The evolution equations of several exactly solvable dynamical systems can be written in Hamiltonian form in two distinct manners, using two different Poisson bracket structures and corresponding Hamiltonians. Such bi Hamiltonian structures lead to the existence of conserved quantities associated with the integrability of the pertinent systems. In this talk we review our results on bi-Hamiltonian structures of integrable many-body models of point particles moving along one dimension, which are also coupled to internal `spin’ degrees of freedom. The models of our interest belong to the celebrated family of Calogero–Moser–Sutherland and Toda type systems. They will be viewed as shadows (alias Poisson reductions) of simple higher dimensional bi-Hamiltonian systems having large symmetry groups.

At a time when the particle physics community is trying to decide what the next large particle collider experiment may be, it becomes crucial to study and establish the potential for indirect tests of new physics at the different projects that have been proposed, in order to make an informed decision. In the absence of a clear indication of what the new physics beyond the Standard Model may be, a model-independent approach for such studies is preferred, to make sure we cover all possibilities. In this talk, I will discuss some of the studies that were prepared for the 2020 Update of the European Strategy for Particle Physics and later updated during the 2021 Snowmass process using the general formalism of the Standard Model Effective Field Theory, with emphasis on the physics of the electroweak and Higgs sectors.

In recent years, there has been a growing interest in the study of chiral hydrodynamics, the hydrodynamic theory that incorporates the effect of quantum anomalies. This theory is expected to be a powerful description of various systems in high-energy nuclear physics, cosmology, astrophysics, and condensed matter. However, chiral hydrodynamics derived in previous works have problems related to causality and stability. These issues prevent the full theory from being used to make theoretical predictions using numerical simulations. In this talk, I will present a novel first-order theory of chiral hydrodynamics which is proven to be causal in the nonlinear regime and linearly stable. I will show that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame. The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. Notably, causality is determined by just three combinations of transport parameters. The results will be presented in a form amenable to numerical hydrodynamic simulations.

We present a new way to study cosmic inflation with gravitational waves. The gravitational signal is generated thanks to nonlinear structures in the inflaton field, called oscillons. This novel probe allows us to test models of inflation which are challenging to test with CMB experiments.

Composite Higgs models consist of four-dimensional asymptotically-free gauge field theories. Each model may lead to a confinement-deconfinement transition and a phase transition associated with the spontaneous breaking of a global symmetry that realizes the standard model Higgs field as a pseudo-Nambu-Goldstone boson. In this talk, I will discuss order of thermal phase transitions in various composite Higgs models based on the argument of universality. In particular, we focus on phase transitions associated with the global symmetry breaking by studying the renormalization group flow using the ϵ-expansion at the one-loop order.
We find that first-order phase transitions are favored in some of composite Higgs models. If I have a time, I would like to discuss the confinement-deconfinement transition in a UV-completed composite Higgs model based on a Sp(2Nc) gauge theory.

https://kds.kek.jp/event/48743/

Most particle production can be solved by approximate methods, but some problems cannot be solved without serious consideration of the Stokes phenomenon. One such particle production is baryon number production from rotating fields. Processes such as particle-antiparticle mixing increase the order of the differential equations to be solved, so new knowledge of ExactWKB, including Virtual Turning Point, is required. The other is particle production from a steady state. This problem includes the Schwinger effect, the Unruh effect and Hawking radiation. In particular, the Stokes phenomenon of the Unruh effect has been unsolved for 50 years. This talk shows how the Exact WKB can be used to solve these problems clearly.

The S-matrix is one of the central objects in quantum field theory and has gained renewed interest recently to better understand the possible structures of low-energy effective field theories, strongly-coupled systems, quantum gravity, etc. However, most of the particles have finite decay widths and thus do not appear in asymptotic states. Therefore, the standard S-matrix arguments may not be directly applied to scatterings of such unstable particles and we need to formulate “the S-matrix theory of unstable particles” to properly understand the availability of the S-matrix arguments in realistic systems. In this talk, I will talk about some progress towards this goal. In particular, I will discuss non-perturbative consequences of unitarity in scattering amplitudes of unstable　particles and their analytic properties.

While the phi meson vacuum properties, such as mass and width, are well known, it is not clear how these properties will change once it is put in a dense environment such as nuclear matter. To study how the phi meson behaves at finite density has been the goal of several past and near future experiments at KEK, COSY-ANKE and J-PARC. Recently, ALICE has also obtained novel experimental data constraining the phi-N interaction. In this talk, I will focus on the in-medium properties of the longitudinal and transverse polarization modes of the phi meson, which due to the breaking of Lorentz symmetry in nuclear matter, can be modified differently. I will review theoretical predictions for these modifications and discuss how the different modes could be measured at the future J-PARC E16 and E88 experiments.

Gravitational waves with frequencies below 1 nHz are notoriously difficult to detect and fall below the typical cutoff frequency for conventional pulsar timing analyses. In this talk, I will present a new means of probing this regime through the correlation of secular drifts in pulsar timing parameters. I will show the results of searches for both continuous and stochastic signals in this regime and will discuss what future observations using this methodology may reveal about the signal recently discovered by pulsar timing collaborations at frequencies above a nanohertz.