This review focuses on diffractive physics, which involves the long-range interactions of the strong nuclear force at high energies described by SU(3) gauge symmetry. It is expected that diffractive processes account for nearly 40% of the total cross-section at LHC energies. These processes consist of soft-scale physics where perturbation theory cannot be applied. Although highly successful and often described as a perfect theory, quantum chromodynamics relies heavily on perturbation theory, a model best suited for hard-scale physics. The study of pomerons could help bridge the soft and hard processes and provide a complete description of the theory of the strong interaction across the full momentum spectrum. Here, we will discuss some of the features of diffractive physics, experimental results from SPS, HERA, and the LHC, and where the field could potentially lead. With the recent publication of the odderon discovery in 2021 by the D0 and TOTEM collaborations and the new horizon of physics that lies ahead with the upcoming Electron-Ion Collider at Brookhaven National Laboratory, interest is seemingly piquing in high energy diffractive physics.

State-resolved laser spectroscopy at the 10$^{-12}$ precision level recently reported in $arXiv$:2406.18719 determined the fractional change in nuclear quadrupole moment between the ground and isomeric state of $^{229}\rm{Th}$, $\Delta Q_0/Q_0$=1.791(2) %. Assuming a prolate spheroid nucleus, this allows to quantify the sensitivity of the nuclear transition frequency to variations of the fine-structure constant $\alpha$ to $K=5900(2300)$, with the uncertainty dominated by the experimentally measured charge radius difference $\Delta \langle r^2 \rangle$ between the ground and isomeric state. This result indicates a three orders of magnitude enhancement over atomic clock schemes based on electron shell transitions. We find that $\Delta Q_0$ is highly sensitive to tiny changes in the nuclear volume, thus the constant volume approximation cannot be used to accurately relate changes in $\langle r^2 \rangle$ and $Q_0$. The difference between the experimental and estimated values in $\Delta Q_0/Q_0$ raises a further question on the octupole contribution to the alpha-sensitivity.

Peculiar phenomena have been observed in analyses of anisotropic flow ($v_n$) fluctuations in ultracentral nucleus-nucleus collisions: The fourth-order cumulant of the elliptic flow ($v_2$) distribution changes sign. In addition, the ATLAS collaboration has shown that cumulants of $v_n$ fluctuations of all orders depend significantly on the centrality estimator. We show that these peculiarities are due to the fact that the impact parameter $b$ always spans a finite range for a fixed value of the centrality estimator. We provide a quantitative determination of this range through a simple Bayesian analysis. We obtain excellent fits of STAR and ATLAS data, with a few parameters, by assuming that the probability distribution of $v_n$ solely depends on $b$ at a given centrality. This probability distribution is almost Gaussian, and its parameters depend smoothly on $b$, in a way that is constrained by symmetry and scaling laws. We reconstruct, thus, the impact parameter dependence of the mean elliptic flow in the reaction plane in a model-independent manner, and assess the robustness of the extraction using Monte Carlo simulations of the collisions where the impact parameter is known. We argue that the non-Gaussianity of $v_n$ fluctuations gives direct information on the hydrodynamic response to initial anisotropies, ATLAS data being consistent with a smaller response for $n=4$ than for $n=2$ and $n=3$, in agreement with hydrodynamic calculations.

Event-by-event fluctuations in the initial stages of ultrarelativistic nucleus-nucleus collisions depend little on rapidity. The hydrodynamic expansion which occurs in later stages then gives rise to correlations among outgoing particles which depend weakly on their relative rapidity. Azimuthal correlations, through which anisotropic flow ($v_n(p_T)$) is defined, have been the most studied. Here we study a new observable introduced in 2020 by Schenke, Shen and Teaney and dubbed $v_0(p_T)$, which quantifies the relative change in the $p_T$ spectrum induced by a fluctuation. We describe how it can be measured. Using hydrodynamic simulations, we make quantitative predictions for $v_0(p_T)$ of charged and identified hadrons. We then discuss how $v_0(p_T)$ relates to two phenomena which have been measured: The increase of the mean transverse momentum in ultracentral collisions, and the event-by-event fluctuations of the transverse momentum per particle $[ p_T]$. We show that $v_0(p_T)$ determines the dependence of these quantities on the $p_T$ cuts implemented in the analysis. We quantitatively explain the rise of $\sigma_{p_T}$ observed by ATLAS as the upper $p_T$-cut is increased from $2$ to $5$~GeV/$c$.