Abstract: Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, as (Q(2)), that varies with the energy scale Q(2) characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of alpha(s) at low momentum transfers limits perturbative calculations to the high-energy region where Q(2) >>Lambda(QCD) (2) similar or equal to (250 MeV)(2). Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. Thesemethods range from the Bethe-Salpeter, Dyson-Schwinger coupled relativistic equations, which are formulated in bothMinkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensionalQCDin a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large Nclimit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected q ($) over barq mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark-Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary partonparton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event

Abstract: This work aims to study the radiative corrections in a vector model with spontaneous Lorentz symmetry violation, known in the literature as the bumblebee model. We consider such a model with self -interaction quadratic smooth potential responsible for spontaneous Lorentz symmetry breaking. The spectrum of this model displays a transversal nonmassive mode, identified as Nambu-Goldstone, and a massive longitudinal mode. Besides the Lorentz symmetry, this model also exhibits gauge symmetry violation. To restore the gauge symmetry, we introduce the Stueckelberg field and calculate the two -point function by employing the principal-value (PV) prescription. The result is nontransversal, leading to a massive excited mode.

Abstract: Cosmological bounds on neutrinos and additional hypothetical light thermal relics, such as QCD axions, are currently among the most restrictive ones. These limits mainly rely on cosmic microwave background temperature anisotropies. Nonetheless, one of the largest cosmological signatures of thermal relics is that on gravitational lensing, due to their free-streaming behavior before their nonrelativistic period. We investigate late-time only hot-relic mass constraints, primarily based on recently released lensing data from the Atacama Cosmology Telescope, both alone and in combination with lensing data from the Planck satellite. Additionally, we consider other local probes, such as baryon acoustic oscillations measurements, shear-shear, galaxy-galaxy, and galaxy-shear correlation functions from the dark energy survey, and distance moduli measurements from Type-Ia Supernovae. The tightest bounds we find are Sigma m(v) < 0.43 eV and m(a) < 1.1 eV, both at 95% CL Interestingly, these limits are still much stronger than those found on e.g., laboratory neutrino mass searches, reassessing the robustness of the extraction of thermal relic properties via cosmological observations. In addition, when considering lensing-only data, the significance of the Hubble constant tension is considerably reduced, while the clustering parameter sigma 8 controversy is completely absent.

Abstract: We study the nonconservation of the chiral charge of Dirac fields between past and future null infinity due to the Adler-Bell-Jackiw chiral anomaly. In previous investigations [A. del Rio, Phys. Rev. D 104, 065012 (2021)], we found that this charge fails to be conserved if electromagnetic sources in the bulk emit circularly polarized radiation. In this article, we unravel yet another contribution coming from the nonzero, infrared “soft” charges of the external, electromagnetic field. This new contribution can be interpreted as another manifestation of the ordinary memory effect produced by transitions between different infrared sectors of Maxwell theory, but now on test quantum fields rather than on test classical particles. In other words, a flux of electromagnetic waves can leave a memory on quantum fermion states in the form of a permanent, net helicity. We elaborate this idea in both 1 + 1 and 3 + 1 dimensions. We also show that, in sharp contrast, gravitational infrared charges do not contribute to the fermion chiral anomaly.

Abstract: Recently, an increasing interest in UV/IR mixing phenomena has drawn attention to the range of validity of standard quantum field theory. Here we explore the consequences of such a limited range of validity in the context of radiative models for neutrino mass generation. We adopt an argument first published by Cohen, Kaplan and Nelson that gravity implies both UV and IR cutoffs, apply it to the loop integrals describing radiative corrections, and demonstrate that this effect has significant consequences for the parameter space of radiative neutrino mass models.