RESUMEN
We discuss spontaneously broken quantum field theories with a continuous global symmetry group via the constraint effective potential. Employing lattice simulations with constrained values of the order parameter, we demonstrate explicitly that the path integral is dominated by inhomogeneous field configurations and that these are unambiguously related to the flatness of the effective potential in the broken phase. We determine characteristic features of these inhomogeneities, including their topology and the scaling of the associated excess energy with their size. Concerning the latter we introduce the differential surface tension-the generalization of the concept of a surface tension pertaining to discrete symmetries. Within our approach, spontaneous symmetry breaking is captured merely via the existence of inhomogeneities, i.e., without the inclusion of an explicit breaking parameter and a careful double limiting procedure to define the order parameter. While here we consider the three-dimensional O(2) model, we also elaborate on possible implications of our findings for the chiral limit of QCD.
RESUMEN
The leptonic decay of charged pions is investigated in the presence of background magnetic fields. In this situation, Lorentz symmetry is broken, and new fundamental decay constants need to be introduced, associated with the decay via the vector part of the electroweak current. We calculate the magnetic field dependence of both the usual and a new decay constant nonperturbatively on the lattice. We employ both Wilson and staggered quarks and extrapolate the results to the continuum limit. With this nonperturbative input, we calculate the tree level electroweak amplitude for the full decay rate in strong magnetic fields. We find that the muonic decay of the charged pion is enhanced drastically by the magnetic field. We comment on possible astrophysical implications.
RESUMEN
We determine the magnetization of quantum chromodynamics for several temperatures around and above the transition between the hadronic and the quark-gluon phases of strongly interacting matter. We obtain a paramagnetic response that increases in strength with the temperature. We argue that due to this paramagnetism, chunks of quark-gluon plasma produced in noncentral heavy ion collisions should become squeezed perpendicular to the magnetic field. This anisotropy will then contribute to the elliptic flow v2 observed in such collisions, in addition to the pressure gradient that is usually taken into account. We present a simple estimate for the magnitude of this new effect and a rough comparison to the effect due to the initial collision geometry. We conclude that the paramagnetic effect might have a significant impact on the value of v2.
RESUMEN
Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron--and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark-gluon plasma phase (for simplicity, we use the word 'phase' to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.
