The neutrino cooling and gamma heating rates are considered as an important input needed to study the final phases of the evolution of high-mass stars. The weak-interaction mediated processes, namely the $\beta$-decay and electron capture, significantly change the lepton to baryon ratio and accelerate the contraction of the core. The emission of resulting neutrinos/antineutrinos tends to cool the stellar core. On the other hand, gamma rays are produced because of electron capture and $\beta$-decay to excited states in daughter nuclei. These gamma rays heat the core and contribute to an increase of entropy which may cause convection to occur. In the present work, the weak-interaction heating and cooling rates on a chain of twenty-two isotopes of vanadium having mass in the range $43-64$ have been estimated using the proton-neutron quasiparticle random phase approximation theory. The rates have been computed for the temperature ranging from ($10^{7} - 3 \times 10^{10}$)\;K and for the density range ($10-10^{11}$)\;g/cm$^{3}$. Our calculated neutrino energy loss rates have also been compared with the previously reported rates calculated using other theoretical models. At high stellar temperatures, our rates are larger by 1-2 orders of magnitude as compared to previous results.

Spin polarization is a novel method for probing the rotational properties of the quark-gluon plasma (QGP) produced in relativistic heavy-ion collisions. In this work, we investigate the effective transport and thermodynamic coefficients in non-central O+O light-ion collisions, considering a parton distribution function that incorporates the spin polarization induced by thermal vorticity during the collision. Using a kinetic theory approach, we find that while the speed of sound squared ($c_s^2$) remains largely unaffected by spin polarization, the specific shear viscosity ($\eta/s$), specific bulk viscosity ($\zeta/s$), and mean free path ($\lambda$) are significantly modified. Notably, when spin polarization is taken into account, both $c_s^2 $ and $\zeta/s$ exhibit a non-monotonic dependence on collision energy, with an inflection point around $\sqrt{s_{NN}} = 27 $~GeV, corresponding to an average parton chemical potential of $\langle\mu_p\rangle = 0.021 $~GeV. This non-monotonic behavior suggests that incorporating spin polarization into theoretical calculations could provide an effective probe for locating the critical point of the QCD phase transition.

This dissertation highlights the contributions I have made to the field of theoretical nuclear physics, specifically in high-energy Quantum Chromodynamics (QCD). High-energy QCD is a robust subject and my research is refined to the sub-field of small-$x$ spin physics; small-$x$ physics is characterized by high-energy and density collisions and is well-suited for the Color Glass Condensate (CGC) effective field theory. Small-$x$ spin physics takes the ultra-relativistic description of high-energy QCD and gives special attention to spin-dependent interactions suppressed by powers of the center-of-mass energy. My expertise lies in exploring the theory and phenomenology relating to the KPS-CTT small-$x$ helicity evolution equations, a rubric that allows one to make predictions of the quarks' and gluons' distributions of spin at small-$x$. These predictions are heavily influenced by the initial conditions of the evolution, and the initial conditions are determined through analyses of world polarized data. My contributions focus on Bayesian parameter analysis, numerical and analytical calculations to discretize and cross-check the evolution equations, and the incorporation of a new observable into the pool of analyzed data. The results of such work show that the net amount of spin from quarks and gluons in the small-$x$ regime is predicted to be negative and/or potentially small; an analysis of polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data resulted in a net small-$x$ spin prediction that can be large and negative, but new results with the inclusion of data for single-inclusive jet production in polarized proton-proton ($pp$) collisions now estimate that the net amount of parton spin at small $x$ is small, with 1-$\sigma$ uncertainty that spans zero.

Any effective field theory relies on power counting rules that allow one to perform a systematic expansion of calculated quantities in terms of some soft scales. However, a naive power counting can be violated due to the presence of various hard scales in a given scheme. A typical example of such a scale is an ultraviolet regulator. This issue is particularly challenging when the interaction is nonperturbative. The power counting is expected to be restored in the course of renormalization, that is by redefining bare low-energy constants in the effective Lagrangian. Whether this procedure eventually leads to a self-consistent framework is not a priory obvious. We discuss various criteria of renormalizability in application to nuclear chiral effective field theory and provide several instructive counterexamples.

High-energy proton-nucleus (pA) collisions have provided various clues for the role of cold nuclear matter effects in hadron production. In particular, multiple rescatterings of an incoming parton by the nuclear target are known to induce the radiation of many soft gluons, with those having a long formation time leading to the modification of hadron production rates due to fully coherent energy loss (FCEL). Here we present a recently derived formula for the induced single soft gluon radiation spectrum beyond leading logarithmic accuracy, whose main features are demonstrated with the example of $q\, g \to q\, g$ scattering.

It is well-known that the momentum spectra of particles confined to finite spatial volumes deviate from the continuous spectra used for unconfined particles. In this article, we consider real scalar particles confined to finite volumes with periodic boundary conditions, such that the particles' spectra are discrete. We directly compute the density matrices describing the decay processes $\phi \to \varphi^2$ and $\phi \to \varphi\chi\nu$, and subsequently derive expressions for the decay probabilities both for confined and unconfined particles. The latter decay process is used as a rough toy model for a neutron decaying into a proton, an electron, and an anti-electron neutrino. We propose that finite volume effects can have an impact on the outcomes of experiments measuring the neutron lifetime. In addition, our findings at the toy model level suggest that taking into account possible initial correlations between neutrons and their daughter particles might be relevant as well.