In this study, the Riccati equation is resolved using the generalized recursive integrating factor method. By applying a non-linear transformation to the dependent variable $y(x)$ of the Riccati equation, a second-order linear differential equation is derived for a variable $u(x)$ that is related to $y(x)$ through the aforementioned transformation. The second-order differential equation is then addressed using the aforementioned integrating factors method to derive the general solution for $u(x)$, which is subsequently transformed back to obtain the general solution for $y(x)$, thereby resolving the Riccati equation. The general solution to the Riccati equation is presented, followed by solving a few illustrative application examples.

We study the decay of a heavy CP-even neutral Higgs into an on-shell Standard Model-like Higgs boson and two photons, $H\to h\gamma\gamma$, in the two-Higgs doublet model. We argue that the decay channel $H\to h\gamma\gamma$, followed by the decay of the Standard Model Higgs $h\rightarrow b\bar b$, could be observed at the 5$\sigma$ level at the High-Luminosity LHC for masses of the heavy Higgs up to 950 GeV for the type-II, 650 GeV for the Lepton Specific and the Flipped 2HDMs, and 350 GeV for the type-I. We also discuss the possible role of the decay $H\to h\gamma\gamma$ in discriminating among different types of 2HDMs and in enhancing the total number of events in the final state $H\rightarrow b\bar b \gamma\gamma$ compared to the cascade decay $H\to hh$ followed by $h\to\gamma\gamma$ $h\to b\bar{b}$ with identical final state (although with different kinematical distributions).

We report our results for the tensor meson pole contributions to the Hadronic Light-by-Light piece of $a_\mu$, using Resonance Chiral Theory in the purely hadronic region. Given the differences between the dispersive and holographic results for it and the resulting discussion of the corresponding uncertainty estimate for the Hadronic Light-by-Light section of the $g\, -\, 2$ theory initiative second White Paper, we consider timely to present an alternative evaluation. In our approach, in addition to the lightest tensor meson nonet, two vector meson resonance nonets are considered. We work in the chiral limit, where all parameters are determined by imposing short-distance QCD constraints, and the radiative tensor decay widths. Within this setting, only the form factor $F_1^T$ is non-vanishing, in agreement with the result put forward by the dispersive study. We obtain the following results for the different contributions (in units of $10^{-11}$): $a_\mu^{\rm a_2-pole}=-1.09(10)_{\rm stat}(^{+0.00}_{-0.11})_{\rm syst}$,$a_\mu^{\rm f_2-pole}=-3.4(3)_{\rm stat}(^{+0.4}_{-0.0})_{\rm syst}$and$a_\mu^{\rm f_2^\prime-pole}=-0.046(14)_{\rm stat}(^{+0.008}_{-0.000})_{\rm syst}$, which add up to $a_\mu^{\rm (a_2+f_2+f_2^\prime)-pole}=-4.5^{+0.5}_{-0.3}$.

We study dynamical chiral symmetry breaking for quarks in the fundamental representation of $SU(N_c)$ for $N_f$ number of light quark flavors. We also investigate the phase diagram of quantum chromodynamics at finite temperature $T$ and/or in the presence of a constant external magnetic field $eB$. The unified formalism for this analysis is provided by a symmetry-preserving Schwinger-Dyson equations treatment of a vector$\times$vector contact interaction model which encodes several well-established features of quantum chromodynamics to mimic the latter as closely as possible. Deconfinement and chiral symmetry restoration are triggered above a critical value of $N_f$ at $T=0=eB$. On the other hand, increasing temperature itself screens strong interactions, thus ensuring that a smaller value of $N_f$ is sufficient to restore chiral symmetry at higher temperatures. We also observe the well-known phenomenon of magnetic catalysis for a strong enough magnetic field. However, we note that if the effective coupling strength of the model decreases as a function of magnetic field, it can trigger inverse magnetic catalysis in a certain window of this functional dependence. Our model allows for the simultaneous onset of dynamical chiral symmetry breaking and confinement for each case. Qualitative as well as quantitative predictions of our simple but effective model are in reasonably satisfactory agreement with lattice results and other reliable and refined predictions based upon intricate continuum studies of quantum chromodynamics.

We study the $\tau^- \to \nu_{\tau} \pi^{-}\pi^{0}\ell^{+}\ell^{-}$ ($\ell=e,\,\mu$) decays, which are $O(\alpha^2)$-suppressed with respect to the dominant di-pion tau decay channel. Both the inner-bremsstrahlung and the structure- (and model-)dependent contributions are considered. In the $\ell=e$ case, structure-dependent effects are $\mathcal{O}(1\%)$ in the decay rate, yielding a clean prediction of its branching ratio, $2.3\times10^{-5}$, measurable with BaBar or Belle(-II) data. For $\ell=\mu$, both contributions have similar magnitude and we get a branching fraction of $(1.6\pm0.3)\times10^{-7}$, reachable by the end of Belle-II operation. These decays allow to study the dynamics of strong interactions with simultaneous weak and electromagnetic probes; their knowledge will contribute to reducing backgrounds in lepton flavor/number violating searches.

The radiative corrections to the $\tau^-\to (P_1P_2)^-\nu_\tau$ ($P_{1,2}=\pi, K$) decays are calculated for the first time including the structure-dependent real photon corrections, which are obtained using Resonance Chiral Theory. Our results, whose uncertainty is dominated by the model-dependence of the resummation of the radiative corrections and the missing virtual structure-dependent contributions, allow for precise tests of CKM unitarity, lepton flavour universality and non-standard interactions.

We computed for the first time the $\tau$ data-driven Euclidean windows for the hadronic vacuum polarization contribution to the muon g-2. We showed that $\tau$-based results agree with the available lattice window evaluations and with the full result. On the intermediate window, where all lattice evaluations are rather precise and agree, $\tau$-based results are compatible with them. This is particularly interesting, given that the disagreement of the $e^+e^-$ data-driven result with the lattice values in this window is the main cause for their discrepancy, affecting the interpretation of the $a_\mu$ measurement in terms of possible new physics.

We analyze the proton$\text{-}$box contribution to the hadronic light$\text{-}$by$\text{-}$light part of the muon's anomalous magnetic moment, which is the first reported baryonic contribution to this piece. We follow the quark$\text{-}$loop analysis, incorporating the relevant data$\text{-}$driven and lattice proton form factors. Although the heavy mass expansion would yield a contribution of $\mathcal{O}(10^{-10})$, the damping of the form factors in the regions where the kernel peaks, explains our finding $a_{\mu}^{\rm{p-box}}=1.82 (7)\times 10^{-12}$, two orders of magnitude smaller than the forthcoming uncertainty on the $a_{\mu}$ measurement and on its Standard Model prediction.

In a previous work \cite{Buttazzo:2020ibd}, it has been pointed out that heavy new physics (NP) contributions to lepton dipole moments and high-energy cross-sections of lepton pairs into Higgs and $\gamma/Z$ bosons are connected, if the electroweak symmetry breaking is realized linearly. As a consequence, a multi-TeV muon collider would provide a unique test of NP in the muon $g$-2 through the study of high-energy processes such as $\mu^+ \mu^-\to h +\gamma /Z$. Since the analysis involved a SMEFT approach to Higgs-processes, it could also be studied by the more general HEFT formulation. We compute the modification of the high-energy cross-section $\mu^+ \mu^-\to h +\gamma/Z$ and $h\to \mu^{+} \mu^{-} +\gamma /Z$ decay using the dimension six HEFT Lagrangian and compare them with the SMEFT analysis. We find that, within the current HEFT analysis, there are plausible scenarios where the HEFT approach could lead to a higher sensitivity to test the NP contributions in the muon $g$-2. However, a more precise knowledge of the new HEFT parameters is needed for a definite conclusion, which motivates the search for complementary measurements.

This thesis is focused in the study of the evolution of the metabolic repertoire of Streptomyces, which are renowned as proficient producers of bioactive Natural Products (NPs). The main goal of my work was to contribute into the understanding of the evolutionary mechanisms behind the evolution of NP biosynthetic pathways. Specifically, the development of a bioinformatic method that helps into the discovery of new NP biosynthetic pathways from actinobacterial genome sequences with emphasis on members of the genus Streptomyces. I developed this method using a comparative and functional genomics perspective. My studies indicate that central metabolic enzymes were expanded in a genus-specific manner in Actinobacteria, and that they have been extensively recruited for the biosynthesis of NPs. Based in these observations, I developed EvoMining, a bioinformatic pipeline for the identificatoon of novel biosynthetic pathways in microbial genomes. Using EvoMining several new NP biosynthetic pathways have been predicted in different members of the phylum Actinobacteria, including the model organism S. lividans 66. To test this approach, the genome sequence of this model strain was obtained, and its analysis led to the discovery of an unprecedented system for peptide bond formation, as well as a biosynthetic pathway for an arsenic-containing metabolite. Moreover, this work also led to the identification of expansions on a conserved metabolic node in the glycolytic pathway of Streptomyces. These expansions occurred before the radiation of Streptomyces and are concomitant with the evolution of their capability to produce NPs. Experimental analyses indicate that this node evolved to mediate the interplay between central an NP metabolism.

This paper investigates resonant neutrino self-interactions in cosmology by employing, for the first time, the effective field theory of large-scale structure to model their impact on the matter distribution up to mildly nonlinear scales. We explore a broad range of mediator masses in two main analyses: one combining BOSS Full Shape (FS) galaxy clustering with Big Bang Nucleosynthesis (BBN), and another combining FS with Planck Cosmic Microwave Background (CMB) data. Our results place the strongest cosmological constraints to date on the resonant self interactions when using FS+Planck data, reaching up to g_\nu< 10.8 \times 10^{-14} at $95\%$ confidence for the 1 eV mediator. Notably, FS+BBN can constrain the interaction for the 10 eV mediator independently of CMB data, yielding g_\nu < 7.33 \times 10^{-12} at $95\%$ confidence. Our results suggest that resonant neutrino self-interactions are unlikely to resolve existing cosmological tensions within the standard $\Lambda$CDM framework.

We revisited the computation of the cross section for the $\mu^+\mu^+\to \ell^+\ell^{+}$ $(\ell^+=\tau^+,\, e^+)$ transitions in the presence of new heavy Majorana neutrinos. We focus on scenarios where the masses of the new states are around some few TeV, the so-called low-scale seesaw models. Our analysis is set in a simple model with only two new heavy Majorana neutrinos considering the current limits on the heavy-light mixings. Our results illustrate the difference between the genuine effects of two nondegenerate heavy Majorana states and the degenerate case where they form a Dirac singlet field.

The mass and decay width of the $\phi$ meson in cold nuclear matter are computed in an effective Lagrangian approach, with the medium dependence of these properties obtained by evaluating kaon-antikaon loop contributions to the $\phi$ self-energy. At normal nuclear matter density, we find a downward shift of the $\phi$ mass by a few percent, while the decay width is enhanced by an order of magnitude. We also present $\phi$--nucleus bound state energies and absorption widths for some selected nuclei, using complex optical potentials obtained in the local density approximation. Our results suggest that the $\phi$ should form bound states with all the nuclei considered. However, the identification of the signal for these predicted bound states will need careful investigation because of their sizable absorption widths.

We review the tau data-driven computation of Euclidean windows for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (a_mu), which agree with the lattice results, making the difference of the $e^+e^-$ data-driven methods with them more intriguing. This conundrum needs to be solved by next year, when the final FNAL a_mu measurement will be published, in order to extract firm conclusions on possible new physics effects.

The present Health Crisis tests the response of modern science and medicine to finding treatment for a new COVID-19 disease. The presentation on the world stage of antivirals such as remdesivir, obeys to the continuous investigation of biologically active molecules with multiple theoretical, computational and experimental tools. Diseases such as COVID:19 remind us that research into active ingredients for therapeutic purposes should cover all available sources, such as plants. In the present work, in silico tools, specifically docking study, were used to evaluate the binding and inhibition capacity of an antiviral such as remdesivir on the NSP-12 protein of SARS-CoV, a polymerase that is key in the replication of the SARS-COV virus. The results are then compared with a docking analysis of two natural products (Alpha-Bisabolol and betalain) with SARS-CoV protein, in order to find more candidates for COVID-19 virus replication inhibitors. in addition to increasing studies that help explain the specific mechanisms of the SARs-CoV-2 virus, remembering that we will have to live with the virus for an indefinite time from now on. Finally, natural products such as betalains may have inhibitory effects of a small order but in conjunction with other synergistic active ingredients they may increase their inhibition effect on NSP-12 protein of SARS-CoV.

We review the tau data-driven computation of Euclidean windows for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (a_mu), which agree with the lattice results, making the difference of the $e^+e^-$ data-driven methods with them more intriguing. This conundrum needs to be solved by next year, when the final FNAL a_mu measurement will be published, in order to extract firm conclusions on possible new physics effects.

We compute the tensor meson pole contributions to the Hadronic Light-by-Light piece of $a_\mu$ in the purely hadronic region, using Resonance Chiral Theory. Given the differences between the dispersive and holographic groups determinations, we consider timely to present an alternative evaluation. In our approach, the lightest tensor meson nonet and two vector meson resonance nonets are considered in the chiral limit. Disregarding operators with derivatives, only the form factor $\mathcal{F}_1^T$ is non-vanishing, as assumed in the dispersive study. All parameters are determined by imposing a set of short-distance QCD constraints, and the radiative decay widths. In this case, we obtain (in units of $10^{-11}$): $a_2$-pole: $-\left(1.02(10)_{\rm stat}(^{+0.00}_{-0.12})_{\rm syst}\right)$, $f_2$-pole: $-\left(3.2(3)_{\rm stat}(^{+0.0}_{-0.4})_{\rm syst}\right)$ and $f_2^\prime$-pole: $-\left(0.042(13)_{\rm stat}\right)$, which add up to $a_\mu^{a_2+f_2+f_2^\prime \rm -pole}=-\left(4.3^{+0.3}_{-0.5}\right)$, in close agreement with the holographic result when truncated to $\mathcal F_1^T$ only. However, with an ad-hoc extended Lagrangian, that also generates $\mathcal F_3^T$, as in the holographic approach, we have found: $a_2$-pole: $+0.47(1.43)_{\rm norm}(3)_{\rm stat}(^{+0.06}_{-0.00})_{\rm syst}$, $f_2$-pole: $+1.18(4.18)_{\rm norm}(12)_{\rm stat}(^{+0.24}_{-0.00})_{\rm syst}$ and $f_2^\prime$-pole: $+0.040(78)_{\rm norm}(2)_{\rm stat}$, summing to $a_\mu^{a_2+f_2+f_2^\prime \rm - pole}=+1.7(4.4)$, which agree with these recent determinations within uncertainties (dominated by the $\mathcal F_3^T$ normalization). We point out that $R\chi T$ generates all form factors, the contributions to $a_\mu$ of $\mathcal F_{2,4,5}$ cannot be evaluated in the current basis, preventing for the moment a complete calculation of $a_\mu^{\rm T-poles}$ within our framework.

We review the radiative corrections to the $\tau \to P (P) \nu_\tau [\gamma]$ decays and their implications for several SM tests: lepton universality, CKM unitarity and non-standard interactions.