The quark mass dependence of octet baryon magnetic polarisabilities is examined at the level of individual quark-sector contributions in the uniform background-field approach of lattice QCD. The aim is to understand the direct impact of increasing the mass of a quark flavour on the magnetic polarisability and indirect or environmental effects associated with changing the mass of spectator quarks, insensitive to the background magnetic field. Noting the need to set the electric charge of some quark flavours to zero, a fractionally charged baryon formalism is introduced. We find that increasing the mass of the charged quark flavour directly causes its contribution to the magnetic polarisability to decrease. However, increasing the mass of the spectator quark flavour indirectly acts to increase the magnetic polarisability. To gain a deeper understanding of these effects, we evaluate the predictions of the constituent quark model in this context. While the model provides a compelling explanation for the environmental effect of varying the spectator quark mass, an explanation of the direct mass dependence is more complicated as competing factors combine in the final result. The lattice results indicate the key factor is a reduction in the constituent quark magnetic moment with increasing quark mass, as it governs the strength of the magnetic transition to the nearby decuplet baryon.

The gradient flow scheme has emerged as a prominent nonperturbative renormalization scheme on the lattice, where flow time is introduced to define the renormalization scale. In this study we perturbatively compute the gradient flow coupling for the SU($N$) Yang-Mills theory in the large-$N$ limit in terms of the lattice bare coupling up to three-loop order. This is achieved by combining the twisted Eguchi-Kawai model with the numerical stochastic perturbation theory. We analyze the flow time dependence of the perturbative coefficients to determine the perturbative beta function coefficients, successfully computing the one-loop coefficient in the large-$N$ limit using three matrix sizes $N=289,441,529$. However, the higher-order coefficients are affected by large statistical errors. We also explore the potential for reducing these statistical errors through variance reduction combined with the large-$N$ factorization property of the SU($N$) Yang-Mills theory, and estimate the required number of samples for the precise determination of the higher-order coefficients.

Inspired by recent advances in the study of $K^{(*)} \bar K^{(*)}$ molecular tetraquarks and the $H$-dibaryon, we focus on the mass spectra and electromagnetic properties of $\bar K^{(*)} \bar K^{(*)}$ systems, which exhibit exotic flavor quantum number of $ss\bar q \bar q$. A dynamical analysis is performed using the one-boson-exchange model to describe the effective interactions for these systems, accounting for both $S$-$D$ wave mixing and coupled-channel effects. By solving the coupled-channel Schr$\ddot{\rm o}$dinger equation, we identify the $I(J^P)=0(1^+)$ $\bar K \bar K^*$ and $I(J^P)=0(1^+)$ $\bar K^* \bar K^*$ states as the most likely candidates for double-strangeness molecular tetraquarks. In addition, we investigate their magnetic moments and M1 radiative decay width, shedding light on their inner structures within the constituent quark model framework. Finally, we encourage experimentalists to focus on these predicted double-strangeness molecular tetraquark candidates, particularly in $B$ meson decays, by analyzing the $\bar K \bar K \pi$ invariant mass spectrum. Such efforts could pave the way for establishing the molecular tetraquark states in the light-quark sector.

We propose a new method to investigate the existence and location of the conjectured high-temperature critical point of strongly interacting matter via contours of constant entropy density. By approximating these lines as a power series in the baryon chemical potential $\mu_B$, one can extrapolate them from first-principle results at zero net-baryon density, and use them to locate the QCD critical point, including the associated first-order and spinodal lines. As a proof of principle, we employ currently available continuum-extrapolated first-principle results from the Wuppertal--Budapest collaboration to find a critical point at a temperature and a baryon chemical potential of $T_c = 114.3 \pm 6.9$ MeV and $\mu_{B,c} = 602.1 \pm 62.1$ MeV, respectively. We advocate for a more precise determination of the required expansion coefficients via lattice QCD simulations as a means of pinpointing the location of the critical endpoint in the phase diagram of strongly interacting matter.