Post on 12-Apr-2020
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Takaya Miyamoto ( Yukawa Institute for Theoretical Physics, Kyoto University )
for HAL QCD Collaboration
Charmed baryon interaction from lattice QCD
格子 QCD による ΛcN 相互作用
S. Aoki, K. Sasaki, D. Kawai T. Doi, T. Hatsuda, T. Iritani T. Inoue N. Ishii, Y. Ikeda, K. Murano H. Nemura S. Gongyo F. Etminan
(YITP Kyoto Univ.) (RIKEN Nishina) (Nihon Univ.) (RCNP Osaka Univ.) (Univ. Tsukuba) (Univ. of Tours) (Univ. of Birjand)
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
Introduction
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Are there any charmed nuclei ??
The charmed baryon systems have more chance to have bound state
due to small kinetic energies.
charm-ness?
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
Introduction
3
Are there any charmed nuclei ??
The charmed baryon systems have more chance to have bound state
due to small kinetic energies.
charm-ness?
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
Theoretically, the formation of the Λc, Σc nuclei was predicted about 40 years ago.
・C. B. Dover and S. H. Kahana, Phys. Rev. Lett. 39, 1506 (1977). ・H. Bandō and S. Nagata, Prog. Theor. Phys. (1983) 69.
One-Boson-Exchange (OBE) model extended to SU(4). + Hard core at the short range.
Introduction
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Are there any charmed nuclei ??
charm-ness?
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
In the recent study, the possibility of ΛcN, ΣcN 2-body bound state was also claimed.
OBEP model based on the heavy quark effective theory.
・Y. R. Liu, M. Oka, Phys. Rev. D85, 014015 (2012).
・S. Maeda, M. Oka, A. Yokota, E. Hiyama
and Y. R. Liu, PTEP., 023D02 (2016). OBEP model + short range repulsion
(Quark Cluster model)
Next talk
The charmed baryon systems have more chance to have bound state
due to small kinetic energies.
Introduction
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Are there any charmed nuclei ??
charm-ness?
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
There are no experimental data for the charmed baryon - nucleon scattering.
Problem
Introduction
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Are there any charmed nuclei ??
charm-ness?
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
Charm nuclei could be investigated at forthcoming facility at J-PARC (K10).
・D-nuclei ・Λc-nuclei ...
There are no experimental data for the charmed baryon - nucleon scattering.
Problem
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Experimental Data
Lattice Data
Good S/N at heavy mass
It is difficult to obtain experimental data for charmed baryon interactions, but easy to calculate on the lattice.
MassThe lattice calculation has advantage to investigate heavy baryon systems.
To extract the baryon interaction from lattice QCD, we use HAL QCD method
Lattice QCD Ab-initio calculation of the QCD.
Introduction
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
S = 0 S = -1 S = -2 S = -3 S = -4 ・・・
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(1) Motivation
(2) HAL QCD method
(3) Simulation setup
(4) Numerical results
(5) Summary and conclusion
Outline
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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Hadron force from lattice QCD
・ Octet Baryon Interactions ・ Decaplet Baryon Interactions ・ Meson Interactions, Meson-Baryon Interactions ・ Three-body forces ・ Charmed Baryon Interactions <- This work !
N. Ishii, S. Aoki, T. Hatsuda, Phys.Rev.Lett. 99, 022001 (2007)
Lattice QCD
NBS wave function
Potential
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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HAL QCD method
Define the energy-independent non-local potential through the Schrödinger-type equation
from Nambu-Bethe-Salpeter (NBS) wave function
At large r
Interaction region
No-interaction region
The behavior of NBS wave function at large r is the same with QM wave function
The potential faithful to the phase shift by construction.
S. Aoki, T. Hatsuda, N. Ishii, Prog. Theor. Phys., 123 (2010).S. Aoki et al, [HAL QCD Collaboration], PTEP., 01A105 (2012).
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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Derivative (velocity) expansion
LO term
HAL QCD method S. Aoki, T. Hatsuda, N. Ishii, Prog. Theor. Phys., 123 (2010).S. Aoki et al, [HAL QCD Collaboration], PTEP., 01A105 (2012).
In the low energy state, LO term of the potential is significant.
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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Derivative (velocity) expansion
- For the case of JP=0+ state of ΛcN,
LO term
HAL QCD method S. Aoki, T. Hatsuda, N. Ishii, Prog. Theor. Phys., 123 (2010).S. Aoki et al, [HAL QCD Collaboration], PTEP., 01A105 (2012).
- For the case of JP=1+ state of ΛcN,
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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NBS wave function can be extracted from hadron 4pt-correlation function on the lattice at t -> ∞
HAL QCD method S. Aoki, T. Hatsuda, N. Ishii, Prog. Theor. Phys., 123 (2010).S. Aoki et al, [HAL QCD Collaboration], PTEP., 01A105 (2012).
We choose the following operator.
For the operator smearing, we employ the wall-source.
(Total momentum to be zero.)ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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Difficulty of ground state saturation
(1) Bad S/N at large t
In general, bad S/N occurs at large t-t0 separation.
(2) Small ΔE at large volume
At large volume, excited state contaminations remain even at a large t due to small ΔE.
To avoid this problem, we use time-dependent HAL QCD method.
E
ψ0
L
ψ1
ψ0
ψ1
ψ2
ψ2
・・・
・・・
HAL QCD method S. Aoki, T. Hatsuda, N. Ishii, Prog. Theor. Phys., 123 (2010).S. Aoki et al, [HAL QCD Collaboration], PTEP., 01A105 (2012).
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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N. Ishii et al [HAL QCD Coll.], PLB712 (2012) 437.
Normalized 4pt-correlation function (R-correlator)
The ground state saturation is not necessary.
We can obtain the signals at small t as long as the contributions of
inelastic scatterings are negligible.
・・・
time-dependent HAL QCD method
Within the approximation up to (ΔW)2.
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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In QCD calculation, the effects of inelastic contribution
are included implicitly.
UΛc Λc
NN
All 2PI contributions are included
EΣc*+NΣc +N
Λc +N
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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(1) Motivation
(2) HAL QCD method
(3) Simulation setup
(4) Numerical results
(5) Summary and conclusion
Outline
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
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Lattice QCD setup
2.9 fm
0.0907 fm
Nf=2+1 full QCD configurations generated by PACS-CS Coll. PACS-CS Collaboration:
S. Aoki, et al., Phys. Rev. D79 (2009) 034503
BG/Q @ KEK
- Iwasaki gauge action - O(a) improved Wilson-clover quark action - a ~ 0.09 fm, L ~ 3 fm ( 323 x 64 )
mπ ~ 700, 570, 410 MeVFor charm quark, we use Relativistic Heavy Quark (RHQ) action to reduce the leading O((ma)n) discretization error.
π 700 570 410
N 1578(6) 1392(6) 1221(10)
Λc 2689(4) 2552(6) 2434(6)
Σc 2783(6) 2674(9) 2568(10)
Hadron masses in units of MeV)
See more details in
Namekawa, et al.,
Phys. Rev. D84 (2011) 074505
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
ΛcN single-channel potential
When mπ became lighter, ・Repulsive core becomes stronger. ・Attractive pocket becomes long range.
ΛcN system has an attractive pocket.
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Results
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
JP=0+ JP=1+
ΛcN single-channel potential
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Results
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
We can extract the tensor force and central force by using NBS wave function for both 3S1 state and 3D1 state.
JP=0+ JP=1+
In the JP=1+ state, 3S1 and 3D1 state couple to each other.
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ΛcN single-channel potentialResu
lts
The range of tensor potential for ΛcN system is short.
Central potential
Tensor potential
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
The strength is weak. The pion mass dependence is small.
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ΛcN single-channel potentialResu
lts
Central potential
Tensor potential
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
Λc (I=0) Λc (I=0)
N (I=1/2) N (I=1/2)
π(I=1)
The strength is weak. The pion mass dependence is small.
The tensor potential of ΛcN channel appears at short range.
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ΛcN single-channel potentialResu
lts
Central potential
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
JP=0+The spin-dependent potential for the ΛcN system is almost zero except for short range.
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Short summary ΛcN single-channel potential
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
JP=0+
Weak WeakSign
ificant
JP=1+
Almost same
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Once we obtain the potential on the lattice, we can calculate the phase shift
in the infinite volume by fitting the potential.
We use the multi-range Gaussians for the fit function
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
The potential data in the finite box
The potential in the infinite volume
Fit the potential
Solve the Schrodinger equation
Phase shfit
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Phase shift analysis
1S0 3S1
The ΛcN system doesn’t form bound state at least mπ > 410MeV.
Scattering length: mπ 1S0 3S1
410 MeV 1.09 (37) fm 0.62 (25) fm570 MeV 0.28 (17) fm 0.33 (20) fm700 MeV 0.38 (14) fm 0.44 (16) fm
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016
Preliminaly
Results
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・We investigate ΛcN interaction by the HAL QCD method. ・Our results show that the ΛcN interaction is attractive.
Our results suggest that ΛcN 2-body state is unbound at least mπ > 410MeV
Summary & conclusion
Prospects: The calculation at the physical pion mass is next step. We will also investigate the possibility of Λc-nuclei by using HAL QCD potentials.
Weak WeakSign
ificant
ELPH 研究会 C015 @ 東北大学, 01 Dec. 2016