Role of the effective range in the weak-binding relation

Kinugawa, Tomona; Hyodo, Tetsuo

doi:10.48550/arxiv.2112.00249

Cited by 7 publications

(10 citation statements)

References 20 publications

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“…This result is in accordance with other general estimates in the large N c limit, which predict the vanishing of the coupling constant in that limit [29,90,91,[114][115][116][117][118]. The behavior (108) should only be considered as a generic one. The power of the decrease may slightly change according to the detailed flavor content of the tetraquark state or other more refined analyses.…”

Section: Large N C Analysissupporting

confidence: 92%

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The Interplay between Compact and Molecular Structures in Tetraquarks

Sazdjian

2022

Symmetry

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Due to the cluster reducibility of multiquark operators, a strong interplay exists in tetraquarks between the compact structures, resulting from the direct confining forces acting on quarks and gluons, and the molecular structure, dominated by the mesonic clusters. This issue is studied within an effective field theory approach, where the compact tetraquark is treated as an elementary particle. The key ingredient of the analysis is provided by the primary coupling constant of the compact tetraquark to the two mesonic clusters, considered here in the framework of a scalar interaction. Under the influence of this coupling, an initially formed compact tetraquark bound state evolves towards a new structure, where a molecular configuration is also present. In the strong-coupling limit, the evolution may end with a shallow bound state of the molecular type. The strong-coupling regime is also favored by the large Nc properties of QCD. The interplay between compact and molecular structures may provide a natural explanation of the existence of many shallow bound states.

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Section: Large N C Analysissupporting

confidence: 92%

“…also Section 7. ) Detailed investigations about the compositeness criterion and its applicability to various tetraquark candidates, as well as to ordinary hadrons, can be found in References [84,[95][96][97][98][99][100][101][102][103][104][105][106][107][108][109].…”

Section: Resonancesmentioning

confidence: 99%

The Interplay between Compact and Molecular Structures in Tetraquarks

Sazdjian

2022

Symmetry

View full text Add to dashboard Cite

show abstract

“…Detailed investigations about the compositeness criterion and its applicability to various tetraquark candidates, as well as to ordinary hadrons, can be found in References [84,[95][96][97][98][99][100][101][102][103][104][105][106][107][108][109].…”

Section: Resonancesmentioning

confidence: 99%

The interplay between compact and molecular structures in tetraquarks

Sazdjian

2022

Preprint

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Due to the cluster reducibility of multiquark operators, a strong interplay exists in tetraquarks between the compact structure, resulting from the direct confining forces acting on quarks and gluons, and the molecular structure, dominated by the mesonic clusters. This issue is studied within an effective field theory approach, where the compact tetraquark is treated as an elementary particle. The key ingredient of the analysis is provided by the primary coupling constant of the compact tetraquark to the two mesonic clusters. Under the influence of this coupling, an initially formed compact tetraquark bound state evolves towards a new structure, where a molecular configuration is also present. In the strongcoupling limit, the evolution may end with a shallow bound state of the molecular type. The strong-coupling regime is also favored by the large-N c properties of QCD. The interplay between compact and molecular structures may provide a natural explanation of the existence of many shallow bound states.

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“…There has been some renewed interest recently [1][2][3][4] in refinements of the concepts of "compositeness" and "elementariness" of bound states and resonances [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], which can be extracted from scattering data, e.g. through the Weinberg relations [21] for the scattering length and effective range in the case of near-threshold bound states.…”

Section: Introductionmentioning

confidence: 99%

“…Generalizations of Eqs. ( 5) and ( 6) are extensively discussed in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14], but for the simple setting studied here, the above relations are adequate. To assess the validity of the linear approximations in Eq.…”

Section: Introductionmentioning

confidence: 99%

A toy model for "elementariness"

Bruns¹

2022

Preprint

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Motivated by recent efforts to analyze corrections to Weinberg's relations for the scattering length and effective range in the presence of a near-threshold bound state, we play around with an instructive toy model for non-relativistic scattering in a central potential. The model allows to interpolate between bound-state configurations of high "compositeness", where the wave function is spread over a wide region beyond the range of the interaction, and compact configurations of high "elementariness", where the wave function is confined to a small region around the center of the potential.

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Role of the effective range in the weak-binding relation

Cited by 7 publications

References 20 publications

The Interplay between Compact and Molecular Structures in Tetraquarks

The Interplay between Compact and Molecular Structures in Tetraquarks

The interplay between compact and molecular structures in tetraquarks

A toy model for "elementariness"

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