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Nuclear Physics from Lattice QCD

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2017/11/10 Workshop @ National Taiwan Univ.

Nuclear Physics from Lattice QCD

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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(?)

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• 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.)

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[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

(5)

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 …

Phen. Potential

5

E-indep (& non-local) Potential:

Faithful to phase shifts

(6)

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

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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]

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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

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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

9

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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

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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

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12

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

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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

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• 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

14

(15)

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

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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

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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

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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 ?

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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

(20)

ΝΩ system ( 5 S 2 )

Potentials Phase Shifts

Strong Attraction

possibly “Bound”

ΝΩ correlation in HIC

(200conf x 4rot x 48src)

preliminary

[T. Iritani]

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[K. Sasaki]

ΛΛ, ΝΞ, (ΣΣ) coupled channel H-dibaryon channel

2x2 Potentials

H-resonance (?)

(22)

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

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Central/Tensor Potentials NN ( 3 S 1 - 3 D 1 )

23

Strong Tensor Force is clearly visible !

preliminary

Central Tensor

Repulsive core

observed Attraction at mid-long range

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Impact on dense matter

24

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)

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[ T. Inoue ] 25

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[ T. Inoue ] 26

[Missing]

P-wave/LS forces 3-baryon forces

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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

27

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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 !

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