Baryon-baryon interaction from constituent quark model (Hadron - - PowerPoint PPT Presentation

Baryon-baryon interaction from constituent quark model

Aaron Park

(Theoretical Nuclear and Hadron Physics Group) Yonsei University

(Hadron Interactions and Polarization from Lattice QCD, Quark Model, and Heavy Ion Coillisions)

YITP HIPLQH2019

• 1. BB Interaction
• collaborated with T. Hatsuda, T. Inoue, S. H. Lee
• 2. BBB Interaction
• collaborated with S. H. Lee

YITP HIPLQH2019

1 2 3 4 5 6

Baryon-baryon interaction

𝑠 → 0

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1 2 3 4 5 6

Baryon-baryon interaction

𝑠 → 0

1 3 2 5 6 4

Dibaryon configuration

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Baryon-baryon interaction

baryon ⊗ baryon  dibaryon

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HAL QCD Collaboration, Prog. Theo. Phys. 124 (2010) 591

Baryon-baryon interaction in lattice QCD (SU(3) symmetric limit)

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Baryon-baryon interaction in Quark Model

baryon ⊗ baryon  dibaryon

Wave function = Orbital ⊗ Color ⊗ Flavor ⊗ Spin

[6]𝑃

• B. Silvestre-Brac and J. Leandri, Phys. Rev. D 45, 4221 (1992)

𝐼 dibaryon 𝑒∗(2380) 𝑂Ω ΩΩ

[222]𝐷 [33]𝐺𝐺

YITP HIPLQH2019 𝐼 -dibaryon : 𝑂Ω : 𝑒∗ : ΩΩ :

Flavor state of dibaryon

𝐺

1

𝐺27 𝐺8 𝐺27 𝐺10 𝐺28

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Comparion with Lattice QCD In SU(3) symmetric case

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• T. Inoue, QNP2018 conference

Baryon-baryon interaction in lattice QCD (SU(3) broken)

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Hamiltonian

: confinement potential : hyperfine potential

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We choose the following Jacobi coordinate and spatial part of the wave function satisfying [1234][56] symmetry.

In SU(3) flavor symmetry breaking case

In order to satisfy the Pauli exclusion principle, we construct the remaining flavor- color-spin part of the wave function to satisfy {1234}{56} symmetry.

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1 2 3

𝑦1 𝑦2

4 5 6

𝑦3 𝑦4 𝑦5

qqs+qqs : ΛΛ or ΣΣ qqq+qss : 𝑂Ξ

Additional kinetic energy

Static binding potential

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Color-spin interaction in SU(3) broken case

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Color-spin interaction in SU(3) broken case

 -24  8  8/3  8/3  -28/3

𝑛𝑣 = 𝑛𝑒 = 1

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Baryon-baryon interaction in Quark model

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Comparison with Lattice QCD

SU(3) symmetric case SU(3) broken case

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• M. Harvey, Nucl. Phys. A 352, 301 (1981)

Transformation coefficients

S-wave orbital

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Transformation coefficients

Baryon ⊗ baryon Dibaryon

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Transformation coefficients and SU(3) isoscalar factors

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Summary of BB interaction

1. We construct orbital-flavor-color-spin wave function of the dibaryon satisfying the Pauli exclusion principle. We estimate the baryon-baryon interaction in a compact multiquark configuration. 2. For both SU(3) flavor symmetric case and SU(3) flavor symmetry broken case, we conclude that our results show good agreement with lattice QCD results at short distance region.

YITP HIPLQH2019

• 1. BB Interaction
• collaborated with T. Hatsuda, T. Inoue, S. H. Lee
• 2. BBB Interaction
• collaborated with S. H. Lee

YITP HIPLQH2019

Hyperon puzzle in neutron stars

Massive (2𝑁⨀) neutron stars vs softening of EOS by hyperon mixing  Hyperon puzzle

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• Y. Sakuragi, PTEP 2016 (2016) 06A106

Hyperon puzzle in neutron stars

Massive (2𝑁⨀) neutron stars vs softening of EOS by hyperon mixing  Hyperon puzzle

• D. Lonardoni et al, PRL 114, 092301 (2015)

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Three-body interaction

1 2 3 1 2 3 1 2 3

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Three-body interaction

1 2 3 1 2 3 1 2 3 1 2 3 4 7 5 8 6 9

Tribaryon configuration

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Orbital state of tribaryon

3 × 3 = 6 + 51 + 42 + [33]

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Orbital state of tribaryon

3 × 3 = 6 + 51 + 42 + [33] antisymmetric symmetric

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Orbital state of tribaryon

In terms of baryon, there are four possibilities.

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Color state of the tribaryon

Wave function = Orbital ⊗ Color ⊗ Flavor ⊗ Spin

Meson Baryon Tetraquark Pentaquark Dibaryon Tribaryon Tetrabaryon # of color basis 1 1 2 3 5 42 462

[9]

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Flavor state of the tribaryon

Wave function = Orbital ⊗ Color ⊗ Flavor ⊗ Spin

Flavor and spin states of tribaryon :

[9] [333]

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Hyperfine potential

𝐿𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝐿𝐶1 + 𝐿𝐶2 + 𝐿𝐶3 

SU(3) flavor symmetric limit

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Hyperfine potential

where 𝐷𝐷𝐺 is the constant that depend on the spatial part of the wave function, which we will take to be universal for all physical states composed of s-wave quarks.

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Strangeness = −1 Λ𝑂𝑂 Σ𝑂𝑂 ⋮

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Strangeness = −2 ΛΛ𝑂 ΛΣ𝑂 ΣΣ𝑂 Ξ𝑂𝑂 ⋮

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S = −3 ΛΛΛ ΛΛΣ ΛΣΣ ΞΛ𝑂 ΞΣ𝑂 ⋮

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Strangeness = −4 ΞΛΛ ΞΛΣ ΞΣΣ ΞΞ𝑂 ⋮

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Strangeness = −5 ΞΞΛ ΞΞΣ ΩΛΛ ΩΞ𝑂 ⋮

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Strangeness = −6 ΞΞΞ ΩΞΛ ΩΞΣ ΩΩ𝑂 ⋮

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𝐶1 𝐶2 𝐶3

𝑈

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𝐶1 𝐶2 𝐶3

𝐸1 𝑈

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𝐶1 𝐶2 𝐶3

𝐸2 𝑈

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𝐸3

𝐶1 𝐶2 𝐶3

𝑈

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𝐶1 𝐶2 𝐶3

𝐸3 𝑈 𝐸2 𝐸1

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Pure three-body force

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Transformation coefficients

Baryon ⊗ baryon Dibaryon

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Transformation coefficients

Tribaryon  Baryon ⊗ Dibaryon

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Transformation coefficients

Tribaryon  Baryon ⊗ Dibaryon Tribaryon Baryon ⊗ Dibaryon

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Summary of BBB interaction

1. We have identified compact tribaryon configurations in terms of SU(3) flavor and spin quantum numbers that are allowed within the Pauli principle. 2. While compact configurations are possible for certain quantum numbers, we found that the color-spin interaction for all the allowed configurations are highly repulsive with respect to three baryon channel. 3. This is the microscopic proof that the three body nuclear force should be repulsive in all channels, which are consistent with the recently established neutron star mass limit.

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Thank you