Session E04: Minisymposium: Exotic Hadrons II

Spectra and Time Evolution of Near-Threshold Structures in Coupled-Channeled Systems: An Approach by Uniformization and the Mittag-Leffler Expansion

Many candidates of exotic hadrons have been found near the two-body threshold of hadronic channels. However, due to the non-trivial structure of the S-matrix in the energy plane, model-independent extraction of the pole positions in the near-threshold domain is a rather challenging task.

In this talk, we focus on the analytic structure of the multi-channel S-matrix and introduce the notion of uniformization, an idea to use a variable where the S-matrix is single-valued. Combining uniformization with a pole expansion called the Mittag-Leffler Expansion, we obtain a simple expression applicable to near-threshold hadronic spectra. We present the Mittag-Leffler Expansion for the 2- and 3-channel case and show that in addition to ordinary resonance poles lying on the lower-half energy plane, poles on the upper-half energy plane, when positioned near the threshold, can manifest themselves as a prominent structure in the spectra.

Also, we extend "survival probability" discussed in single-channel systems to the 2-channel case and demonstrate that "threshold cusps" which correspond to near-threshold poles in the upper-half energy plane decay non-exponentially in time.   

Hadron-hadron potentials coupled to quark degrees of freedom for exotic hadrons

We study the properties of the hadron-hadron potentials and quark-antiquark potentials from the viewpoint of the channel coupling. It is also shown that the elimination of the different degrees of freedom induces the nonlocality and energy dependence of the effective potentials[1]. For the obtained nonlocal potentials, we apply two methods of the local approximation proposed previously, the formal derivative expansion and the derivative expansion in the HAL QCD method, by carefully examining the energy dependence of the potential. As an application, we construct a coupled-channel model of $car{c}$ and $Dar{D}$ to describe $X(3872)$, and discuss the property of the effective $D ar{D}$ potentials. We confirm that the local approximation by the HAL QCD method works better than the formal derivative expansion also for the energy-dependent potential. At the same time, we show that, in the HAL QCD method, the resulting phase shift is sensitive to the choice of the wavefunction to construct the local potential when the system has a shallow bound state such as $X(3872)$.

[1] I. Terashima and T. Hyodo, arXiv:2305.10689 [hep-ph].   

Diabatic Representation for Exotic Heavy Hadrons

The Born-Oppenheimer approximation for QCD provides an intuitive yet rigorous framework for the study of hadrons containing two heavy quarks. The energy levels of QCD with two static color sources, numerically accessible on the lattice, are translated into potentials for the nonrelativistic motion of the heavy quarks. The mass spectrum is then determined simply by solving a multichannel Schrödinger equation. In this talk, I discuss the diabatic representation of the Born-Oppenheimer approximation for QCD, where the coupled equations for the heavy-quark motion take a particularly simple form. I show that the diabatic representation provides an effective framework in which to study the effects of string breaking and heavy-quark spin symmetry breaking, which are essential ingredients for accurate calculations of exotic heavy hadrons.   

Decay properties of $N(1535)$ in the holographic QCD

We study one pion emission decay of the first excited state of the nucleon with negative parity $N(1535)$ in the holographic model of QCD. We have obtained the values of the off-diagonal axial coupling constant and hence the decay width, which is smaller than but reasonably compared to the experimental data.   

The dynamical properties of nucleon resonances by top-down approach of holographic QCD

Due to the non-perturbative nature of low-energy QCD, we do not always understand the properties of the nucleons, the fundamental excitations created by its vacuum. To understand low-energy QCD, it is useful to investigate nucleon resonances. In this study, we investigate various properties of nucleon resonances using the Sakai-Sugimoto model, one of the holographic QCD models. It is difficult to theoretically explain the various properties of the Roper resonance, even though it is one of the most experimentally established nucleon resonances. We have attempted to calculate the properties of the Roper resonance, especially the electromagnetic transition amplitude and the decay width of the one-pion emission. We also attempted the same analysis for other nucleon resonances (Δ(1232), N<span style="font-size:10.8333px">*(1535)). For this purpose, it is necessary to obtain the wave function and chiral current of baryons in the Sakai-Sugimoto model. In the Sakai-Sugimoto model, the wave function is obtained by collective coordinate quantization of instanton (baryon). We then define the current using the GKP-Witten relation and obtain the electromagnetic transition amplitude and the decay width of the one-pion emission, which are shown to reproduce the experimental data well. The results strongly suggest that the contribution of the collective motion of mesons is important for a comprehensive understanding of nucleon resonances.   

From Pentaquarks to the Proton's Matter Structure: Novel Insights from J/ψ-007

Heavy quarkonium production offers a unique avenue to probe the gluonic structure of the nucleon. In the 12 GeV era, the latest generation of experiments at Jefferson Lab employs near-threshold J/ψ production to delve into topics such as the matter structure of the proton, the dynamic origins of its mass, and the hidden-charm pentaquarks first observed by LHCb.

I will present new findings from the J/ψ-007 experiment conducted in Hall C at Jefferson Lab. I will discuss the latest updated results regarding the search for LHCb hidden-charm pentaquarks, including a first look at our combined J/ψ → ee and J/ψ → μμ datasets. I will then focus on our determination of the proton's gluonic gravitational form factors based on our 2-D J/ψ cross section measurement from our J/ψ → ee dataset, which we recently published in Nature. Remarkably, our results suggest the existence of a dense, energetic core within the proton, localized at a substantially smaller radius than the proton's electric charge radius. I will follow this with new results from our combined J/ψ → ee and J/ψ → μμ datasets, including a preliminary analysis of the pressure and shear forces of the gluonic fields in the proton.   

Exploring Exotic Hadrons Using Hyperon Spectrometer at J-PARC

Experimental programs on searching for exotic hadrons at the J-PARC hadron facility are presented. Recently, the J-PARC E42 completed a data collection to search for the six-quark state, H-dibaryon, in the bound and unbound mass regions near the ΛΛ threshold in 12C(K-,K+) reactions at 1.8 GeV/c. The H-dibaryon can be reconstructed exclusively from Λpπ−, ΛΛ and Ξ−p systems using the large-acceptance Hyperon Spectrometer, which consists mainly of a 1-T superconducting magnet and a GEM time projection chamber (HypTPC). The ongoing analysis progress and the anticipated results are reported. Furthermore, the recent observation of narrow hidden-charm pentaquark states by the LHCb Collaboration raises the question about the existence of the light pentaquarks. In light of this, the experimental attempts to search for the light pentaquark in K+d → K0pp reactions using the Hyperon Spectrometer at J-PARC are also discussed.   

Analysis of Xi(1620) resonance with chiral unitary approach

The excited states of Xi(1620) has not been theoretically analyzed for a long time. However, more detailed experimental results have recently been obtained, starting with spectra obtained by the Belle experiment in 2019. In 2021, the ALICE experiment determined the Kbar lambda scattering length with femtoscopy in lead-lead collisions.

In this talk, we construct a coupled-channel meson-baryon scattering amplitude which reproduces the Kbar Lambda scattering length from ALICE experiment using the chiral unitary method, and discuss nature of the Xi(1620) that exists near the KbarLambda threshold[1].

[1]T.Nisihibuchi and T.Hyodo, arXiv:2305.10753 [hep-ph]