VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 55 (2022)

Subnuclear System Research Division
RIKEN BNL Research Center
Computing Group
1. Abstract
The computing group founded in 2011 as a part of the RIKEN BNL Research Center established at Brookhaven National Laboratory in New York, USA, and dedicated to conduct researches and developments for large-scale physics computations important forparticle and nuclear physics. The group was forked from the RBRC Theory Group.
The main mission of the group is to provide important numerical information that is indispensable for theoretical interpretationof experimental data from the ﬁrst principle theories of particle and nuclear physics. Their primary area of research is lattice quantum
chromodynamics (QCD), which describes the sub-atomic structures of hadrons, which allow us the ab-initio investigation for stronglyinteracting quantum ﬁeld theories beyond perturbative analysis.
The RBRC group and its collaborators have emphasized the necessity and importance of precision calculations, which will precisely check the current understandings of nature, and will have a potential to ﬁnd a physics beyond the current standard model offundamental physics. We have therefore adopted techniques that aim to control and reduce any systematic errors. This approach has
yielded many reliable results.
The areas of the major activities are R&D for high performance computers, developments for computing algorithms, and researches of particle, nuclear, and lattice theories. Since the inception of RBRC, many breakthroughs and pioneering works has carriedout in computational forefronts. These are the use of the domain-wall fermions, which preserve chiral symmetry, a key symmetry forunderstanding nature of particle nuclear physics, the three generations of QCD devoted supercomputers, pioneering works for QCD
calculation for Cabibbo-Kobayashi-Maskawa theory, QCD + QED simulation for isospin breaking, novel algorithm for error reduction
in general lattice calculation. Now the chiral quark simulation is performed at the physical up, down quark mass, the precision formany basic quantities reached to accuracy of sub-percent, and the group is aiming for further important and challenging calculations,such as the full and complete calculation of CP violating K → ππ decay and ε /ε, or hadronic contributions to muon’s anomalous
magnetic moment g − 2. Another focus area is the nucleon’s shape, structures, and the motion of quarks and gluon inside nucleon
called parton distribution, which provide theoretical guidance to physics for sPHENIX and future Electron Ion Collider (EIC), Hyper
Kamiokande, DUNE, or the origin of the current matter rich universe (rather than anti-matter). Towards ﬁnite density QCD, they also
explore Quantum Computing to overcome the sign problem. The Machine Learning (ML) and Artiﬁcial Intelligence (AI) are the new
topics some of members are enthusiastically studying lately.

2. Major Research Subjects(1) Search for new law of physics through tests for Standard Model of particle and nuclear physics, especially in the frameworkof the Cabibbo-Kobayashi-Maskawa (CKM), hadronic contributions to the muon’s anomalous magnetic moment (g − 2) for
FNAL and J-PARC’s experiments, as well as B physics at Belle II and LHCb
(2) Nuclear Physics and dynamics of QCD or related theories, including study for the structures of nucleons related to physics
for Electron Ion Collider (EIC or eRHIC), Hyper Kamiokande, T2K, DUNE
(3) Theoretical and algorithmic development for lattice ﬁeld theories, QCD machine (co-)design and code optimization

3. Summary of Research Activity
In 2011, QCD with Chiral Quarks (QCDCQ), a third-generation lattice QCD computer that is a pre-commercial version of IBM’s
Blue Gene/Q, was installed as an in-house computing resource at the RBRC. The computer was developed by collaboration among
RBRC, Columbia University, the University of Edinburgh, and IBM. Two racks of QCDCQ having a peak computing power of 2 × 200
TFLOPS are in operation at the RBRC. In addition to the RBRC machine, one rack of QCDCQ is owned by BNL for wider use forscientiﬁc computing. In 2013, 1/2 rack of Blue Gene/Q is also installed by US-wide lattice QCD collaboration, USQCD. The group
has also used the IBM Blue Gene supercomputers located at Argonne National Laboratory and BNL (NY Blue), and Hokusai and
RICC, the super computers at RIKEN (Japan), Fermi National Accelerator Laboratory, the Jeﬀerson Lab, and others. From 2016, thegroup started to use the institutional cluster both GPU and Intel Knight Landing (KNL) clusters installed at BNL and University ofTokyo extensively.
Such computing power enables the group to perform precise calculations using up, down, and strange quark ﬂavors with proper
handling of the important symmetry, called chiral symmetry, that quarks have. The group and its collaborators carried out the ﬁrst
calculation for the direct breaking of CP (Charge Parity) symmetry in the hadronic K meson decay (K → ππ) amplitudes, ε /ε, which
provide a new information to CKM paradigm and its beyond. They also provide the hadronic contribution in muon’s anomalous magnetic moment (g − 2)μ . These calculation for ε /ε, hadronic light-by-light of (g − 2), are long waited calculation in theoretical physics
delivered for the ﬁrst time by the group. The K → ππ result in terms of ε /ε currently has a large error, and deviates from experimental
results by 2.1σ. To collect more information to decide whether this deviation is from the unknown new physics or not, the group continues to improve the calculation in various way to reduce their error. Hadronic light-by-light contribution to (g − 2)μ is improved bymore than two order of magnitudes compared to our previous results. As of 2019 summer, their calculation is among the most precise
determination for the g − 2 hadronic vacuum polarization (HVP), and only one calculation in the world for the hadronic light-by-light(HLbL) contribution at physical point. These (g − 2)μ calculations provide the ﬁrst principle theoretical prediction for on-going newexperiment at FNAL and also for the planned experiment at J-PARC. Other projects including ﬂavor physics in the framework of the- 328 -

VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 55 (2022)

48I-64I
24D
32D
48D
32Dﬁneaμ × 1010

25
20
15
10

−4
−6
−8
−10

5
0

0
−2

aμ × 1010

30

−12
0

0.05

0.1

0.15

0.2

−14

1/(mμ L)2

Connected diagrams

Fig. 1. Feynman diagrams for Lattice QCD computations of Muon’s anomalous magnetic moment (g − 2)μ to take into account for the eﬀects ofquark’s electric charges. Each diagram, in which the black dots connecting the quark propagators (solid curves) are the electric current emmitting or absorbing photons (wave curves), represents a part of the isospin
breaking eﬀects to hadronic vacuum polarization contribution to (g−2)μ(top plot).

0

0.05

0.1

0.15

0.2

1/(mμ L)2

Disconnected diagrams

Fig. 2. Current summary of the Hadronic Vacuum Polarization (HVP) contribution for Muon’s anomalous magnetic moment (g − 2)μ . Above theupper horizontal line shows various Lattice QCD determinations of HVP
while the red results from hadronic decay of electron positron scattering(R-ratio), the green bands is the experimental results of (g − 2)μ showing
a 3–4σ discrepancies.

CKM theory for kaons and B mesons that include the new calculation of b-baryon decay, Λb → p; the electromagnetic propertiesof hadrons; the proton’s and neutron’s form factors and structure function including electric dipole moments; proton decay; nucleon
form factors, which are related to the proton spin problem or neutrino-nucleon interaction; Neutron-antineutron oscillations; inclusive
hadronic decay of τ leptons; nonperturbative studies for beyond standard model such composite Higgs or dark matter models fromstrong strongly interacting gauge theories; a few-body nuclear physics and their electromagnetic properties; QCD thermodynamics
in ﬁnite temperature/density systems such as those produced in heavy-ion collisions at the Relativistic Heavy Ion Collider; Quantum
Information, Quantum Computing; and applications of Machine Learning (ML) in ﬁeld theories.
The RBRC group and its collaborators have emphasized the necessity and importance of precision calculations, which will provide
stringent checks for the current understandings of nature, and will have a potential to ﬁnd physics beyond the current standard modelof fundamental physics. We have therefore adopted techniques that aim to control and reduce any systematic errors. This approach
has yielded many reliable results, many of basic quantities are now computed within sub-percent accuracies.
The group also delivers several algorithmic breakthroughs, which speed up generic lattice gauge theory computation. These novel
technique divides the whole calculation into frequent approximated calculations, and infrequent expensive and accurate calculation
using lattice symmetries called All Mode Averaging (AMA), or a compression for memory needs by exploiting the local-coherenceof QCD dynamics. Together with another formalism, zMobius fermion, which approximate chiral lattice quark action eﬃciently, thetypical calculation is now improved by a couple of orders of magnitudes, and more than an order of magnitude less memory needs
compared to the traditional methods. RBRC group and its collaborators also provide very eﬃcient and generic code optimized to thestate-of-arts CPU or GPU, and also improve how to eﬃciently generate QCD ensemble.

Members
Group Leader
Taku IZUBUCHI
RBRC Researchers
Luchang JIN

Sergey SYRITSYNSpecial Postdoctoral Researchers
Nobuyuki MATSUMOTO

Akio TOMIYA

Visiting Scientists
Thomas BLUM (Univ. of Connecticut)

Hiroshi OKI (Nara Women’s Univ.)

List of Publications & Presentations
Publications[Original Papers]
M. Abramczyk, T. Blum, T. Izubuchi, C. Jung, M. Lin, A. Lytle, S. Ohta, and E. Shintani, “Nucleon mass and isovector couplings in
2+1-ﬂavor dynamical domain-wall lattice QCD near physical mass,” Phys. Rev. D 101, 034510 (2020).
T. Izubuchi, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, C. Shugert, and S. Syritsyn, “Valence parton distributionfunction of pion from ﬁne lattice,” Phys. Rev. D 100, 034516 (2019).

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VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 55 (2022)

N. H. Christ, X. Feng, L. C. Jin, and C. T. Sachrajda, “Finite-volume eﬀects in long-distance processes with massless leptonic propagators,” Phys. Rev. D 103, 014507 (2021).
Y. Li, S. C. Xia, X. Feng, L. C. Jin, and C. Liu, “Field sparsening for the construction of the correlation functions in lattice QCD,” Phys.
Rev. D 103, 014514 (2021).
C. Y. Seng, X. Feng, M. Gorchtein, L. C. Jin, and U. G. Meißner, “New method for calculating electromagnetic eﬀects in semileptonic
beta-decays of mesons,” J. High Energy Phys. 10, 179 (2020).
X. Gao, L. Jin, C. Kallidonis, N. Karthik, S. Mukherjee, P. Petreczky, C. Shugert, S. Syritsyn, and Y. Zhao, “Valence parton distributionof the pion from lattice QCD: Approaching the continuum limit,” Phys. Rev. D 102, 094513 (2020).
HI +HI

X. Feng, L. C. Jin, Z. Y. Wang, and Z. Zhang, “Finite-volume formalism in the 2 −−−−−→ 2 transition: An application to the lattice QCD
calculation of double beta decays,” Phys. Rev. D 103, 034508 (2021).
R. Abdul Khalek et al., “Science requirements and detector concepts for the electron-ion collider: EIC yellow report,” arXiv:2103.05419.
X. Gao, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, and Y. Zhao, “Pion form factor and charge radius from Lattice QCD at
physical point,” arXiv:2102.06047.
X. Gao, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, and Y. Zhao, “Towards studying the structural diﬀerences between the pionand its radial excitation,” Phys. Rev. D 103, 094510 (2021).
G. Silvi, S. Paul, C. Alexandrou, S. Krieg, L. Leskovec et al., “P-wave nucleon-pion scattering amplitude in the Δ(1232) channel fromlattice QCD,” Phys. Rev. D 103, 094508 (2021).
M. Yu. Barabanov, M. A. Bedolla, W. K. Brooks, G. D Cates, C. Chen et al., “Diquark correlations in hadron physics: Origin, impact andevidence,” Prog. Part. Nucl. Phys. 116, 103835 (2021).
M. Engelhardt, J. R. Green, N. Hasan, S. Krieg, S. Meinel, J. Negele, A. Pochinsky, and S. Syritsyn, “From Ji to Jaﬀe-Manohar orbital
angular momentum in lattice QCD using a direct derivative method,” Phys. Rev. D 102, 074505 (2020).
G. Rendon, L. Leskovec, S. Meinel, J. Negele, S. Paul et al., “I = 1/2 S -wave and P-wave Kπ scattering and the κ and K ∗ resonancesfrom lattice QCD,” Phys. Rev. D 102, 114520 (2020).
Z. Fan, X. Gao, R. Li, H. -W. Lin, N. Karthik et al., “Isovector parton distribution functions of the proton on a superﬁne lattice,” Phys.
Rev. D 102, 074504 (2020).
H. T. Ding, S. T. Li, Swagato Mukherjee, A. Tomiya, X. D. Wang, and Y. Zhang, “Correlated Dirac eigenvalues and axial anomaly inchiral symmetric QCD,” Phys. Rev. Lett. 126, 082001 (2021).
M. Kawaguchi, S. Matsuzaki, and A. Tomiya, “Nonperturbative ﬂavor breaking in topological susceptibility at HotQCD criticality,” Phys.
Lett. B 813, 136044 (2021).
H. -T. Ding, C. Schmidt, A. Tomiya, and X. -D. Wang, “Chiral phase structure of three ﬂavor QCD in a background magneticﬁeld,” Phys.
Rev. D 102, 054505 (2020).
B. Chakraborty, M. Honda, T. Izubuchi, Y. Kikuchi, and A. Tomiya, “Digital quantum simulation of the Schwinger model with topologicalterm via adiabatic state preparation,” arXiv:2001.00485.

[Review Article]
T. Aoyama, N. Asmussen, M. Benayoun, J. Bijnens, T. Blum, M. Bruno, I. Caprini, C. M. Carloni Calame, M. Cè, G. Colangelo et al.,“The anomalous magnetic moment of the muon in the standard model,” Phys. Rept. 887, 1–166 (2020).

[Books]A. Tomiya, “An introduction to machine learning in physics,” (in Japanese), Kodansha, March 2021.
K. Hashimoto, A. Tanaka, and A. Tomiya, “Deep learning and physics,” Springer, February 2021.

[Proceedings]
T. Izubuchi, H. Ohki, and S. Syritsyn, “Computing nucleon electric dipole moment from lattice QCD,” Proc. Sci. LATTICE2019, 290(2020).
M. Bruno, T. Izubuchi, C. Lehner, and A. S. Meyer, “Exclusive channel study of the muon HVP,” Proc. Sci. LATTICE2019, 239 (2019).
M. Kawaguchi, S. Matsuzaki, and A. Tomiya, “Analysis on nonperturbative ﬂavor violation at chiral crossovercriticality in QCD,”
arXiv:2005.07003.
A. Tomiya and Y. Nagai, “Gauge covariant neural network for 4 dimensional non-abelian gaugetheory,” arXiv:2103.11965.
M. Kawaguchi, S. Matsuzaki, and A. Tomiya, “A new critical endpoint in thermomagnetic QCD,” arXiv:2102.05294.
Y. Nagai, A. Tanaka, and A. Tomiya, “Self-learning Monte-Carlo for non-abelian gauge theory withdynamical fermions,”
arXiv:2010.11900.
H. -T. Ding, S. -T. Li, A. Tomiya, X. -D. Wang, and Y. Zhang, “Chiral properties of (2+1)-ﬂavor QCD in strong magnetic ﬁelds atzerotemperature,” arXiv:2008.00493.
H. -T. Ding, S. -T. Li, S. Mukherjee, A. Tomiya, and X. -D. Wang, “Meson masses in external magnetic ﬁelds with HISQ fermions,”
arXiv:2001.05322.

Presentations[International Conferences/Workshops]
L. Jin (invited), “Lattice calculations in muon g − 2.,” The Hadron Mass and Structure Forum, Online, April 2021.

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VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 55 (2022)

L. Jin (invited), “Muon g − 2: hadronic light-by-light contribution and lattice QCD,” The Muon g-2 Discussion Forum, Peking University,
Online, April 2021.
L. Jin (invited), “Pion electric polarizability,” the χ QCD Collaboration Meeting, Online, January 2021.
L. Jin (invited), “Lattice calculation of the hadronic light-by-light contribution to the muon magnetic moment,” The Hadron Physics
Online Forum, Online, August 2020.
S. Syritsyn (invited), “Nucleon form factors at high momentum transfer from lattice QCD,” Nuclear & Particle Theory Seminar, MIT/CTP,
March 9, 2020.
A. Tomiya (oral), “Self-learning Monte-Carlo for non-abelian gauge theory withdynamical fermions,” APS April Meeting, Virtual, April
20, 2020.
A. Tomiya (invited), “Self-learning Monte-Carlo for non-abelian gauge theory with dynamical fermions,” Workshop on Non-equilibrium
Systems and Machine Learning, Virtual, March 30, 2020.
A. Tomiya (oral), “Quantum computing for QCD phase diagram? Finite chemicalpotential and temperature?,” Kickoﬀ Meeting of C2QACenter, Virtual, BNL, October 30, 2020.
A. Tomiya (invited), “Machine learning and theoretical physics,” Progress of Particle Physics 2020, Virtual, Yukawa Institute for Theoretical Physics, Japan, Sepember 4, 2020.
A. Tomiya (oral), “Thermal ﬁeld theory with pure states,” Asia-Paciﬁc Symposium for Lattice Field Theory (APLAT 2020), Virtual, KEK,
August 6, 2020.
A. Tomiya (invited), “Applications of machine learning to computational physics,” A.I. for Nuclear Physics, JeﬀersonLaboratory, Virginia,
USA, March 3, 2020.

[Domestic Conferences/Workshops]
A. Tomiya (oral), “Gauge covariant neural network for 4 dimensional non-abelian gaugetheory,” Deep Learning and Physics, Virtual,
April 7, 2020.
A. Tomiya (oral), “Self-learning Monte-Carlo for QCD,” JPS, Virtual, March 13, 2020.
A. Tomiya (invited), “Machine learning for physics,” 5th Symposium on Statistical Machine Learning, Virtual, Nagoya University, December 5, 2020.
A. Tomiya (oral), “A lecture on usage of neural nets in physics,” DLAP 2020 Lecture, Virtual, Osaka University, November 26, 2020.

[Seminars]
L. Jin (invited), “Lattice calculations in muon g − 2.,” The Theory Seminar at the Department of Physics and Astronomy, University ofCalifornia, Davis, Online, May 2021.
L. Jin (invited), “Lattice calculations in muon g − 2.,” The Lunch Seminar at the Institute of Theoretical Physics, Chinese Academy of
Sciences, Online, April 2021.
L. Jin (invited), “First-principles calculation of electroweak box diagrams from lattice QCD,” The Physics Seminar in Hunan University,
Online, December 2020.
L. Jin (invited), “First-principles calculation of electroweak box diagrams from lattice QCD,” The Theory Seminar at the Institute ofModern Physics, Chinese Academy of Sciences, July 2020.
L. Jin (invited), “First-principles calculation of electroweak box diagrams from lattice QCD,” The BNL Nuclear Theory Seminar, Online,
May 2020.
L. Jin (invited), “Lattice calculation of the hadronic light-by-light contribution to the muon magnetic moment,” The QCD Seminar, Online,
May 2020.
S. Syritsyn (invited), “From quarks and gluons to nucleons and nuclei,” Seminar at IACS (Inst. Adv. Comp. Sci), Stony Brook, October
8, 2020.
A. Tomiya (oral), “Gauge covariant neural network for 4 dimensional non-abelian gaugetheory,” Virtual, MIT, April 29, 2020.
A. Tomiya (oral), “Applications of machine learning on theoretical physics,” Virtual, Ochanomizu University, Japan, May 19, 2020.
A. Tomiya (oral), “Gauge covariant neural network for 4 dimensional non-abelian gaugetheory,” Virtual, RIKEN Center for Computational
Science, Japan, April 28, 2020.
A. Tomiya (oral), “Applications of machine learning for theoretical physics,” Virtual, JPARC, Japan, March 18, 2020.
A. Tomiya (oral), “Self-learning Monte-Carlo for non-abelian gauge theory withdynamical fermions,” Virtual, Yukawa Institute for Theoretical Physics, Japan, December 7, 2020.
A. Tomiya (oral), “Applications of machine learning on theoretical physics,” Virtual, Shimane University, Japan, October 29, 2020.
A. Tomiya (oral), “Lattice gauge theory with quantum computers,” Virtual, RIKEN Center for Computational Science, Japan, June 3,2020.
A. Tomiya (oral), “Lattice gauge theory with quantum computers,” Virtual, Osaka University, Japan, May 12, 2020.

Award
A. Tomiya “Best presentation award,” SPDR program, RIKEN, 2021.

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Press Releases
Brookhaven National Laboratory, “Background on Brookhaven Lab’s Involvement in the Muon g-2 Experiment,” April 7, 2021. https://www.bnl.gov/newsroom/news.php?a=218814 .
CERN Courier, “An anomalous moment for the muon,” April 14, 2021. https://cerncourier.com/a/an-anomalous-moment-forthe-muon/ .
UConn Today, “UConn Physicists Focus on a Law-Breaking Particle,” May 20, 2021. https://today.uconn.edu/2021/05/
uconn-physicists-focus-on-a-law-breaking-particle/ .

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