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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 forhigh energy particle and nuclearphysics. 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 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. The ﬁrst-principle studies also elucid intrecate nature of various phenomena in quantitive and unambiguous
manners. 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 computing codes, developments for computing algorithms,
and researches of particle, nuclear, and lattice theories. Since the inception of RBRC, many breakthroughs and pioneering works
has carried out in computational forefronts. These are the use of the domain-wall fermions, which preserve chiral symmetry, a key
symmetry for understanding dynamics of subnuclear elementary particle quark, the three generations of QCD devoted supercomputersand very eﬃcient software library for lattice gauge theories, pioneering works for QCD calculation for Cabibbo-Kobayashi-Maskawa
theory, QCD + QED simulation for isospin breaking, novel algorithms for statistical error reduction in general lattice calculation etc.
The chiral quark simulation has been performed in a uncompromised setup at the physical up, down quark mass, the precision formany basic quantities reached to accuracy of sub-percent, and the group is working 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.
Recent focus area is stusies of 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. Closely related calculation has been carried out for the origin of the current matter rich universe (rather than anti-matter).
Towards ﬁnite density QCD, they also explored Quantum Computing for ﬁeld theories. Applications of the Machine Learning (ML)and Artiﬁcial Intelligence (AI) for novel and more eﬃcient ways to carry out lattice QCD calculations are among the new topics ofthe group.

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 sPHENIX, Electron Ion Collider (EIC or eRHIC), Hyper Kamiokande, T2K, DUNE, or the matter rich universe(3) Theoretical and algorithmic development for lattice ﬁeld theories, QCD machine (co-)design and software development

3. Summary of Research Activity

Research activities during the current report period by RBRC members include various nulcleon formfactor and structure calculations, hadronic contributions to the anomalous magnetic moment (g − 2)µ , kaon and B meson physics, and algorithm & softwaredevelopments.
In April 2020, (g − 2)µ experiment collaboration at FNAL carried out a very precise measurement of precession rate of muons
under magnetic ﬁeld to 0.14 parts per million accuracy. This provides a very stringent test of the current understanding of elementary
particle physics so called the Standard Model of particle physics. The strong interaction of quark and gluon is described by Quantum
Chromo Dyanics (QCD) and is a dominant source of uncertainty in the theoretical prediction of (g − 2)µ . Members of RBRC has
been working on the two separate mode of QCD contributions, Hadronic Vacuum Polarization (HVP) and Hadronic Light-by-Light(HLbL). This year, an update of HVP was reported with an improved precision by adding calculation on the ﬁnner space-time lattice
to remove systematic error due to non-zero lattice spacing. The quantities are not yet the ﬁnal total conribution for (g − 2)µ but a largepart of QCD contributionfrom intermediate energies scale, roughly 200 MeV–1 GeV. The new results of HVP contribution turned out
signiﬁcantly larger than our previous results and consistent with other lattice QCD calcuation by other groups, which emphasis theimportance and diﬃculty of removing lattice spacing error. No an interesting observation is our new value (and other lattice QCD
values) has about 4+σ tention to the HVP prediction from hadronic cross section in electron-position collision. It is important to note
this is still a comparison of the partial HVP contribution from the intemediate energy region, and the ﬁnal total HVP contribution
including other energies as well as the other systematic eﬀects is ongoing to updated with greater precision soon.
This is only a selected research highlight of members of RBRC this year among other various researches: Machine Learning- 366 -

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RIKEN Accel. Prog. Rep. 56 (2023)

q = p′ − p, νpp′

RBC/UKQCD 2018
ETMC 2021
BMW 2020
Mainz 2022
ETMC 2022
RBC/UKQCD 2023
RBC/UKQCD 2018/FJ
Aubin et al. 2019/CL/KNT
BMW 2020/KNT
Colangelo et al. 2022
224 226 228 230 232 234 236 238 240Waµ (0.4 fm, 1.0 fm, 0.15 fm) × 10

10

Hadron Models
Dispersive + Data
Lattice
PdRV 09

q = p′ − p, ν

N/JN 09
FJ 17
White paper 20pp′

RBC-UKQCD 19
Mainz 21
This Work

Fig. 1. Feynman diagrams for Lattice QCD computations of Muon’s anomalous magnetic moment (g − 2)µ . Hadronic Vaccum Polarization contribution (Left) and Hadronic Light-by-Light contribution (Right).

4

6

8

10

12

14

16

18

aHLbL
× 1010µFig. 2. Current summary of the Hadronic Light-by-Light contribution(HLbL) contribution for Muon’s anomalous magnetic moment (g − 2)µ .
Above the upper 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 resultsof (g − 2)µ showing a 3–4σ discrepancies.

for Lattice QCD ensemble generation, Lattice QCD sampling for non-zero baryon density and sign problem, real-time lattice QCD
formulation in Minkowski space-time, solving critical slowing down problem via trivializing maps, lattice QCD+QED and isospin
breaking of hadrons and their decays, HLbL for (g−2)µ , nucleon electric dipole moment and matter-rich universe, nucleon anti-nucleon
oscillation, proton decay, CP violating K → ππ decay and ε′ /ε, etc.
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

Bollweg DENNIS- 367 -

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Special Postdoctoral Researcher
Nobuyuki MATSUMOTO
Visiting Scientists
Thomas BLUM (Univ. of Connecticut)
Hiroshi OKI (Nara Women’s Univ.)

Akio TOMIYA (In’l Professional Univ. of Technology in Osaka)

List of Publications & Presentations
Publications[Original Papers]
T. Blum, P. A. Boyle, M. Bruno, D. Giusti, V. Gülpers, R. C. Hill, T. Izubuchi, Y. C. Jang, L. Jin, and C. Jung et al., arXiv:2301.08696.
T. Blum et al. [RBC and UKQCD], “Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic
boundary conditions in lattice QCD,” Phys. Rev. D 107, 094512 (2023).
J. S. Yoo, Y. Aoki, P. Boyle, T. Izubuchi, A. Soni, and S. Syritsyn, “Proton decay matrix elements on the lattice at physical pion mass,”
Phys. Rev. D 105, 074501 (2022).
G. Rendon, T. Izubuchi and Y. Kikuchi, “Eﬀects of cosine tapering window on quantum phase estimation,” Phys. Rev. D 106, 034503(2022).
B. Chakraborty, M. Honda, T. Izubuchi, Y. Kikuchi, and A. Tomiya, “Classically emulated digital quantum simulation of the Schwinger
model with a topological term via adiabatic state preparation,” Phys. Rev. D 105, 094503 (2022).
X. Gao, A. D. Hanlon, J. Holligan, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, and Y. Zhao, “The Unpolarized Proton PDF at
NNLO from Lattice QCD with Physical Quark Masses,” arXiv:2212.12569.
X. Gao, A. D. Hanlon, N. Karthik, S. Mukherjee, P. Petreczky, P. Scior, S. Shi, S. Syritsyn, Y. Zhao, and K. Zhou, “Continuum-extrapolated
NNLO valence PDF of the pion at the physical point,” Phys. Rev. D 106, 114510 (2022).
X. Gao, A. D. Hanlon, N. Karthik, S. Mukherjee, P. Petreczky, P. Scior, S. Syritsyn, and Y. Zhao, “Pion distribution amplitude at thephysical point using the leading-twist expansion of the quasi-distribution-amplitude matrix element,” Phys. Rev. D 106, 074505 (2022).
X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, P. Scior, S. Syritsyn, and Y. Zhao, “Lattice QCD determination of the Bjorken-x
dependence of parton distribution functions at next-to-next-to-leading order,” Phys. Rev. Lett. 128, 142003 (2022).
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,” Phys. Rev. D 104, 11 (2021).
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 Delta(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
and evidence,” Prog. Part. Nucl. Phys. 116, 103835 (2021).
Y. Hamada and N. Matsumoto, “Energy of the boundary of spacetime,” Prog. Theor. Exp. Phys. 2023, 033B02 (2023).
N. Matsumoto, “Comment on the subtlety of deﬁning a real-time path integral in lattice gauge theories,” Prog. Theor. Exp. Phys. 2022,
093B03 (2022).
X. Y. Tuo, X. Feng, and L. C. Jin, “Lattice QCD calculation of the light sterile neutrino contribution in 0ν2β decay,” Phys. Rev. D 106,
074510 (2022).
Y. Fu, X. Feng, L. C. Jin, and C. F. Lu, “Lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen lambshift,” Phys. Rev. Lett. 128, 172002 (2022).
X. Feng, L. Jin, and M. J. Riberdy, “Lattice QCD calculation of the pion mass splitting,” Phys. Rev. Lett. 128, 052003 (2022).
X. Y. Tuo, X. Feng, L. C. Jin, and T. Wang, “Lattice QCD calculation of K → ℓνℓℓ′ + ℓ′ -decay width,” Phys. Rev. D 105, 054518 (2022).
P. X. Ma, X. Feng, M. Gorchtein, L. C. Jin, and C. Y. Seng, “Lattice QCD calculation of the electroweak box diagrams for the kaon
semileptonic decays,” Phys. Rev. D 103, 114503 (2021).

[Review Articles]
N. Craig, C. Csáki, A. X. El-Khadra, Z. Bern, R. Boughezal, S. Catterall, Z. Davoudi, A. de Gouvêa, P. Draper, and P. J. Fox et al.,“Snowmass Theory Frontier Report,” arXiv:2211.05772.
Z. Davoudi, E. T. Neil, C. W. Bauer, T. Bhattacharya, T. Blum, P. Boyle, R. C. Brower, S. Catterall, N. H. Christ, and V. Cirigliano et al.,“Report of the snowmass 2021 topical group on lattice gauge theory,” arXiv:2209.10758.
A. S. Kronfeld et al. [USQCD], “Lattice QCD and particle physics,” arXiv:2207.07641.
P. Boyle, D. Bollweg, R. Brower, N. Christ, C. DeTar, R. Edwards, S. Gottlieb, T. Izubuchi, B. Joo, and F. Joswig et al. “Lattice QCD andthe computational frontier,” arXiv:2204.00039.
G. Colangelo, M. Davier, A. X. El-Khadra, M. Hoferichter, C. Lehner, L. Lellouch, T. Mibe, B. L. Roberts, T. Teubner, and H. Wittig etal. “Prospects for precise predictions of aµ in the standard model,” arXiv:2203.15810.
T. Blum, P. Boyle, M. Bruno, N. Christ, F. Erben, X. Feng, V. Guelpers, R. Hill, R. Hodgson, and D. Hoying et al., “Discovering new
physics in rare kaon decays,” arXiv:2203.10998.

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R. Alarcon, J. Alexander, V. Anastassopoulos, T. Aoki, R. Baartman, S. Baeßler, L. Bartoszek, D. H. Beck, F. Bedeschi, and R. Berger etal. “Electric dipole moments and the search for new physics,” arXiv:2203.08103.
D. Bollweg, D. A. Clarke, J. Goswami, O. Kaczmarek, F. Karsch, S. Mukherjee, P. Petreczky, C. Schmidt, and S. Sharma, ‘Equation of state and speed of sound of (2+1)-ﬂavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density,”
arXiv:2212.09043.

[Proceedings]
M. Engelhardt, N. Hasan, T. Izubuchi, C. Kallidonis, S. Krieg, S. Meinel, J. Negele, A. Pochinsky, G. Silvi, and S. Syritsyn, “Transverse
momentum-dependent parton distributions for longitudinally polarized nucleons from domain wall fermion calculations at the physicalpion mass,” PoS LATTICE2022, 103 (2023).
P. Boyle, T. Izubuchi, L. Jin, C. Jung, C. Lehner, N. Matsumoto, and A. Tomiya, “Use of Schwinger-Dyson equation in constructing anapproximate trivializing map,” PoS LATTICE2022, 229 (2023).
J. S. Yoo, S. Syritsyn, Y. Aoki, P. Boyle, T. Izubuchi, and A. Soni, PoS LATTICE2021, 522 (2022).
J. S. Yoo, S. Syritsyn, Y. Aoki, P. Boyle, T. Izubuchi, and A. Soni, “Proton decay amplitudes with physical chirally-symmetric quarks ona lattice,” PoS PANIC2021, 443 (2022).
M. Tomii, T. Blum, D. Hoying, T. Izubuchi, L. Jin, C. Jung, and A. Soni, “K → ππ decay matrix elements at the physical point withperiodic boundary conditions,” PoS LATTICE2021, 394 (2022).
X. Feng, T. Izubuchi, L. Jin, and M. Golterman, “Pion electric polarizabilities from lattice QCD,” PoS LATTICE2021, 362 (2022).
M. Engelhardt, J. Green, N. Hasan, T. Izubuchi, C. Kallidonis, S. Krieg, S. Liuti, S. Meinel, J. Negele, and A. Pochinsky et al., PoS
LATTICE2021, 413 (2022).
S. Foreman, T. Izubuchi, L. Jin, X. Y. Jin, J. C. Osborn, and A. Tomiya, “HMC with normalizing ﬂows,” PoS LATTICE2021, 073 (2022).
M. Fukuma, N. Matsumoto, and Y. Namekawa, “Applying the worldvolume hybrid Monte Carlo method to lattice ﬁeld theories,” PoS
LATTICE2022, 011 (2023).
M. Fukuma, N. Matsumoto, and Y. Namekawa, “Numerical sign problem and the tempered Lefschetz thimble method,” PoS
CORFU2021, 254 (2022).
M. Fukuma and N. Matsumoto, “Tempered Lefschetz thimble method as a solution to the numerical sign problem,” J. Phys. Conf. Ser.
2207, 012054 (2022).
M. Fukuma and N. Matsumoto, “The basics and applications of the tempered Lefschetz thimble method for the numerical sign problem,”
PoS LATTICE2021, 395 (2022).
M. Fukuma, N. Matsumoto, and Y. Namekawa, “Worldvolume tempered Lefschetz thimble method and its error estimation,” PoS LATTICE2021, 446 (2022).
P. A. Boyle, D. Bollweg, C. Kelly, and A. Yamaguchi, “Algorithms for domain wall Fermions,” PoS LATTICE2021, 470 (2022).

Presentations[International Conferences/Workshops]
S. Syritsyn (invited), “Nucleon electromagnetic form factors at large momentum from lattice QCD,” Triangle Nuclear Theory Colloquium
at UNC Chapel Hill, November 29, 2022.
S. Syritsyn (invited), “Nucleon electromagnetic form factors at large momentum from lattice QCD,” Baryons 2022, Seville, Spain, November 7, 2022.
S. Syritsyn (invited), “Baryon number-violating amplitudes on a lattice with physical chirally-symmetric quarks,” 14th Conference on theIntersections of Particle and Nuclear Physics (CIPANP), Orlando, FL, August 31, 2022.
S. Syritsyn (invited), “Nucleon & nuclear structure inputs to beyond-SM searches,” SNOWMASS Rare Processes & Precision Frontier,Cincinnati, OH, May 17, 2022.
S. Syritsyn (invited), “Proton decay amplitudes with physical chirally-symmetric quarks,” BNL-HET & RBRC Joint Workshop“DWQ@25,” December 16, 2021.
S. Syritsyn (invited), “A more perfect universe: Role of lattice QCD in constraining violations of fundamental symmetries,” Physics &Astronomy Colloquium, Stony Brook University, November 9, 2021.
L. Jin (Invited), “The hadronic light-by-light scattering contribution to the muon g − 2,” χ QCD annual collaboration meeting, Online,
December 17, 2022.
L. Jin (Invited plenary talk), “Muon g − 2 from lattice QCD,” The 13th International Workshop on e + e− collisions from Phi to Psi, Online,
August 17, 2022.
L. Jin (Invited), “Lattice QCD input for the ﬁrst row CKM unitarity tests,” Seattle Snowmass Summer Meeting 2022, Online, July 19,
2022.
L. Jin (Invited), “Combining inﬁnite-volume photons and ﬁnite-volume hadronic matrix elements computed on the lattice,” QED in Weak
Decays, Higgs Centre for Theoretical Physics, JCMB, Online, June 24, 2022.
L. Jin (Invited), “The hadronic light-by-light scattering contribution to the muon g − 2 (RBC/UKQCD),” SchwingerFest 2022: muon g − 2,
Physics and Astronomy Building, Mani L. Bhaumik Institute, UCLA, June 17, 2022.
L. Jin (Invited), “QCD + QED studies,” USQCD All Hands’ Meeting 2022, MIT, Online, April 22, 2022.
L. Jin (Invited), “Lattice calculation of the pion mass splitting using the inﬁnite volume reconstruction method,” χ QCD annual collaboration meeting, Online, December 19, 2021.

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L. Jin, (Invited), “Attice calculation of the pion mass splitting using the inﬁnite volume reconstruction method,” BNL-HET & RBRC Joint
Workshop “DWQ@25,” Online, December 16, 2021.
L. Jin (Invited plenary talk), “Hadronic light-by-light contribution to muon g − 2,” The 10th International Workshop on Chiral Dynamics,
Institute of High Energy Physics (IHEP), CAS, Online, November 19, 2021.
L. Jin (Invited), “Lattice calculation of the muon g − 2,” The ﬁrst annual meeting of lattice QCD in China, Online, November 2, 2021.
L. Jin (Invited), “Lattice QCD input for the ﬁrst row CKM unitarity tests,” Fall Meeting of the Division of Nuclear Physics of the American
Physics Society, DNP 2021, Online, October 13, 2021.
L. Jin (Invited), “Lattice QCD results on the hadronic contributions to the muon g − 2,” The XXVIII International Conference on Supersymmetry and Uniﬁcation of Fundamental Interactions, SUSY 2021, Online, August 23, 2021.
L. Jin, “Pion electric polarizabilities from lattice QCD,” LATTICE 2021, MIT, Online, July 29, 2021.
L. Jin (Invited), “Lattice calculation of the hadronic light-by-light contribution to the muon g − 2 by the RBC-UKQCD collaborations,”
Muon g − 2 theory initiative workshop in memoriam of Simon Eidelman, KEK IPNS, High energy physics laboratory in Nagoya
University, Online, July 2, 2021.
L. Jin (Invited plenary talk), “Kaon decays from lattice QCD,” Flavor Physics and CP violation (FPCP), Online, June 9, 2021.
L. Jin (Invited), “Quark and lepton ﬂavor physics,” DOE Virtual Annual Progress Review of USQCD, Online, May 18, 2021.
N. Matsumoto, “Search for an eﬀective change of variable in QCD simulations,” DWQ@25, USA (BNL), Online, December 13, 2021.

[Seminars]
N. Matsumoto, “Sign problem and worldvolume tempered Lefschetz thimble method, RIKEN Radiation Laboratory,” Wako, Japan(RIKEN), Online, July 14, 2021.
N. Matsumoto, “Worldvolume tempered Lefschetz thimble method as an algorithm towards solving the sign problem,” RBRC seminar,
USA (BNL), Online, November 18, 2021.
N. Matsumoto, “Comment on the subtlety of deﬁning real-time path integral in lattice gauge theories,” Colorado University informal
seminar, Colorado, USA, Online, July 21 2022.
N. Matsumoto, “Comment on the subtlety of deﬁning real-time path integral in lattice gauge theories,” KEK theory seminar, Tsukuba,
Japan, Online, July 12, 2022.
N. Matsumoto, “Comment on the subtlety of deﬁning real-time path integral in lattice gauge theories,” Osaka University Particle Physics
Group seminar, Osaka, Japan, Online, November 8, 2022.
N. Matsumoto, “Use of Schwinger-Dyson equation in constructing an approximate trivializing map,” LATTICE 2022, Bonn, Germany,
August 8, 2022.
L. Jin, “Lattice calculations in muon g − 2,” Department of Physics and Astronomy, University of California, Davis, Online, May 3, 2021.
L. Jin, “Lattice calculations in muon g − 2,” Hadron mass and structure forum, Online, April 20, 2021.
L. Jin, “Lattice calculations in muon g − 2,” Institute of Theoretical Physics, Chinese Academy of Sciences, Online, April 15, 2021.
L. Jin, “Muon g − 2: hadronic light-by-light contribution and lattice QCD,” Muon g − 2 discussion forum, Peking University, Online,
April 13, 2021.

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