Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

ΛN and ΣN interactions from 2 + 1 lattice QCD with almost
physical masses †∗1Nemura∗1H. Nemura,†∗11)
Ref. 1
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Description of the nuclear force from a fundamental
perspective is a challenging problem in physics. Characterization of an atomic nucleus as a nucleonic many
body system provides successful results although a nucleon is not a true rudimentary constituent of atomic
nucleus but a composition of quarks and gluons deﬁned in quantum chromodynamics (QCD). Especially,
precise determination of the nucleon-nucleon (N N ),hyperon-nucleon (Y N ), and hyperon-hyperon (Y Y )interactions has a large impact on the studies of both
hypernuclei and hyperonic matter inside neutron stars
since phenomenological descriptions of Y N and Y Y interactions are not well constrained from experimental
data because of the short life time of hyperons.
In the recent few years, 2+1 ﬂavor lattice QCD
calculations have been widely performed. This is an
opportune moment to investigate beyond the baryonbaryon (BB) potentials at the ﬂavor SU (3) point since
exploring breakdown of the ﬂavor symmetry is not
only an intriguing subject but also a major concern ofthe phenomenological Y N and Y Y interaction models. Therefore, it is beneﬁcial to take account of alarge number of BB channels. We have proposed anapproach for the eﬃcient calculation of a large number of four-point correlation functions for various BB
channels, and implemented a hybrid parallel C++ program at the very beginning (the ﬁrst quarter of 2013)
for calculating such a large number (e.g., 52 channels)
for the BB interactions from N N to ΞΞ.1)
Based on those works, an extremely large scale lattice QCD calculation is now being performed to unveil
the nature of nuclear forces with strangeness S = 0(N N ) to −4 (ΞΞ) and almost physical quark masses
corresponding to (mπ , mK ) ≈ (146, 525) MeV andlarge volume (La)4 = (96a)4 ≈ (8.1 fm)4 with latticespacing a ≈ 0.085 fm.
Figure 1 shows preliminary result of ΛN → ΣN tensor potential in the 3 S1 −3 D1 channel (top), ΣN central potential in the I = 1/2, 1 S0 channel (middle), andΣN central potential in the I = 3/2, 3 S1 −3 D1 channel(bottom). In the ﬁgure, the potentials are obtained at
imaginary time (t − t0 = 5 − 12) in the lattice QCD,
which might be slightly smaller than the region where
the excited state contamination above pion production
is suppressed because the statistics is not large enoughat this moment. See Ref.2)2 for detail. Calculation isunderway to improve both the signal/noise ratio andthe systematic uncertainty. Nevertheless, the presentresults show remarkable behaviors. For example, the0.40
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§N tensor
potential inin thethe 33SS11 −Fig. 1. Top:
Top: ¤N
ΛN −− ΣNtensor potential−33
DD11 channel
physical point latchannel obtained
obtained with
with nearly
nearly physicaltice QCD calculation on a volume (96a)4 ≈(8.1 fm)4
with lattice spacing a ≈ 0.085 fm and (mπ , mK ) ≈(146, 525) MeV. Middle: ΣN central potential in theI = 1/2, 1 S0 channel. Bottom: ΣN central potential in
the I = 3/2, 3 S1 −3 D1 channel.

top ﬁgure shows a sizable strength of ΛN → ΣN tensor interaction, which is expected to play an importantrole to have a light hypernucleus bounded. The lower
two ﬁgures show that these two ΣN interaction channels are repulsive, which is consistent with the quark
model’s prediction. Hence, lattice QCD would be apromising approach to clarify the origin of repulsive
nature of the ΣN interaction.
References1) H. Nemura, Comput. Phys. Commun. 207, 91 (2016)[arXiv:1510.00903 [hep-lat]].
2) H. Nemura et al., arXiv:1702.00734 [hep-lat].