VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 54 (2021)

Subnuclear System Research Division
Quantum Hadron Physics Laboratory
1. Abstract

Atomic nuclei are made of protons and neutrons bound by the exchange of pion and other mesons. Also, protons and neutrons
are made of quarks bound by the exchange of gluons. These strong interactions are governed by the non-Abelian gauge theory
called the quantum chromodynamics (QCD). On the basis of theoretical and numerical analyses of QCD, we study the interactions
between the nucleons, properties of the dense quark matter realized at the center of neutron stars, and properties of the hot quark-gluon
plasma realized in the early Universe. Strong correlations common in QCD and cold atoms are also studied theoretically to unravel
the universal features of the strongly interacting many-body systems. Developing perturbative and non-perturbative techniques inquantum field theory and string theory are of great importance not only to solve gauge theories such as QED and QCD, but also to findthe theories beyond the standard model of elementary particles. Various theoretical approaches along this line have been attempted.

2. Major Research Subjects
(1)
(2)
(3)
(4)
(5)

Perturbative and non-perturbative methods in quantum field theories
Quantum computing
Lattice gauge theory
QCD under extreme conditions
Nuclear and atomic many-body problems

3. Summary of Research Activity(1) Perturbative and non-perturbative methods in quantum field theories(1-1) Theory of the anomalous magnetic moment of the electron
The anomalous magnetic moment of the electron ae measured in a Penning trap occupies a unique position among high precision
measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α, with an eﬀective
parameter α/π. Both numerical and analytic evaluations of ae up to (α/π)4 were firmly established. The coeﬃcient of (α/π)5 has
been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been
estimated. The sum of all these terms leads to ae (theory) = 1 159 652 181.606 (11)(12)(229) × 10−12 , where the first two uncertainties
are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current bestvalue of the fine-structure constant derived from the cesium recoil measurement: α−1 (Cs) = 137.035 999 046 (27). The discrepancy
between ae (theory) and ae (experiment) is 2.4σ. Assuming that the standard model is valid so that ae (theory) = ae (experiment)
holds, we obtained α−1 (ae ) = 137.035 999 1496 (13)(14)(330), which is nearly as accurate as α−1 (Cs). The uncertainties are from thetenth-order QED term, hadronic term, and the best measurement of ae , in this order.
(1-2) Transport theory of chiral fermions under external gravity and fluid field
We formulated the kinetic theory of chiral matter in external gravitational fields, based on quantum field theory. The resulting
kinetic theory reveals that the Riemann curvature induces non-dissipative transport phenomena of chiral fermions. In particular, wefound that the spin-gravity coupling results in the antiparallel flow of the charge current and energy current of fermions, which is never
explained in the classical picture. These novel framework and phenomena takes place not only in cosmological systems involving
neutrinos but also in chiral matter aﬀected by background fluid, such as quark-gluon plasma, graphene and Dirac/Weyl semimetals.
We demonstrated that a temperature gradient and fluid vorticity induce a pressure correction and charge and energy flow in Dirac/Weylsemimetals.
(1-3) Spin transport of massive fermion
We derived the spin kinetic theory under external electromagnetic and gravitational fields. We derived the global equilibrium
conditions from the kinetic equations and find that the finite Riemann curvature or an external electromagnetic field is necessary to
determine the spin-thermal vorticity coupling. Solving the equation of motion of axial vector part of the Wigner transformed fermion
propagator, we evaluated the Pauli-Lubanski vector, which expresses the spin polarization of massive fermions, at the local equilibriumand out of equilibrium. This formula is potentially important of the Λ polarization puzzle found in heavy-ion collisions, which cannot
be understood in the calculations based on global equilibrium assumption.
(1-4) Chiral vortical eﬀect in condensed matter systems
We revisited the chiral vortical eﬀect in condensed matter physics, by using the semiclassical wave-packet theory. In high-energy
physics, the chiral vortical current is conventionally defined as the Noether current. Such a definition is however improper in thecontext of condensed matter systems since there potentially exists the contributions of the magnetization current. Indeed we showedthat the chiral vortical current is compensated by the magnetization current. Hence the chiral vortical eﬀect cannot be observed inpseudo-relativistic condensed matter systems, such as Dirac/Weyl semimetals. Instead, we demonstrated that the chiral vortical eﬀect
is an observable in several nonrelativistic matter, and suggested possible table-top experimental setups.
(1-5) Lorentzian conformal field theories through sine-square deformation
In quantum field theories, symmetry plays an essential and exceptional role. Focusing on some proper symmetry and delving
into its meaning have been proven to be one of the most fruitful strategies. We reexamined two-dimensional Lorentzian conformal
field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We- 301 -

VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 54 (2021)

construct three types of Virasoro algebra. One of them reproduces the result by Luscher and Mack, while another type exhibits thedivergence in the central charge term. The other leads the continuous spectrum and contains no closed time-like curve in the system.
(2) Quantum computing(2-1) Hybrid quantum annealing via molecular dynamics
A novel quantum-classical hybrid scheme was proposed to eﬃciently solve large-scale combinatorial optimization problems. The
key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum spins of the transversefield Ising model. Molecular dynamics of the classical fluxes can be used as a powerful preconditioner to sort out the frozen andambivalent spins for quantum annealers. It was demonstrated that the performance and accuracy of our smooth hybridization are
better in comparison to the standard classical algorithms (the tabu search and the simulated annealing) by employing the MAX-CUTand Ising spin-glass problems.
(3) Lattice gauge theory(3-1) Most charming dibaryon near unitarity
The interaction between Ωccc –Ωccc in the S -wave and spin-0 channel was studied from the (2 + 1)-flavor lattice QCD with nearly
physical light-quark masses and the relativistic heavy quark action with the physical charm quark mass. The time-dependent HAL
QCD method was employed to extract the Ωccc Ωccc potential from the lattice QCD data of two-baryon spatial correlation, and thescattering observables were calculated. The potential was found to be attractive at mid-range and weakly repulsive at short-range.
Taking into account the Coulomb repulsion with the charge form factor of Ωccc as well, the scattering length aC0 ∼= 19 fm and theCC∼= 0.45 fm were obtained. The ratio reﬀ/aC0 ∼= −0.024, whose magnitude is considerably smaller than that of theeﬀective range reﬀ
dineutron (−0.149), indicates that Ωccc Ωccc is located in the unitary region.
(3-2) d∗ (2380) dibaryon from lattice QCD
The ∆∆ dibaryon resonance d∗ (2380) with (J π , I) = (3+ , 0) was studied from the 3-flavor lattice QCD with heavy pion masses (mπ= 0.68, 0.84, 1.02 GeV). The central ∆∆ potential in 7 S3 channel obtained by HAL QCD method shows a strong short-range attraction,
so that a quasi-bound state corresponding to d*(2380) is formed with the binding energy 25–40 MeV below the ∆∆ threshold for theheavy pion masses. The tensor part of the transition potential from ∆∆ to NN was also extracted. Although the obtained transition
potential is strong at short distances, the decay width of d∗ (2380) to NN in the D-wave was found to be kinematically suppressed.
(3-3) Stress tensor around static quark-anti-quark from Yang-Mills gradient flow
The spatial distribution of the stress tensor around the quark-anti-quark pair in SU(3) lattice gauge theory was studied. The
YangMills gradient flow plays a crucial role to make the stress tensor well-defined and derivable from the numerical simulations on
the lattice. The resultant stress tensor with a decomposition into local principal axes shows, for the first time, the detailed structureof the flux tube along the longitudinal and transverse directions in a gauge invariant manner. The linear confining behavior of thepotential at long distances is derived directly from the integral of the local stress tensor.
(4) QCD under extreme conditions(4-1) Finite density QCD based on complex Langevin method
The complex Langevin method (CLM) is one of a promising approach to overcome the sign problem. The central idea of thisapproach is that the stochastic quantization does not require the probabilistic interpretation of the Boltzmann weight e−S even when theaction takes complex values. Although the equivalence between CLM and the familiar path integral quantization is quite nontrivial, it
is pointed out that the probability distribution of the drift term can judge the correctness of the CLM. This enable us to perform latticesimulation of QCD based on CLM in the finite density region in a self-contained manner. We discussed the applicability of the CLM
with four-flavor staggered fermions on a 83 × 16 lattice with quark mass m = 0.01. In particular, we focus on the behavior of theeigenvalue distribution of the fermion mass matrix which is closely related to the appearance of the singular drift problem.
(4-2) Non-equilibrium quantum transport of chiral fluids from kinetic theory
We introduced the quantum-field-theory (QFT) derivation of chiral kinetic theory (CKT) from the Wigner-function approach,which manifests side jumps and non-scalar distribution functions associated with Lorentz covariance and incorporates both background fields and collisions. The formalism is utilized to investigate second-order responses of chiral fluids near local equilibrium. Such nonequilibrium anomalous transport is dissipative and aﬀected by interactions. Contributions from both quantum corrections in anomalous hydrodynamic equations (EOM) of motion and those from the CKT and Wigner functions (WF) are considered in a relaxation-time approximation (RTA). Anomalous charged Hall currents engendered by background electric fields andtemperature/chemical-potential gradients are obtained. Furthermore, chiral magnetic/vortical eﬀects (CME/CVE) receive viscous corrections as non-equilibrium modifications stemming from the interplay between side jumps, magnetic-moment coupling, and chiralanomaly.
(4-3) Hadron-quark crossover in cold and hot neutron stars
We presented a much improved equation of state for neutron star matter, QHC19, with a smooth crossover from the hadronic
regime at lower densities to the quark regime at higher densities. We now use the Togashi et al. equation of state, a generalization of
the Akmal-Pandharipande-Ravenhall equation of state of uniform nuclear matter, in the entire hadronic regime; the Togashi equation ofstate consistently describes nonuniform as well as uniform matter, and matter at beta equilibrium without the need for an interpolation
between pure neutron and symmetric nuclear matter. We describe the quark matter regime at higher densities with the NambuJonaLasinio model, now identifying tight constraints on the phenomenological universal vector repulsion between quarks and thepairing interaction between quarks arising from the requirements of thermodynamic stability and causal propagation of sound. The
resultant neutron star properties agree very well with the inferences of the LIGO/Virgo collaboration, from GW170817, of the pressure- 302 -

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versus baryon density, neutron star radii, and tidal deformabilities. The maximum neutron star mass allowed by QHC19 is 2.35 MS,
consistent with all neutron star mass determinations.
(4-4) Gluonic energy and momentum distribution at finite temperature
We studied the energy-momentum distribution of the gluons around a static quark at finite temperature on the basis of theeﬀective field theory (EFT) of thermal QCD. Spatial correlations between the Polyakov loop and the energy-momentum tensor
were calculated up to the next-to-leading order in EFT. The results were compared with the recent quenched lattice QCD calculation
obtained by using the gradient flow formalism. The EFT results and the lattice QCD data agree quite well without any fitting
parameters at high temperature above deconfinement. On the other hand, there is a substantial diﬀerence near the critical temperatureespecially in the distribution of the energy density, which indicates some non-perturbative eﬀect.
(5) Nuclear and atomic many-body problems(5-1) Density functional theory for nuclear structure
The atomic nuclei are composed of protons and neutrons interacting via the nuclear and Coulomb interactions. The density
functional theory (DFT) is widely used to calculate the ground-state properties. Nevertheless, because of the lack of knowledge of
nuclear interaction in medium (eﬀective interaction), the eﬀective interaction is fitted to experimental data, and it has been attained todevelop a high-accuracy one. In contrast, the nucleons have finite charge distributions, while this is not considered in DFT calculation.
Because it is indispensable to treat the Coulomb interaction more accurately to achieve high-accuracy nuclear eﬀective interaction, we
consider such finite-size eﬀects to nuclear DFT, and we reveal that such eﬀects give a non-negligible contribution to nuclear binding
energies. In nuclear structure calculation, both non-relativistic and relativistic schemes of DFT are used, while the connection between
them, especially in terms of the eﬀective interaction, is not understood well. To reveal it, we also develop the eﬃcient non-relativistic
reduction of the many-body systems.
(5-2) Fundamental problems of density functional theory
The density functional theory (DFT) is one of the powerful methods to calculate ground-state properties of the quantum manybody problems, including atomic nuclei, atoms, molecules, and solids. The accuracy of the DFT depends on the energy density
functional (EDF), which contains information on the interaction. We develop a method to calculate EDF for electronic systems
purely microscopically using the functional renormalization group. In this method, energy density for so many various densities canbe calculated, and eventually, DFT calculation can be performed without fitting energy density to some functional forms. We also
develop the relativistic DFT in which the finite-light-speed correction to the Coulomb interaction is also considered to calculate theground-state properties of super-heavy elements.
(5-3) One-dimensional Bose and Fermi gases with contact interactions
We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which
are closely connected with each other by Girardeau’s Bose-Fermi mapping. While the Lagrangian for bosons includes only a twobody interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-bodycoupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of thesum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy
and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in thesense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bosegas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.
(5-4) Mesoscopic spin transport between strongly interacting Fermi gases
We investigate a mesoscopic spin current for strongly interacting Fermi gases through a quantum point contact. Under thesituation where spin polarizations in left and right reservoirs are same in magnitude but opposite in sign, we calculate the contributionof quasiparticles to the current by means of the linear response theory and many-body T -matrix approximation. For a small spin-bias
regime, the current in the vicinity of the superfluid transition temperature is strongly suppressed due to the formation of pseudogaps.
For a large spin-bias regime where the gases become highly polarized, on the other hand, the current is aﬀected by the enhancement ofa minority density of states due to Fermi polarons. We also discuss the broadening of a quasiparticle peak associated with an attractive
polaron at a large momentum, which is relevant to the enhancement(5-5) Optical spin conductivity in ultracold quantum gases
Measurement of frequency-resolved spin transport is a subject of much interest in condensed matter physics. Here we show thatthe optical spin conductivity, which is a small AC response of a spin current, can be measured with existing methods in ultracold atom
experiments. We point out that once interatomic interactions are turned on, the optical spin conductivity becomes nontrivial even inclean ultracold atomic gases and thereby can be a probe of generic quantum states of matter. This is a sharp contrast to the optical massconductivity which becomes trivial in typical cold-atom systems without disorder and lattice potential. For systems with arbitrary spin
degrees of freedom, we construct a general formalism of the optical spin conductivity and derive the f -sum rule. To demonstrate
the availability of the optical spin conductivity, our formalism is applied to a spin-1/2 Fermi superfluid and a spin-1 Bose-Einsteincondensate. It turns out that both superfluids show nontrivial responses that cannot be captured with the Drude conductivity. The
application of our proposed method to generic ultracold atomic gases with spin degrees of freedom is feasible.

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VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 54 (2021)

Members
Director
Masahiko IWASAKI
Vice Chief Scientist
Tsukasa TADA
Research/Technical Scientist
Takumi DOI (Senior Research Scientist)
Senior Scientist
Makiko NIO
Contract Researcher
Dang NGUYEN DINH
Special Postdoctoral Researchers
Matthias W.G. BERWEIN
Kazuya MAMEDA

Shoichiro TSUTSUI

Research Consultant
Takeo INAMI (Inst. of Phys. Vietnamese Academy of Sci. andTech.)
Visiting Scientists
Shinya AOKI (Kyoto Univ.)
Tatsumi AOYAMA (KEK)
Gergely P. FEJOS (Eotvos Lorand Univ.)
Kenji FUKUSHIMA (Univ. of Tokyo)
Hideki HAMAGAKI (Nagasaki Inst. of Applied Sci.)
Koji HASHIMOTO (Osaka Univ.)
Masashi HAYAKAWA (Nagoya Univ.)
Tomoya HAYATA (Keio Univ.)
Takashi INOUE (Nihon Univ.)
Noriyoshi ISHII (Osaka Univ.)
Yuki KAMIYA (Chinese Academy of Sci.)
Yoichi KAZAMA (Univ. of Tokyo)
Phuc T. LE (Inst. of Fundamental and Applied Sci. Duy Tan
Univ.)
Haozhao LIANG (Univ. of Tokyo)
Takaya MIYAMOTO (NEC Corporation)

Kenji MORITA (QST)
Masaki MURATA (Japan Univ. of Economics)
Atsushi NAKAMURA (Osaka Univ.)
Takashi NAKATSUKASA (Tsukuba Univ.)
Hung NGUYEN (Duy Tan Univ.)
Yoji OHASHI (Keio Univ.)
RHINE KUMAR ARAYAKKANDI KEECH (Cochin Univ. ofSci. and Tech.)
Shoichi SASAKI (Tohoku Univ.)
Kenji SASAKI (Kyoto Univ.)
Hiroshi SUZUKI (Kyushu Univ.)
Motoi TACHIBANA (Saga Univ.)
Sachiko TAKEUCHI (The Social Work Research Institute)
Hiroshi TOKI (Osaka Univ.)
Di-Lun YANG (Keio Univ.)

Visiting Researcher
Yuta SEKINO (JSPS)
Student Trainees
Yutaro AKAHOSHI (Kyoto Univ.)
Asahi CHIKAOKA (Univ. of Tokyo)
Yixin GUO (Univ. of Tokyo)
Akira HIRAYAMA (Saitama Univ.)
Xun LIU (Univ. of Tokyo)

Yan LYU (Peking Univ.)
Kotaro MURAKAMI (Kyoto Univ.)
Tomoya NAITO (Univ. of Tokyo)
Hui TONG (Peking Univ.)
Tingyu ZHANG (Univ. of Sci. and Tech. of China)

List of Publications & Presentations
Publications[Original Papers]
G. Accorto, T. Naito, H. Liang, T. Niksic, and D. Vretenar, “Nuclear energy density functionals from empirical ground-state densities,”
Phys. Rev. C 103, 044304 (2021).
T. Hayata, Y. Hidaka, and K. Mameda, “Second order chiral kinetic theory under gravity and antiparallel charge-energy flow,” J. HighEnergy Phys. 2021, 23 (2021).
N. Itagaki and T. Naito, “Consistent description for cluster dynamics and single-particle correlation,” Phys. Rev. C 103, 044303 (2021).
T. Yokota and T. Naito, “Ab initio construction of the energy density functional for electron systems with the functional-renormalizationgroup-aided density functional theory,” Phys. Rev. Res. 3, L012015 (2021).

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VI. RNC ACTIVITIESRIKEN Accel. Prog. Rep. 54 (2021)

Y. Sekino, H. Tajima, and S. Uchino, “Optical spin transport in ultracold quantum gases,” arXiv:2103.02418 [cond-mat.quant-gas] (2021).
Y. Lyu, H. Tong, T. Sugiura, S. Aoki, T. Doi, T. Hatsuda, J. Meng, and T. Miyamoto, “Most charming dibaryon near unitarity,”
arXiv:2102.00181 [hep-lat] (2021).
T. Naito, G. Colò, H. Liang, and X. Roca-Maza, “Second and fourth moments of the charge density and neutron-skin thickness of atomic
nuclei,” arXiv:2101.07680 [nucl-th] (2021).
Z. Wang, T. Naito, H. Liang, and W. H. Long, “Exploring eﬀects of tensor force and its strength via neutron drops,” arXiv:2101.04860[nucl-th] (2021).
Y. Tanabe, Y. Ito, K. Sugawara, M. Koshino, S. Kimura, T. Naito, I. Johnson, T. Takahashi, and M. Chen, “Dirac Fermion kinetics inthree-dimensionally curved graphene,” Adv. Mater. 32, 202005838 (2020).
X. Liu and T. Tada, “Analysis for Lorentzian conformal field theories through sine-square deformation,” Prog. Theor. Exp. Phys. 2020,
061B01225 (2020).
Z. Wang, T. Naito, and H. Liang, “Tensor eﬀects on shell-structure evolution in N = 82 isotones and Z = 50 isotopes in the relativistic
Hartree-Fock theory,” arXiv:2012.13143 [nucl-th] (2020).
Y. Sekino and Y. Nishida, “Field theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions,” Phys. Rev. A
103, 043307 (2021).
T. Naito, S. Endo, K. Hagino, and Y. Tanimura, “Are atoms spherical?” arXiv:2009.05955 [physics.atom-ph] (2020).
K. Murakami, Y. Akahoshi, and S. Aoki, “S-wave kaon-nucleon potentials with all-to-all propagators in the HAL QCD method,” Prog.
Theor. Exp. Phys. 2020, 093B03 (2020).
H. Irie, H. Liang, T. Doi, S. Gongyo, and T. Hatsuda, “Hybrid quantum annealing via molecular dynamics,” Sci. Rep. 11, 8426 (2021)
Y. Akahoshi, S. Aoki, T. Aoyama, T. Doi, T. Miyamoto, and K. Sasaki, “The HAL QCD potential in I = 1 ππ system with the ρ mesonbound state,” (2020). Prog. Theor. Exp. Phys. 2020, 073B07 (2020).

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