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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 **

**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

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**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 shifts**

**Analog to … **

**Analog to …**

**Phen. Potential **

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**E-indep (& non-local) Potential: **

**Faithful to phase shifts **

**The Challenge in multi-baryons on the lattice **

**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 *

**E-indep of potential U(r,r’)**

**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 **

**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 (^{1}S_{0})
(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/(E**_{1}**-E**_{0}**) NOT satisfied **

**t [a] **

**“fake plateaux” **

**at t ~ 1fm **

**“real plateau” **

**at t ~ 10fm **
(E_{1}-E_{0}=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/(E**_{1}**-E**_{0}**) NOT satisfied **

**t [a] **

**“fake plateaux” **

**at t ~ 1fm **

**“real plateau” **

**at t ~ 10fm **
(E_{1}-E_{0}=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 **

**r**_{eff [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. }

^{3}

^{S}1)

(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(^{1}S_{0}) and ΞΞ(^{1}S_{0}) 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 !