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2017/11/10 Workshop @ National Taiwan Univ.
Nuclear Physics from Lattice QCD
Nuclear Forces
EoS of Dense Matter
1st-principle Lattice QCD
ab-initio nuclear calc.
The Odyssey from Quarks to Universe
QCD
Y dof J-PARC
Nuclear Forces / Hyperon Forces
QCD vacuum Nuclei Neutron Stars / Supernovae
© Leinweber
Baryons
Nucleosynthesis
Baryon Forces
RIBF/FRIB
LIGO/Virgo
KAGRA NS-NS merger YNN(?)
• Outline
– Introduction
– Theoretical framework (HAL QCD method) – (Results at heavy quark masses)
– Results at physical quark masses – Summary / Prospects
3 S. Aoki, T. Aoyama, D. Kawai,
T. Miyamato, K. Sasaki (YITP) T. Doi, T. M. Doi, S. Gongyo, T. Hatsuda, T. Iritani (RIKEN) F. Etminan (Univ. of Birjand) Y. Ikeda, N. Ishii, K. Murano, H. Nemura (RCNP)
T. Inoue (Nihon Univ.)
[HAL QCD method]
• Nambu-Bethe-Salpeter (NBS) wave function
– phase shift at asymptotic region
• Consider the wave function at “interacting region”
– U(r,r’): faithful to the phase shift by construction
• U(r,r’): E-independent, while non-local in general – Non-locality derivative expansion
R L
M.Luscher, NPB354(1991)531
CP-PACS Coll., PRD71(2005)094504 C.-J.Lin et al., NPB619(2001)467 N.Ishizuka, PoS LAT2009 (2009) 119
R L
Aoki-Hatsuda-Ishii PTP123(2010)89 S. Aoki et al., PRD88(2013)014036
Extended to multi-particle systems
HAL QCD method
L a tt ice Q C D
NBS wave func. Lat Baryon Force
(at asymptotic region)
Sc a tt er ing E x p.
Phase shiftsAnalog to …
Phen. Potential
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E-indep (& non-local) Potential:
Faithful to phase shifts
The Challenge in multi-baryons on the lattice
Elastic Inelastic
NNπ NN
Signal/Noise issue
Parisi(‘84), Lepage(‘89)
Existence of elastic scatt. states
Naïve plateau fitting at t ~ 1fm is unreliable (“mirage” of true signal)
(almost) No Excitation Energy
LQCD method based on G.S. saturation impossible
L=8fm @ physical point
T. Iritani et al. (HAL) JHEP1610(2016)101 T. Iritani et al. (HAL) PRD96(2017)034521
Time-dependent HAL method
G.S. saturation “Elastic state” saturation
N.Ishii et al. (HAL QCD Coll.) PLB712(2012)437
E-indep of potential U(r,r’) (excited) scatt states share the same U(r,r’) They are not contaminations, but signals
Original (t-indep) HAL method
Many states contribute
. . .
New t-dep HAL method
All equations can be combined as
Elastic Inelastic
NNπ
NN potential
[Exponential Improvement]
The Challenge in multi-baryons on the lattice
Elastic Inelastic
NNπ NN
Existence of elastic scatt. states
(almost) No Excitation Energy
LQCD method based on G.S. saturation impossible
HAL QCD method
Baryon Forces
Direct method
Savage et al. (NPL Coll.) Yamazaki et al.QC D Exp eri men ts
“Time-dependent method”
G.S. saturation NOT required w/ E-indep pot
N.Ishii et al. PLB712(2012)437
G.S. saturation required
Example of failure of the direct method
Wall and Smeared are Inconsistent:
one cannot judge which (or neither) is reliable
ΞΞ (1S0) (L=4.3fm) Physics should NOT depend on source op.
T. Iritani et al. (HAL) JHEP1610(2016)101
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∆E (MeV)
wall
∆E (MeV)
“Plateau-like structure”
but t >> 1/(E1-E0) NOT satisfied
t [a]
“fake plateaux”
at t ~ 1fm
“real plateau”
at t ~ 10fm (E1-E0=50MeV) HAL method is crucial !
“Anatomy” of sympton in direct method
T. Iritani (HAL Coll.), arXiv:1710.06147
∆E (MeV)
wall
∆E (MeV)
“Plateau-like structure”
but t >> 1/(E1-E0) NOT satisfied
t [a]
“fake plateaux”
at t ~ 1fm
“real plateau”
at t ~ 10fm (E1-E0=50MeV) HAL method is crucial !
“Anatomy” of sympton in direct method
T. Iritani (HAL Coll.), arXiv:1710.06147
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Singular behaviors
Data from Yamazaki et al (‘12)
“Sanity Check” for results from direct method
Data from NPL Coll. (‘15)
Inconsistent ERE Unphysical pole residue
T. Iritani et al. (HAL Coll.) PRD96(2017)034521
The fate of the direct method (check on NN)
T. Iritani et al. (HAL Coll.) PRD96(2017)034521
All data for NN by the direct method fail these “minimum” tests so far
Studies w/ the variational method are mandatory
• Outline
– Introduction
– Theoretical framework (HAL QCD method) – (Results at heavy quark masses)
– Results at physical quark masses
• Nuclear forces and Hyperon forces
• Impact on dense matter – Summary / Prospects
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Ishii-Aoki-Hatsuda (2007)
[Theory]
= HAL QCD method• Exponentially better S/N Ishii et al. (2012)
• Coupled channel systems Aoki et al. (2011,13)
• Baryon Forces from LQCD
= Unified Contraction Algorithm
[Software]
・Exponential speedup Doi-Endres (2013)
[Hardware]
= K-computer [10PFlops]
+ FX100 [1PFlops] @ RIKEN + HA-PACS [1PFlops] @ Tsukuba
・ HPCI Field 5 “Origin of Matter and Universe”
Baryon Interactions
at Physical Point
Lattice QCD Setup
• Nf = 2 + 1 gauge configs
– clover fermion + Iwasaki gauge w/ stout smearing – V=(8.1fm)4, a=0.085fm (1/a = 2.3 GeV)
– m(pi) ~= 146 MeV, m(K) ~= 525 MeV – #traj ~= 2000 generated
• Measurement
– All of NN/YN/YY for central/tensor forces in P=(+) (S, D-waves)
PACS Coll., PoS LAT2015, 075
Predictions for Hyperon forces
reff [fm]
r eff / a 0
Potential
ΩΩ system ( 1 S 0 ) The “most strange”
dibaryon system
Strong Attraction
Vicinity of bound/unbound [~ Unitary limit]
Phase Shifts
S. Gongyo et al. (HAL Coll.), arXiv:1709.00654
Potential
ΞΞ system ( 1 S 0 )
Strong Attraction yet Unbound
ΞΞ correlation in HIC
(2-gauss + 2-OBEP)
Phase Shifts
Flavor SU(3)-partner of dineutron
• “Doorway” to NN-forces
• Bound by SU(3) breaking ?
ΞΞ system ( 3 S 1 - 3 D 1 )
Central: Strong Repulsion Tensor: Weak
Potentials
Central
Tensor
Phase Shifts
(eff. 3S1)(2-gauss + 2-OBEP)
Flavor SU(3)-partner of Σ- n
• Σ- in neutron star ?
10plet ⇔ unique w/ hyperon DoF
ΝΩ system ( 5 S 2 )
Potentials Phase Shifts
Strong Attraction
possibly “Bound”
ΝΩ correlation in HIC
(200conf x 4rot x 48src)
preliminary
[T. Iritani]
[K. Sasaki]
ΛΛ, ΝΞ, (ΣΣ) coupled channel H-dibaryon channel
2x2 Potentials
H-resonance (?)
Repulsive core
observed Attraction at mid-long range
Central Potential NN ( 1 S 0 )
NN ΞΞ
The effect of SU(3)f breaking
Repulsive core enhanced for lighter quark mass ? OGE ?
NN(1S0) and ΞΞ(1S0) belong to 27-plet
Single N
Central/Tensor Potentials NN ( 3 S 1 - 3 D 1 )
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Strong Tensor Force is clearly visible !
preliminary
Central Tensor
Repulsive core
observed Attraction at mid-long range
Impact on dense matter
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LQCD YN/YY-forces + Phen NN-forces (AV18) used in Brueckner-Hartree-Fock (BHF)
Single-particle energy of Hyperon in nuclear matter
(Only diagonal YN/YY forces in SU(3) irrep used)
[ T. Inoue ] 25
[ T. Inoue ] 26
[Missing]
P-wave/LS forces 3-baryon forces
3N-forces (3NF)
Nf=2+1, mπ=0.51 GeV Nf=2, mπ=0.76-1.1 GeV
Kernel: ~50% efficiency achieved !
Triton channel
Magnitude of 3NF is similar for all masses
Range of 3NF tend to get longer (?) for m(pi)=0.5GeV
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• Baryon forces: Bridge between particle/nuclear/astro-physics
• HAL QCD method crucial for a reliable calculation
– Direct method suffers from excited state contaminations
• The 1st LQCD for Baryon Interactions at ~ phys. point
– m(pi) ~= 146 MeV, L ~= 8fm, 1/a ~= 2.3GeV
– Central/Tensor forces for NN/YN/YY in P=(+) channel
• Prospects
– Exascale computing Era ~ 2020s
– LS-forces, P=(-) channel, 3-baryon forces, etc., & EoS
Summary
© Leinweber
Nuclear Physics from LQCD New Era is dawning !