The existence of a nucleon–ϕ (N–ϕ) bound state has been subject of theoretical and experimental investigations for decades. In this letter, indication of a p–ϕ bound state is found, using for the first time two-particle correlation functions as alternative to invariant mass spectra. Newly available lattice calculations for the spin 3/2 N–ϕ interaction by the HAL QCD collaboration are used to constrain the spin 1/2 counterpart from the fit of the experimental p–ϕ correlation function measured by ALICE. The corresponding scattering length and effective range are <math><msubsup><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><mo>(</mo><mo>−</mo><msubsup><mrow><mn>1.54</mn></mrow><mrow><mo>−</mo><mn>0.53</mn></mrow><mrow><mo>+</mo><mn>0.53</mn></mrow></msubsup><msubsup><mrow><mo>(</mo><mrow><mi>stat</mi><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>−</mo><mn>0.09</mn></mrow><mrow><mo>+</mo><mn>0.16</mn></mrow></msubsup><mo>(</mo><mrow><mi>syst</mi><mo>.</mo></mrow><mo>)</mo><mo>+</mo><mi>i</mi><mo>⋅</mo><msubsup><mrow><mn>0.00</mn></mrow><mrow><mo>−</mo><mn>0.00</mn></mrow><mrow><mo>+</mo><mn>0.35</mn></mrow></msubsup><msubsup><mrow><mo>(</mo><mrow><mi>stat</mi><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>−</mo><mn>0.00</mn></mrow><mrow><mo>+</mo><mn>0.16</mn></mrow></msubsup><mo>(</mo><mrow><mi>syst</mi><mo>.</mo></mrow><mo>)</mo><mo>)</mo></mrow></math> fm and <math><msubsup><mrow><mi>d</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><mo>(</mo><msubsup><mrow><mn>0.39</mn></mrow><mrow><mo>−</mo><mn>0.09</mn></mrow><mrow><mo>+</mo><mn>0.09</mn></mrow></msubsup><msubsup><mrow><mo>(</mo><mrow><mi>stat</mi><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>−</mo><mn>0.03</mn></mrow><mrow><mo>+</mo><mn>0.02</mn></mrow></msubsup><mo>(</mo><mrow><mi>syst</mi><mo>.</mo></mrow><mo>)</mo><mo>+</mo><mi>i</mi><mo>⋅</mo><msubsup><mrow><mn>0.00</mn></mrow><mrow><mo>−</mo><mn>0.04</mn></mrow><mrow><mo>+</mo><mn>0.00</mn></mrow></msubsup><msubsup><mrow><mo>(</mo><mrow><mi>stat</mi><mo>.</mo></mrow><mo>)</mo></mrow><mrow><mo>−</mo><mn>0.02</mn></mrow><mrow><mo>+</mo><mn>0.00</mn></mrow></msubsup><mo>(</mo><mrow><mi>syst</mi><mo>.</mo></mrow><mo>)</mo><mo>)</mo></mrow></math> fm, respectively. The results imply the appearance of a p–ϕ bound state with an estimated binding energy in the range of <math><mn>12.8</mn><mo>−</mo><mn>56.1</mn></math> MeV.

Germany

Emma Chizzali

Japan

Yuki Kamiya

Raffaele Del Grande

Takumi Doi

Laura Fabbietti

Tetsuo Hatsuda

China

Yan Lyu

Indication of a p– Bound State From a Correlation Function Analysis

Starting from the SU(3) limit, we consider the nature of the dynamically generated resonances <math><mi>Λ</mi><mo>(</mo><mn>1380</mn><mo>)</mo></math>, <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> and <math><mi>Λ</mi><mo>(</mo><mn>1680</mn><mo>)</mo></math> as the pion and kaon masses are tuned to their physical values. We show that the accidental symmetry of the two octets due to the leading order Weinberg-Tomozawa term is broken by the next-to-leading order terms. Most interestingly, we observe an interchange of the two trajectories of the <math><mi>Λ</mi><mo>(</mo><mn>1380</mn><mo>)</mo></math> and the <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> away from the SU(3) limit at next-to-leading order. This remarkable phenomenon can be investigated using lattice QCD calculations that start from the SU(3) limit.

Feng-Kun Guo

United States

Maxim Mai

Georgia

Ulf-G. Meißner

New insights into the nature of the Λ(1380) and Λ(1405) resonances away from the SU(3) limit

It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the  $$D_0^*(2300)$$  <math> <mrow> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mn>2300</mn> <mo>)</mo> </mrow> </mrow> </math>  , can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off D mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of  $$D\pi $$  <math> <mrow> <mi>D</mi> <mi>π</mi> </mrow> </math>   scattering at different pion masses only one pole was reported in the  $$D_0^*$$  <math> <msubsup> <mi>D</mi> <mn>0</mn> <mo>∗</mo> </msubsup> </math>   channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the K-matrix formalism to reduce the number of parameters.

Anuvind Asokan

Meng-Na Tang

Christoph Hanhart

Can the two-pole structure of the  $$D_{0}^{*}(2300)$$  <math> <mrow> <msubsup> <mi>D</mi> <mrow> <mn>0</mn> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mn>2300</mn> <mo>)</mo> </mrow> </mrow> </math>   be understood from recent lattice data?

The effects of the <math><msub><mi>Σ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>−</mo><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math>, are reinvestigated. Both the pion and <math><mi>ρ</mi></math>-meson exchanges are considered for the <math><msub><mi>Σ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mtext>−</mtext><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> coupled-channel dynamics. It is found that the role of the <math><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> channel in the descriptions of the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term of the one-pion exchange (OPE) keep failing to reproduce the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> states simultaneously. The OPE potential with the full <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term results in a too large mass splitting for the <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup><mtext> </mtext><mtext> </mtext><msub><mi>Σ</mi><mi>c</mi></msub><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> bound states with total isospin <math><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math>. The OBE model with only the OPE <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> potential and find that the masses of the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4312</mn><mo>)</mo></math>, <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math>, and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> can be reproduced simultaneously with the <math><mi>δ</mi><mo>(</mo><mover><mi>r</mi><mo>→</mo></mover><mo>)</mo></math> term in the OBE model reduced by about 80%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4440</mn><mo>)</mo></math> and <math><msub><mi>P</mi><mi>c</mi></msub><mo>(</mo><mn>4457</mn><mo>)</mo></math> are <math><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> and <math><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math>, respectively.

Nijiati Yalikun

Yong-Hui Lin

Bing-Song Zou

Coupled-channel effects of the <math><msubsup><mi>Σ</mi><mi>c</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mover><mi>D</mi><mo>¯</mo></mover><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>−</mo><msub><mi>Λ</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mover><mi>D</mi><mo>¯</mo></mover></math> system and molecular nature of the <math><msub><mi>P</mi><mi>c</mi></msub></math> pentaquark states from one-boson exchange model

Based on a baryon-baryon interaction model with meson exchanges, we investigate the origin of the strong attraction in the <math><mrow><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mi>S</mi><mn>2</mn><none></none><mprescripts></mprescripts><none></none><mn>5</mn></mmultiscripts><mo>)</mo></mrow></math> interaction, which was indicated by recent lattice QCD simulations. The long-range part of the potential is constructed by the conventional mechanisms, the exchanges of the <math><mi>η</mi></math> meson and of the correlated two mesons in the scalar-isoscalar channel, denoted by “<math><mi>σ</mi></math>” in the literature. The short-range part is represented by the contact interaction. We find that the meson exchanges do not provide sufficient attraction. This means that most of the attraction is attributed to the short-range contact interaction. We then evaluate the effect of the coupled channels to the <math><mrow><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mi>S</mi><mn>2</mn><none></none><mprescripts></mprescripts><none></none><mn>5</mn></mmultiscripts><mo>)</mo></mrow></math> interaction. We find that, while the <math><mi>D</mi></math>-wave mixing of the <math><mrow><mi>N</mi><mi>Ω</mi></mrow></math> channel is negligible, the inelastic <math><mrow><mi>Λ</mi><mi>Ξ</mi></mrow></math>, <math><mrow><mi>Σ</mi><mi>Ξ</mi></mrow></math>, and <math><mrow><mi>Λ</mi><mi>Ξ</mi><mo>(</mo><mn>1530</mn><mo>)</mo></mrow></math> channels via the <math><mi>K</mi></math> meson exchange give the attraction of the <math><mrow><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mi>S</mi><mn>2</mn><none></none><mprescripts></mprescripts><none></none><mn>5</mn></mmultiscripts><mo>)</mo></mrow></math> interaction to the same level with the elastic meson exchanges. Although the elimination of these channels induces the energy dependence of the single-channel <math><mrow><mi>N</mi><mi>Ω</mi></mrow></math> interaction, this effect is not significant. With the present model parameters fit to reproduce the scattering length of the HAL QCD result of the nearly physical quark masses, we obtain the <math><mrow><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mi>S</mi><mn>2</mn><none></none><mprescripts></mprescripts><none></none><mn>5</mn></mmultiscripts><mo>)</mo></mrow></math> quasibound state with its eigenenergy <math><mrow><mn>2611.3</mn><mo>−</mo><mn>0.7</mn><mi>i</mi><mspace width="4.pt"></mspace><mtext>MeV</mtext></mrow></math>, which corresponds to the binding energy <math><mrow><mn>0.1</mn><mspace width="4.pt"></mspace><mtext>MeV</mtext></mrow></math> and width <math><mrow><mn>1.5</mn><mspace width="4.pt"></mspace><mtext>MeV</mtext></mrow></math> for the decay to the <math><mrow><mi>Λ</mi><mi>Ξ</mi></mrow></math> and <math><mrow><mi>Σ</mi><mi>Ξ</mi></mrow></math> channels. From the analysis of the spatial structure and the compositeness, the quasibound state is shown to be the molecular state of <math><mrow><mi>N</mi><mi>Ω</mi></mrow></math>. We also construct an equivalent local potential for the <math><mrow><mi>N</mi><mi>Ω</mi><mo>(</mo><mmultiscripts><mi>S</mi><mn>2</mn><none></none><mprescripts></mprescripts><none></none><mn>5</mn></mmultiscripts><mo>)</mo></mrow></math> system which is useful for various applications.

Takayasu Sekihara

Tetsuo Hyodo

<math><mrow><mi>N</mi><mi>Ω</mi></mrow></math> interaction: Meson exchanges, inelastic channels, and quasibound state

We discuss the relation between the analytic structure of the scattering amplitude and the origin of an eigenstate represented by a pole of the amplitude. If the eigenstate is not dynamically generated by the interaction in the channel of interest, the residue of the pole vanishes in the zero coupling limit. Based on the topological nature of the phase of the scattering amplitude, we show that the pole must encounter with the Castillejo-Dalitz-Dyson (CDD) zero in this limit. It is concluded that the dynamical component of the eigenstate is small if a CDD zero exists near the eigenstate pole. We show that the line shape of the resonance is distorted from the Breit-Wigner form as an observable consequence of the nearby CDD zero. Finally, studying the positions of poles and CDD zeros of the <math><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>N</mi><mtext>−</mtext><mi>π</mi><mi>Σ</mi></mrow></math> amplitude, we discuss the origin of the eigenstates in the <math><mrow><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></mrow></math> region.

Structure of hadron resonances with a nearby zero of the amplitude

We study the compositeness of near-threshold states to investigate the internal structure of exotic hadron candidates. Within the framework of effective field theory, Weinberg's weak-binding relation is extended to more general cases by easing several preconditions. First, by evaluating the contribution from the decay channel, we obtain the generalized relation for unstable quasibound states. Next, we generalize the relation to include the nearby CDD (Castillejo–Dalitz–Dyson) pole contribution with the help of the Padé approximant. The validity of the estimation with the generalized weak-binding relations is examined by numerical calculations. A method to systematically evaluate the error in the weak-binding relation is presented. Finally, by applying the extended relation to Λ(1405) , f0(980) , and a0(980) , we discuss their internal structure, in comparison with other approaches.

Generalized weak-binding relations of compositeness in effective field theory