12020/11/04 ELPH2020 @ Tohoku U. (on-line)

Recent progress on Hadron

Interactions from Lattice QCD

Takumi Doi

(RIKEN Nishina Center / iTHEMS)

EoS of Dense Matter

1st-principle Lattice QCD

ab-initio nuclear calc.

The Odyssey from Quarks to Universe

QCD

Y dof

QCD vacuum NucleiNeutron Stars / Supernovae

© Leinweber

BaryonsNucleosynthesis

Baryon Forces

RIBF/FRIB

aLIGO/KAGRALHC/RHIC

J-PARC

YNN(?)

NICER

3

Hadrons to Atomic nuclei from Lattice QCD (HAL QCD Collaboration)

「20XX年宇宙の旅」20XX:

from Quarks to Universe

Y. Akahoshi, S. Aoki, K. Murakami,

K. Sasaki (YITP)

T. Aoyama (KEK)

T. Doi, S. Gongyo, T. Hatsuda, T. Iritani, Y. Lyu,

T. Miyamoto, T. Sugiura, H. Tong (RIKEN)

T. M. Doi, N. Ishii, K. Murano, H. Nemura (RCNP)

F. Etminan (Univ. of Birjand)

Y. Ikeda (Kyushu Univ.)

T. Inoue (Nihon Univ.)

• E-indep potentail from NBS w.f.

– Faithful to Phase Shifts by construction

• Time-dependent HAL method

– G.S. saturation NOT required

• Coupled Channel formalism

– Above inelastic threshold ➔ Essential for YN/YY-forces, Exotics

Latt

ice

QC

DNBS wave func. Lat Baryon Force

(non-locality: derivative expansion)

HAL QCD method

Aoki-Hatsuda-Ishii PTP123(2010)89

N.Ishii et al. (HAL Coll.) PLB712(2012)437

S. Aoki et al. (HAL Coll.) Proc.Jpn.Acad.B87(2011)509

“Signal” from (elastic) excited states

t~10fm

t~1fm

Luscher’s formula vs. HAL method [case closed]

NN @ heavy quark masses

T. Iritani et al. (HAL) JHEP10(2016)101, PRD96(2017)034521, PRD99(2019)014514, JHE03(2019)007

“Pseudo-Plateau” by excited states

HAL QCD pot = Luscher’s formula w/ Eigenstate projection

≠ Direct method w/ naïve plateau fitting

HAL method (HAL) : unbound

Direct method (PACS-CS (Yamazaki et al.)/NPL/CalLat): bound

Semi-improved calc w/ Luscher’s formula (Mainz2019) : unbound

Variational calc w/ Luscher’s formula (CalLat2020) : unbound

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 / Post K Priority Issue 9

Baryon Interactionsnear the 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

Candidates of di-baryons

X 8 x 8 = 27 + 8s + 1 + 10* + 10 + 8s

H-dibaryon(J=0)

Deuteron(J=1)

dineutron, XX etc. (J=0)

X 8 x 10 = 35 + 8 + 10 + 27

NW (J=2) Goldman et al. (‘87)Oka (‘88)

X 10 x 10 = 28 + 27 + 10* + 35

WW (J=0)Dyson-Xuong (‘64)Kamae-Fujita (‘77)Oka-Yazaki (‘80)

DD (J=3)

Zhang et al. (‘97)

“Most Strange” Dibaryon ： WW

ΩΩ (1S0) potential

S. Gongyo et al. (HAL Coll.), PRL120(2018)212001

“di-Omega”

[~ Unitary limit]

Phase Shifts

NW system (5S2)

(Quasi) Bound state

[~ Unitary limit ]

Potentials

T. Iritani et al. (HAL Coll.), PLB792(2019)284

Phase Shifts

reff [fm]

r eff

/ a

0

S = -2 Hypernuclei

c.f. H-dibaryon (1S0, LL-NX-SS)

NAGARA-event (2001)

B.E. = 4.38(25) MeV or 1.11(25) MeV

KISO-event (2014)

X-hypernuclei

[KEK-PS E373]

MINO-event (2019)

[KEK-PS E373]

[J-PARC E07]

LL-hypernuclei

➔[J-PARC E07, E05/E70] etc.

LL, NX (effective) 2x2 coupled channel analysis

K. Sasaki et al., (HAL Coll.), NPA998(2020)12137

LL, NX 2x2 coupled channel analysis

NX ~ unitary limitremnant of “H-dibaryon”

a0 = -0.81(23)(+0.00/-0.13) [fm]reff = 5.47(78)(+0.09/-0.55) [fm]

K. Sasaki et al., (HAL Coll.), NPA998(2020)12137

Spin-Isospin dependence of NX potentials

I=0 I=1

S=

0S

=1

c.f. ESC08cI=0, S=0: weakly repulsiveI=0, S=1: strongly attractiveI=1, S=0: weakly repulsiveI=1, S=1: strongly attractive

(8a)

(1,27,8s) (8s,27)

(8a,10,10*)

K. Sasaki et al., (HAL Coll.), NPA998(2020)12137

S= -2 Hypernuclei from LQCD

15

Particle Physics

First-principles LQCD calc

Nuclear Physics

Ab initio many-body calc

NX (1S0, I=0)

E. Hiyama et al., PRL124(2020)092501Guiding experiments

HIC@LHC, J-PARC, …

(+ physical point extrapolation)

S= -2 Hypernuclei from Experiments

16

Fig from

Nakazawa @ JPS2020/09

Indication of small LL-NX coupling?

Fit of the LL, NX int. in 11S0 channel

LL: gausses + 2piLL-NX: gausses + KNX: gausses + 2pi + pi

N.B. Decomposition has larger uncertainties than the total potential“Interpretation” is generally non-trivial,but OBEP terms seem to be reasonable

LL-NXLL

NX

[K. Sasaki]

Fit of the NX potentials

I=0 I=1

S=

0S

=1

NX: gausses + 2pi + pi[K. Sasaki]

BB-correlation ➔ BB- (final state) interaction

K. Morita et al., PRC94(2016)031901

Baryon-Baryon correlation in HIC

Fig. from K. Morita

Ratio of correlation between small/large source size is useful to mask Coulomb effect K. Morita et al., PRC102(2020)015201

ALICE Coll., arXiv:2005.11495

LL ALICE Coll., PLB797(2019)134822

pX- pW

HIC-exp data are coming !

HAL

ALICE Coll., PRL123(2019)112002

[S. Gongyo]

d*(2380) dibaryon from Lattice

S. Gongyo et al., (HAL Coll.) arXiv: 2006.00856

@ heavy quark mass

m(p) = 0.68, 0.84, 1.02 GeV

m(N) = 1.48, 1.74, 2.02 GeVm(D) = 1.68, 1.94, 2.21 GeV

DD potential in I=0, J=3 channel(D is a bound state)

Nf=3 clover fermionL3=(3.87fm)3, a = 0.121fm

t-dep of Potential

m(p)=1.02GeV

mass-dep of Potential

d*(2380) dibaryon from Lattice

@ heavy quark mass

m(p) = 0.68, 0.84, 1.02 GeV

m(N) = 1.48, 1.74, 2.02 GeVm(D) = 1.68, 1.94, 2.21 GeV

DD potential in I=0, J=3 channel(D is a bound state)

Nf=3 clover fermionL3=(3.87fm)3, a = 0.121fm

Phase shifts Bound state energy

S. Gongyo et al., (HAL Coll.) arXiv: 2006.00856

Resonances

I=1 pipi system (rho-meson) w/ HAL method + all-to-all propagators

Y. Akahoshi et al., (HAL Coll.), PTEP2019(2019)083B02, PTEP2020(2020)073B07

Resonances

New method w/ one-end trick

[Y. Akahoshi @ APLAT2020]

McNeile-Michael (2006)

Diagrams for I=1 pipi

AMA is used for x (trans. inv.)

➔ x1/10 stat error!

Potentials for I=1 pipi

Y. Akahoshi@ APLAT2020

LO analysis

NLO analysis

Phase shifts for I=1 pipi

[Y. Akahoshi @ APLAT2020]

mass & g(rpp)

Rho-resonance from NLO analysismass: consistent w/ FV methodwidth: improvement of NLO pot necessary

m(pi) ~= 0.40GeV m(rho) ~= 0.89GeV

• Hadron Int.: Bridge between particle/nuclear/astro-physics

• The 1st LQCD for Baryon Interactions near the phys. point

– m(pi) ~= 146 MeV, L ~= 8fm, 1/a ~= 2.3GeV

– Central/Tensor forces for NN/YN/YY in P=(+) channel

– Dibaryons, Applications to Hypernuclei, EoS started

• New development to study resonances

– One-end trick + sequential method + AMA ➔ annihilation diagrams

– I=1 pipi ➔ rho resonance obtained

• Fugaku (2021-)

– Baryon forces on the physical point

– Dibaryons, Hypernuclei

– Future: LS-forces, P=(-) channel, 3-baryon forces, etc., & EoS

– Resonances & Exotics

Summary