after applying a symmetry transformation g.
NG ð) 1Þby OðappxÞ , which is reduced by averaging overStandard• bridge
theoriesand define
experiments
measurements with smaller cost (appx-2). Balance
Model beUsingbetween
O and newOðappxÞ
one canan improved
observable(GUTs)(SuperKamiokande etc) tween these opposing parts of the method allows CAA to
New Physics
reduce statistical errors significantly while keepingtheðappxÞ for a testðimpÞðrestÞ
non-chiralfermions
usedO¼Oþ OG ;
computational cost low.
(2)
• chiral extrapolation : largest systematic
uncertainty
In the framework of CAA the best choice of approxi1 XðappxÞ
ðrestÞ
ðappxÞ
ðappxÞ;g1/Proton∝ [QCDparam.]* [NewPhys.
param]
O
¼O'O
;
OG
¼
O
;
mationdepends Lifetimeon the target
observables
and latticepa• physical point simulation willsolve N
thiscompletely
G g2G
rameters such as quark mass and volume. In principle, any• small mass, large volume (644, 964) required
set of lattice symmetries, G, can DWF
be used inoldCAA. We limit
where an average over NG symmetry transformations in G
4of translation• is
WF 64 symmetries in the
Alltaken.
mode averaging (AMA) with many sloppy linear solv ourselves to the case
0.025
) new
4
WF 96
following
examples.
ðimpÞFor• appx-1,
the statistical
error
of N
hOG=256
i iscorrelation:r≃0.9994
OK:
The first example is LMA. In LMA eigensystems of thesﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Hermitian Dirac operator
are obtained for the part of the
0.02
1errðimpÞ ( err 2ð1 ' rÞ þ;(3)long• old:
spectrumclosest to zero,
distanceNG
extrapolation
DH vi ¼ !0.015
ði ¼ 1; 2; . . . ; Neig Þ;(4)
i vi ;
which can be made smaller than the original (err) by avsexpected fromjudicious choice of OðappxÞ . The fluctuation from OðrestÞ , the0 < j!1 j * j!2 j * + + +an* effective
j!Neig j ¼theory!cut ;(5)
first term in (3), is suppressed due to r (1, •while
the on physical
new:
0.01
second term is reduced by 1=NG without too muchpoint
addi- simulation
which is then used to construct,
through0.2spectral0.3decom00.1
0.4
tional cost as required by appx-2 (correlations among O,
22
position, the low-mode approximation mπof[GeVthe] fermionOðappxÞ , and OðappxÞ;g have been ignored, which is a good
propagator, Aoki, Kuramashi, Shintani, Tsukamoto @ Lattice 2019 7
approximation for noisy observables or large volume). DueTHOMAS BLUM, TAKU IZUBUCHI, AND EIGO SHINTANIREVIEW D 88, 094503 (2013)
Kamioka PHYSICAL
protondecay

holds:forOðappxÞ
covarianton eachnew
configuration,rather
QCD
theistooltobridgephysicsðappxÞ
gðappxÞ;g3α [GeV ]error from OðrestÞ is below, say, one-half of the desired final
precision. Too accurate an approximation wastes
resour½U $ ¼ O½U$).
than on average, O
QCD
ces. In OðimpÞ , most of the statistical fluctuation is carried
Note that OðappxÞ and OðappxÞ;g refer to the approximations
proton decay matrix element as an example
before and after applying a symmetry transformation g.
NG ð) 1Þby OðappxÞ , which is reduced by averaging overStandard• bridge
theoriesand define
experiments
measurements with smaller cost (appx-2). Balance
Model beUsingbetween
O and newOðappxÞ
one canan improved
observable(GUTs)(SuperKamiokande etc) tween these opposing parts of the method allows CAA to
New Physics
reduce statistical errors significantly while keepingtheðappxÞ for a testðimpÞðrestÞ
non-chiralfermions
usedO¼Oþ OG ;
computational cost low.
(2)
• chiral extrapolation : largest systematic
uncertainty
In the framework of CAA the best choice of approxi1 XðappxÞ
ðrestÞ
ðappxÞ
ðappxÞ;g1/Proton∝ [QCDparam.]* [NewPhys.
param]
O
¼O'O
;
OG
¼
O
;
mationdepends Lifetimeon the target
observables
and latticepa• physical point simulation willsolve N
thiscompletely
G g2G
rameters such as quark mass and volume. In principle, any• small mass, large volume (644, 964) required
set of lattice symmetries, G, can DWF
be used inoldCAA. We limit
where an average over NG symmetry transformations in G
4of translation• is
WF 64 symmetries in the
Alltaken.
mode averaging (AMA) with many sloppy linear solv ourselves to the case
0.025
) new
4
WF 96
following
examples.
ðimpÞFor• appx-1,
the statistical
error
of N
hOG=256
i iscorrelation:r≃0.9994
OK:
The first example is LMA. In LMA eigensystems of thesﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Hermitian Dirac operator
are obtained for the part of the
0.02
1errðimpÞ ( err 2ð1 ' rÞ þ;(3)long• old:
spectrumclosest to zero,
distanceNG
extrapolation
DH vi ¼ !0.015
ði ¼ 1; 2; . . . ; Neig Þ;(4)
i vi ;
which can be made smaller than the original (err) by avsexpected fromjudicious choice of OðappxÞ . The fluctuation from OðrestÞ , the0 < j!1 j * j!2 j * + + +an* effective
j!Neig j ¼theory!cut ;(5)
first term in (3), is suppressed due to r (1, •while
the on physical
new:
0.01
second term is reduced by 1=NG without too muchpoint
addi- simulation
which is then used to construct,
through0.2spectral0.3decom00.1
0.4
tional cost as required by appx-2 (correlations among O,
22
position, the low-mode approximation mπof[GeVthe] fermionOðappxÞ , and OðappxÞ;g have been ignored, which is a good
propagator, Aoki, Kuramashi, Shintani, Tsukamoto @ Lattice 2019 7
approximation for noisy observables or large volume). Due×

THOMAS BLUM, TAKU IZUBUCHI, AND EIGO SHINTANIREVIEW D 88, 094503 (2013)
Kamioka PHYSICAL
protondecay

holds:forOðappxÞ
covarianton eachnew
configuration,rather
QCD
theistooltobridgephysicsðappxÞ
gðappxÞ;g3α [GeV ]error from OðrestÞ is below, say, one-half of the desired final
precision. Too accurate an approximation wastes
resour½U $ ¼ O½U$).
than on average, O
QCD
ces. In OðimpÞ , most of the statistical fluctuation is carried
Note that OðappxÞ and OðappxÞ;g refer to the approximations
proton decay matrix element as an example
before and after applying a symmetry transformation g.
NG ð) 1Þby OðappxÞ , which is reduced by averaging overStandard• bridge
theoriesand define
experiments
measurements with smaller cost (appx-2). Balance
Model beUsingbetween
O and newOðappxÞ
one canan improved
observable(GUTs)(SuperKamiokande etc) tween these opposing parts of the method allows CAA to
New Physics
reduce statistical errors significantly while keepingtheðappxÞ for a testðimpÞðrestÞ
non-chiralfermions
usedO¼Oþ OG ;
computational cost low.
(2)
• chiral extrapolation : largest systematic
uncertainty
In the framework of CAA the best choice of approxi1 XðappxÞ
ðrestÞ
ðappxÞ
ðappxÞ;g1/Proton∝ [QCDparam.]* [NewPhys.
param]
O
¼O'O
;
OG
¼
O
;
mationdepends Lifetimeon the target
observables
and latticepa• physical point simulation willsolve N
thiscompletely
G g2G
rameters such as quark mass and volume. In principle, any• small mass, large volume (644, 964) required
AchievementsK
set of withlattice symmetries,
G, can DWF
be used inoldCAA. We limit
where an average over NG symmetry transformations in G
4of translation• is
WF 64 symmetries in the
Alltaken.
mode averaging (AMA) with many sloppy linear solv ourselves to the case
0.025
) new
4
WF 96
following
examples.
ðimpÞFor• appx-1,
the statistical
error
of N
hOG=256
i iscorrelation:r≃0.9994
OK:
The first example is LMA. In LMA eigensystems of thesﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
HermitianDirac operator
are obtained for the part of the
0.02
HokusaiBW1errðimpÞ ( err 2ð1 ' rÞ þ;(3)long• old:
spectrumclosest to zero,
distanceNG
extrapolationand other
DH vi ¼ !0.015
ði ¼ 1; 2; . . . ; Neig Þ;(4)
i vi ;
which can be made smaller than the original (err) by a
HPCI resources
vsexpected fromjudicious choice of OðappxÞ . The fluctuation from OðrestÞ , the0 < j!1 j * j!2 j * + + +an* effective
j!Neig j ¼theory!cut ;(5)
first term in (3), is suppressed due to r (1, •while
the on physical
new:
0.01
second term is reduced by 1=NG without too muchpoint
addi- simulation
which is then used to construct,
through0.2spectral0.3decom00.1
0.4
tional cost as required by appx-2 (correlations among O,
22
position, the low-mode approximation mπof[GeVthe] fermionOðappxÞ , and OðappxÞ;g have been ignored, which is a good
propagator, Aoki, Kuramashi, Shintani, Tsukamoto @ Lattice 2019 7
approximation for noisy observables or large volume). Due×QCD for the tool to bridge new physics

operator renormalization• RI/SMOM non-perturbative renormalization

proton decay form factors• application: proton decay, nucleon charges• more demanding comp.

• improved Wilson fermions with 6 stout-link smeared• directly related to proton lifetime• admixture from chiral symmetry breaking is as
small as 1%• obtaining promising resultsa,bM

for nucleon decay4

Nf=2+1, PACS, 64 , 99 configurations

W0 (GeV2)000<π |(ud)RuL|p><K |(us)RuL|p>

0.1

new

-0.05

(on physical mass)

0.05

-0.1

old
(after long extrpl.)-0.15-0.15 -0.1 -0.05 0

0

0.05

q2 GeV200

Projector × Vertex

1.1

on-shell lepton: —q2=ml2=0-0.15 -0.1 -0.05 0

diagonal

1

LL,LL
RL,LL
A(LV),LL
LL,RL
RL,RL
A(LV),RL
LL,A(LV)
RL,A(LV)
A(LV),A(LV)

0.9
0.8

off diagonal

0.02
0

-0.02
0

0.05

0.5

1

1.5

2

2.5

2

(pa)

8

poster: Aoki, Kuramashi, Tsukamoto, Shintani @ Lattice 2019

QCD for the tool to bridge new physics

operator renormalization• RI/SMOM non-perturbative renormalization

proton decay form factors• application: proton decay, nucleon charges• more demanding comp.

• improved Wilson fermions with 6 stout-link smeared• directly related to proton lifetime• admixture from chiral symmetry breaking is as
small as 1%• obtaining promising resultsa,bM

for nucleon decay4

Nf=2+1, PACS, 64 , 99 configurations

W0 (GeV2)000<π |(ud)RuL|p>-0.05<K |(us)RuL|p>0.1

diagonal

1

LL,LL
RL,LL
A(LV),LL
LL,RL
RL,RL
A(LV),RL
LL,A(LV)
RL,A(LV)
A(LV),A(LV)

0.9

new
Extending this to all possible
final state mesons0.8(on physical mass)

0.05

-0.1

old
(after long extrpl.)-0.15-0.15 -0.1 -0.05 00

Projector × Vertex

1.1

on-shell lepton: —q2=ml2=0

0.05

q2 GeV200-0.15 -0.1 -0.05 0

off diagonal

0.02
0

-0.02
0

0.05

0.5

1

1.5

2

2.5

2

(pa)

8

poster: Aoki, Kuramashi, Tsukamoto, Shintani @ Lattice 2019

Fermilab/ J-Parc(g-2)μheavy flavor KEK
QCD

QCD like

Standard
Model
New Physics

proton decay

composite Higgs

CERN

Kamioka
9

BNL / CERN

Fermilab/ J-Parc(g-2)μDark
Matterheavy flavor KEK
QCD phase
QCD

QCD like

Standard
Model
New Physics

proton decay

composite Higgs

CERN

Kamioka9

Revealing the historyof Universe

BNL / CERN

Dark
Matter
QCD phase
QCD
Standard
Model

10

BNL / CERN

QCD phase : Post-K priority issues #9
Scientific motivation•

fundamental understanding of QCD
phase transition•

Through the use of methods with nocompromise•

spontaneous breakdown of chiralsymmetry•use of chiral fermion algorithm•

in-depth study••

role of the symmetry•role of the anomaly : U(1)A symmetry

will give most precise description of the
QCD at finite temperature➡ experiment / early universe

QCD phase
QCD
Standard
Model

Columbia plot

2nd order transition

∞
ms

∞

?

physical pt.

cross overms

1st order transition

0

mud

∞

0

mud

∞

BNL / CERN

QCD phase : Post-K priority issues #9
Scientific motivation•

fundamental understanding of QCD
phase transition•

Through the use of methods with nocompromise•

spontaneous breakdown of chiralsymmetry•use of chiral fermion algorithm•

in-depth study•

Dark
Matter•role of the symmetry•role of the anomaly : U(1)A symmetry

will give most precise description of the
QCD at finite temperature➡ experiment / early universe

QCD phase
QCD
Standard
Model
New Physics

Columbia plot

2nd order transition

∞
ms

∞

?

physical pt.

cross overms

1st order transition

0

mud

∞

0

mud

∞

QCD phase : Post-K priority issues #93

T=220 MeV, V=L x12•

use of chiral fermion algorithm
•

2

0
0

5

10

15
m [MeV]

20

25

1.0×10essential: interplay of symmetry andquantum anomaly•

demanding comp.

•

Nf=2 (ms→∞) phase: yet to be conclusive•

1.5×10knowledges being acquired•

interesting development of fate of U(1)A•around physical point → Fugaku

5.0×10

0

5

10

15
m [MeV]

2nd order transition

∞
ms

8

4

spontaneous breakdown of chiral symmetry

0.05

χt [MeV ]•∆π−δ [GeV ]Columbia plot (phase diagram for Nf=2+1 as
function of quark mass)

volume scaling study
underway

L=24
L=32
L=40
L=48

0.1

20

25

8

7

0.0

[JLQCD collab.]∞?

physical pt.

cross overms

1st order transition

0

mud

∞

0

mud

∞

QCD phase : Post-K priority issues #93

T=220 MeV, V=L x12•

use of chiral fermion algorithm•

2

1.5×100
0

demanding comp.
•

5

10

15
m [MeV]

20

25

1.0×10essential: interplay of symmetry andAchievements w/o K
quantum anomaly

KEK Blue Gene/Q
Oakforest PACS
• Nf=2 (ms→∞) phase: yet to be conclusive•

knowledges being acquired•

interesting development of fate of U(1)A•around physical point → Fugaku

5.0×10

0

5

10

15
m [MeV]

2nd order transition

∞
ms

8

4

spontaneous breakdown of chiral symmetry

0.05

χt [MeV ]•∆π−δ [GeV ]Columbia plot (phase diagram for Nf=2+1 as
function of quark mass)

volume scaling study
underway

L=24
L=32
L=40
L=48

0.1

20

25

8

7

0.0

[JLQCD collab.]∞?

physical pt.

cross overms

1st order transition

0

mud

∞

0

mud

∞

plans for QCD phasedirect access to physical point and surrounding area∞

1st order

ms∞

1st order

ms
1st order0

degenerate 3 quark system: simpler

crossover

1st order

mud∞

Planned to be explored on

Fugaku0

crossovermud∞Started using HPCI resources and Hokusai-BW
13

computational technologies and developments
Post-K/Fugaku development in the teamongoing projects and plans
1) QCD code packaging and tuning for Fugaku•

lowest revel taken from co-design
activity•

higher level, packaging, tuning

QCD codes for Fugaku and future machines2) algorithms for chiral fermions for big volume•

mostly for linear solvers•

AMA, multigrid, etc[25+] x K3) new algorithms / developments••

AI: may be used for optimizing implicit
parameters / initial guess•

integration path (start, end fixed)•

MD parameters

BQCD

QCD wide
simd library forfugakuBridge++tensor network

4) collaborations for developments and science•

priority issue #9 and successors•

international

Grid

FS
2020

Priority
issue #9co-design

Iroiro++Priority
issue #9/
JLDCD

BNL/
Edinburgh/
Regensburg
14Use of Fugaku w/ our developments
extends the reach of simulation• with Domain-wall Fermions (chiral)• QCD phase✴Nt=16 for Nf=2+1 (dynamical u,d,s quarks)‣ real chiral simulation for phase transition• Heavy flavor✴MB a ≲ 1
‣ to control discretization error‣ B→πlν, etc∞

Use of Fugaku w/ our developments

1st order

ms
1st order0

crossovermud

1st order∞

Ultimate understandingof QCD phase

Planned to be explored on Fugaku• QCD phase

1st orderms

extends the reach of simulation• with Domain-wall Fermions (chiral)∞

0crossovermud∞Started using HPCI resources and Hokusai-BW✴Nt=16 for Nf=2+1 (dynamical u,d,s quarks)

Previously, Nf=2 (only u,d quarks) or Nt=8

‣ real chiral simulation for phase transition→ lattice spacing anew/aold = 1/2• Heavy flavor✴MB a ≲ 1
‣ to control discretization error‣ B→πlν, etc∞

Use of Fugaku w/ our developments

ms
1st order0

crossovermud

1st order∞

Ultimate understandingof QCD phase

Planned to be explored on Fugaku• QCD phase

1st orderms

extends the reach of simulation• with Domain-wall Fermions (chiral)∞

1st order0

crossover∞mud

Figure 34: Summary of |Vub | and |Vcb | determinations.
to using the BGL and CLN parameterization for the B
using
HPCIlines
resourcesand Hokusai-BW
TheStarted
solid anddashedcorrespondto 68% and 95
the text, baryonic modes are not included in our avera
two cases are (|Vcb |, |Vub |) × 103 = (41.47 ± 0.70, 3.76 ±(|Vcb |, |Vub |) × 103 = (39.45 ± 0.60, 3.74 ± 0.14) with a p-v
B → D ∗ parameterizations, respectively.

More stringent constraint
on Standard Model✴Nt=16 for Nf=2+1 (dynamical u,d,s quarks)

Previously, Nf=2 (only u,d quarks) or Nt=8

‣ real chiral simulation for phase transition→ lattice spacing anew/aold = 1/2• Heavy flavor
193✴MB a ≲ 1
‣ to control discretization error‣ B→πlν, etc

Previously MB a ≃ 2→ lattice spacing anew/aold ≲ 1/2