By applying copositivity criterion to the scalar potential of the economical 3 − 3 − 1 model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the dimensionless parameters of the scalar potential, we present general enlightening relations in this work. Additionally, we use constraints coming from the minimization of the scalar potential by means of the orbit space method, the positivity of the squared masses of the extra scalars, the Higgs boson mass, the Z gauge boson mass and its mixing angle with the SM Z boson in order to further restrict the parameter space of this model.

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We introduce the phenomenology of elliptic flow in nuclear collisions, and argue that its scaling across energies, rapidities and system sizes could be suggestive of a QCD-based rather than a hydrodynamical explanation. As a hypothesis for such an explanation, we show that the GLR equation develops unstable modes when the parton distribution function is generalized to depend on azimuthal angle. This generally means that the structure function acquires an azimuthal dependence. We argue that this process is a plausible alternative explanation for the origin of elliptic flow, one that naturally respects the scaling experimentally observed.

The core-cusp problem persists as an unresolved tension between the pre- dictions of ΛCDM cosmology and observations of dark matter (DM) profiles in dwarf spheroidal and other galaxies. We present a novel scenario for converting cusps into cores through reactivation of DM annihilation in galaxies at late times. This can happen in asymmetric DM models when there is a very small DM-number violating mass term that causes oscillations between DM and its antiparticle. Using analytic methods as well as gravitational N-body simulations, we show that this mechanism can robustly eliminate cusps from galactic DM profiles for light fermionic DM of mass mχ ∼ (0.1 − 1) GeV and a lighter mediator into which the DM can annihilate. We identify regions of parameter space where annihilation of DM particles is more efficient than elastic scattering at reducing the inner density of the DM profile. Dark matter annihilation is therefore a qualitatively distinct alternative to the mechanism of elastic self-interacting dark matter for addressing the cusp-core problem.