Research Group for Advanced Theoretical Physics
Group Leader : HOSAKA Atsushi
Members : UTSUNO Yutaka, MARUYAMA Toshiki, KOURA Hiroyuki, Philipp Gubler,
UCHINO Shun, YOSHIDA Kazuki, SUZUKI Kei, YAMAGUCHI Yasuhiro, MORI Michiyasu,
IEDA Jun'ichi, ONISHI Hiroaki, NAKATA Koki, YAMAMOTO Kei, ARAKI Yasufumi,
HIYAMA Emiko, OTSUKA Takaharu, Seiji MIYASHITA (Adviser)

The Advanced Theoretical Physics (ATP) Group conducts theresearch of fundamental sciences related to atomic energy. Ourmissions are to support experimental researches in JAEA and toexplore interdisciplinary researches with new ideas. We also
form a platform to exchange new ideas, to stimulateinternational collaborations and to train young researchers. Coremembers interests cover theoretical physics on hadrons andnuclei, the strongly interacting systems. In addition, condensed
matter physicists working on spintronics join the ATP.
As activities of Japanese Fiscal Year 2020, we would like toreport two items, the international workshop as a REIMEI
project and a collaboration among members of the group.
Workshop on "Physics of heavy-quark and exotic hadrons
2021" (Co-organized by KEK and JAEA)The entitled international workshop was held on 15-17
February, 2021 as a Reimei project activity. There were 121
participants of 66 Japanese and 55 foreigners altogether from 16countries. The workshop started with the invited lecture of threehours by Prof. Hatano who is the PI of the Reimei project about“Resonant states of open quantum systems” (Fig. 1). Other
invited talks from various fields were also presented including
nuclear and hadron physics. One hour was given to each talk,aiming at intensive discussions. Different approaches toresonance physics were discussed which gave usefulsuggestions to the current works of participants.

Fig.1: Snapshots showing typical contents of the discussions
from the lecture slide of Prof. Hatano.
Stable double-heavy tetraquarks
This work was performed as a collaboration in part among thetheory group members (Philipp Gubler, HIYAMA Emiko,HOSAKA Atsushi and OKA Makoto), and the results were
published in Physics Letters [1].
One of long-standing questions in hadron physics is whether
stable exotic hadrons exist or not. If so, the relevant questions
are what structure, what property, and how best measured. Theanswers to them have been conjectured; double heavy quarks
stabilize four and five quark systems. Consequently, double
heavy tetraquarks and pentaquarks were predicted [2]. The
basic principle is the strong color-Coulomb attractive interaction
between the heavy quarks and the location of the threshold of
two or more particles which exotic states decay to. A wellknown feature of the Coulomb force helps to stabilize thesystem; the binding energy becomes larger for heavier particles,

EB ~ α2μ/n2 (n: principal quantum number), where α is the finestructure constant of the strong interaction that is of order 0.5,
and μthe reduced mass of the two heavy quarks.
For this problem, we have studied the double heavy tetraquark
systems such as bbq*q* (b: bottom quark, q* = anti u or d quark)in the quark model. The four-body systems were analyzed in
the full four-body calculations to find stable states for various
quark flavor contents. The results are summarized in Fig. 2
below. One conclusive result is that there should exist a deeply
bound state of isospin I = 0 and spin-parity JP =1+ with a binding
energy nearly 200 MeV, which confirms the previous conjecture[2]. In addition to the masses, we have also studied the density
distributions of the obtained states to examine the internalstructure. It is interesting to observe that two very different
structures were found for the deeply bound state and the shallow
one with 4 MeV binding energy. The former has a compact
three-body like structure with strongly bound heavy diquark(bb) and q*q* moving around it, while the latter forms amolecular like structure of (bq*)-(bq*). These results answer thequestion of what structure and what property. We have also
discussed possible decays of these states including weak andradiative decays to answer how best measured in terms of weakand electromagnetic processes.

Fig.2 Bound tetraquarks with their energies −EB (MeV) measured fromthe thresholds for various flavor contents. The labels beside eachbar indicate isospin and spin-parity quantum numbers I(JP). The
hatch pattern in the bcq*q* sector indicates that the distance
between the DB*-D*B* thresholds does not reflect the actual scale.

References[1] Q. Meng, E. Hiyama, A. Hosaka, M. Oka, P. Gubler,K.U.Can, T.T.Takahashi, H.S.Zong, Phys.Lett.B 814 (2021)
136095, doi: 10.1016/j.physletb.2021.136095.
[2] M. Karliner, J.L. Rosner, Phys. Rev. Lett. 119(20) (2017)202001,doi:10.1103/PhysRevLett.119.202001. Also in Nature551 (2017) 89. doi: 10.1038/nature24289.