Charmed baryon interaction from lattice QCD 格子 …...2016/12/01 · ・ Charmed Baryon...

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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?


Introduction

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charm-ness?


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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charm-ness?


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



Introduction

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charm-ness?


There are no experimental data for the charmed baryon - nucleon scattering.

Problem

Introduction

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charm-ness?


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


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


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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


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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).


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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.


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Derivative (velocity) expansion

- For the case of JP=0+ state of ΛcN,

LO term


- For the case of JP=1+ state of ΛcN,


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NBS wave function can be extracted from hadron 4pt-correlation function on the lattice at t -> ∞


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

・・・

・・・



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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.


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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


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(1) Motivation

(2) HAL QCD method

(3) Simulation setup

(4) Numerical results

(5) Summary and conclusion

Outline


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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


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


JP=0+ JP=1+

ΛcN single-channel potential

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Results


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


The strength is weak. The pion mass dependence is small.

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lts

Central potential

Tensor potential


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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lts

JP=0+ Central potential


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lts

Central potential


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


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


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


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



Comparison of ΛN and ΛcN

mπ ~ 700 MeV mπ ~ 410 MeV

JP = 0+


Comparison of ΛN and ΛcN

mπ ~ 700 MeV mπ ~ 410 MeV

JP = 1+


Comparison of ΛN and ΛcNmπ ~ 700 MeV

JP = 0+ JP = 1+

Preliminary

Charmed baryon interaction from lattice QCD 格子 …...2016/12/01 · ・ Charmed Baryon...

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