Complex Scalar DM in a B-L Model

In this work, we implement a complex scalar Dark Matter (DM) candidate in a $U(1)_{B-L}$ gauge extension of the Standard Model. The model contains three right handed neutrinos with different quantum numbers and a rich scalar sector, with extra doublets and singlets. In principle, these extra scalars can have VEVs ($V_{\Phi}$ and $V_{\phi}$ for the extra doublets and singlets, respectively) belonging to different energy scales. In the context of $\zeta\equiv\frac{V_{\Phi}}{V_{\phi}}\ll1$, which allows to obtain naturally light active neutrino masses and mixing compatible with neutrino experiments, the DM candidate arises by imposing a $Z_{2}$ symmetry on a given complex singlet, $\phi_{2}$, in order to make it stable. After doing a study of the scalar potential and the gauge sector, we obtain all the DM dominant processes concerning the relic abundance and direct detection. Then, for a representative set of parameters, we found that a complex DM with mass around $200$ GeV, for example, is compatible with the current experimental constraints without resorting to resonances. However, additional compatible solutions with heavier masses can be found in vicinities of resonances. Finally, we address the issue of having a light CP-odd scalar in the model showing that it is safe concerning the Higgs and the $Z_{\mu}$ boson invisible decay widths, and also the energy loss in stars astrophysical constraints.Comment: 20 pages, 3 figure

Vacuum stability conditions of the economical 3-3-1 model from copositivity

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.Comment: 22 pages, 7 figures, added text and references. Matches published versio

Accidental symmetries and massless quarks in the economical 3-3-1 model

In the framework of a 3-3-1 model with a minimal scalar sector, known as the economical 3-3-1 model, we study its capabilities of generating realistic quark masses. After a detailed study of the symmetries of the model, before and after the spontaneous symmetry breaking, we find a remaining axial symmetry that prevents some quarks to gain mass at all orders in perturbation theory. Since this accidental symmetry is anomalous, we also consider briefly the possibility to generate their masses for non-perturbative effects. However, we find that non-perturbative effects are not enough to generate the measured masses for that three massless quarks. Hence, these results imply that the economical 3-3-1 model is not a realistic description of the electroweak interaction and it has to be modified.Comment: 11 pages, no figure

Axion Like Particles and the Inverse Seesaw Mechanism

Light pseudoscalars known as axion like particles (ALPs) may be behind physical phenomena like the Universe transparency to ultra-energetic photons, the soft $\gamma$-ray excess from the Coma cluster, and the 3.5 keV line. We explore the connection of these particles with the inverse seesaw (ISS) mechanism for neutrino mass generation. We propose a very restrictive setting where the scalar field hosting the ALP is also responsible for generating the ISS mass scales through its vacuum expectation value on gravity induced nonrenormalizable operators. A discrete gauge symmetry protects the theory from the appearance of overly strong gravitational effects and discrete anomaly cancellation imposes strong constraints on the order of the group. The anomalous U$(1)$ symmetry leading to the ALP is an extended lepton number and the protective discrete symmetry can be always chosen as a subgroup of a combination of the lepton number and the baryon number.Comment: 29pp. v4: published version with erratum. Conclusions unchange

Natural PQ symmetry in the 3-3-1 model with a minimal scalar sector

In the framework of a 3-3-1 model with a minimal scalar sector we make a detailed study concerning the implementation of the PQ symmetry in order to solve the strong CP problem. For the original version of the model, with only two scalar triplets, we show that the entire Lagrangian is invariant under a PQ-like symmetry but no axion is produced since an U(1) subgroup remains unbroken. Although in this case the strong CP problem can still be solved, the solution is largely disfavored since three quark states are left massless to all orders in perturbation theory. The addition of a third scalar triplet removes the massless quark states but the resulting axion is visible. In order to become realistic the model must be extended to account for massive quarks and invisible axion. We show that the addition of a scalar singlet together with a Z_N discrete gauge symmetry can successfully accomplish these tasks and protect the axion field against quantum gravitational effects. To make sure that the protecting discrete gauge symmetry is anomaly free we use a discrete version of the Green-Schwarz mechanism.Comment: 18 pages, 1 figure, 3 table

String dynamics in cosmological and black hole backgrounds: The null string expansion

We study the classical dynamics of a bosonic string in the $D$--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet $\tau$--coordinate is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma, \tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$ are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string proper size, at first order in the fluctuations, grows like the conformal factor $R(\eta)$ and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime $D$ generic. In the null string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are $r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n} (\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at $r=0$. First and higher order string perturbations contribute with higher powers of $\tau$. The integrated string energy-momentum tensor corresponds to that of a null fluid in $D-1$ dimensions. As the string approaches the $r=0$ singularity its proper size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. We end the paper giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure