Understanding the dynamics of hadrons with strangeness has received a lot attention over the past decades in connection with the study of exotic atoms, the analysis of strangeness production and propagation in particle and nuclear research facilities, and the investigation of the possible strange phases in the interior of neutron stars. One venue of interest in the field of strangeness is the study of strange baryons, the so-called hyperons. In this talk I will review the dynamics of hyperons with nucleons and nuclear matter. I will also discuss the presence of hyperons in the inner core of neutron stars as well as the consequences for the structure of these compact stars and their dynamics in neutron starmergers.

We investigate how a dense nuclear medium affects the D_s(2317)^± and T_cc(3875)^± states. In vacuum, these states are modeled as isoscalar DK (Dbar Kbar) and DD* (Dbar Dbar*) S-wave bound states, formed through effective interactions that correspond to different Weinberg compositeness models. Matter effects are introduced via two-meson loop functions, incorporating the self-energies acquired by D^(*), Dbar^(*), K, and Kbar mesons when they interact in a nuclear medium. Although D_s(2317) and T_cc(3875) have identical particle-antiparticle lineshapes in vacuum, they display highly distinct density patterns in nuclear matter. This charge-conjugation asymmetry mainly arises from the differing interactions of kaons (Dbar and Dbar*) and antikaons (D and D*) with the nucleons in the dense medium. Our findings demonstrate that the in-medium lineshapes of these resonances are closely tied to their molecular DK and DD* components, offering a new approach to determine/constrain the internal structure of these exotic states.

Many candidates of exotic hadrons have recently been found near the two-body threshold of hadronic channels. Due to the non-trivial analytic structure of the S-matrix in the complex energy plane, however, extraction of pole positions is a rather challenging task. Combining uniformization with the Mittag-Leffler Expansion, we can obtain a general pole expansion of the coupled-channel S-matrix applicable to near-threshold hadronic spectra. We will formulate the Mittag-Leffler Expansion for the 2- and 3-channel case and show that in addition to ordinary resonance poles positioned on the lower-half energy plane, poles on the upper-half energy plane, when positioned near the threshold, can manifest themselves as a prominent cusp-like structure in the spectra. Naturally, the time evolution of an excited state in the presence of a near-threshold positive-imaginary pole is a case of interest. We will introduce the “Survival Amplitude” of excited states previously formulated in single-channel systems [G. Ordonez and N. Hatano (2017)] and extend it to the 2-channel case using the Mittag-Leffler expansion. Under this formalism, we show that the “Survival Amplitude,” in the presence of a near-threshold positive-imaginary pole, decays non-exponentially in all time regions. We will also formulate a similar pole expansion for temporal correlation functions in Euclidean spacetime and introduce a way to extract pole positions. We anticipate that this method can be used to analyze LQCD data in the future.

ポテンシャルVからLippmann-Schwinger方程式を解いて得られるT行列は、観測量である位相差を含め散乱波と同等の情報を持っている。その為に、ポテンシャルからではなくT行列から出発して散乱理論を構築することができれば、観測量を制御した散乱理論（およびポテンシャル）が構成できるはずである。しかしながら、ポテンシャルのHermite性に対応してT行列が満たさなければならない条件は長らく不明であり、このような相互作用の構築法は不可能であった。そこで本セミナーではT行列が満たすべき条件として一般化された光学定理(Generalized optical theorem, GOT)を紹介し、その応用として実際に観測量を再現するようなポテンシャルの構成法（逆散乱問題の一般解法）について説明を行う。最後に原子核分野への応用についても述べる。