Fermion masses in the economical 3-3-1 model

We show that, in frameworks of the economical 3-3-1 model, all fermions get masses. At the tree level, one up-quark and two down-quarks are massless, but the one-loop corrections give all quarks the consistent masses. This conclusion is in contradiction to the previous analysis in which, the third scalar triplet has been introduced. This result is based on the key properties of the model: First, there are three quite different scales of vacuum expectation values: \om \sim {\cal O}(1) \mathrm{TeV}, v \approx 246 \mathrm{GeV} and $u \sim {\cal O}(1) \mathrm{GeV}$. Second, there exist two types of Yukawa couplings with different strengths: the lepton-number conserving couplings $h$'s and the lepton-number violating ones $s$'s satisfying the condition in which the second are much smaller than the first ones: $s \ll h$. With the acceptable set of parameters, numerical evaluation shows that in this model, masses of the exotic quarks also have different scales, namely, the $U$ exotic quark ($q_U = 2/3$) gains mass $m_U \approx 700$ GeV, while the D_\al exotic quarks (q_{D_\al} = -1/3) have masses in the TeV scale: m_{D_\al} \in 10 \div 80 TeV.Comment: 20 pages, 8 figure

12CO emission from EP Aqr: Another example of an axi-symmetric AGB wind?

The CO(1-0) and (2-1) emission of the circumstellar envelope of the AGB star EP Aqr has been observed using the IRAM PdBI and the IRAM 30-m telescope. The line profiles reveal the presence of two distinct components centered on the star velocity, a broad component extending up to ~10 km/s and a narrow component indicating an expansion velocity of ~2 km/s. An early analysis of these data was performed under the assumption of isotropic winds. The present study revisits this interpretation by assuming instead a bipolar outflow nearly aligned with the line of sight. A satisfactory description of the observed flux densities is obtained with a radial expansion velocity increasing from ~2 km/s at the equator to ~10 km/s near the poles. The angular aperture of the bipolar outflow is ~45 deg with respect to the star axis, which makes an angle of ~13 deg with the line of sight. A detailed study of the CO(1-0) to CO(2-1) flux ratio reveals a significant dependence of the temperature on the star latitude, smaller and steeper at the poles than at the equator at large distances from the star. Under the hypothesis of radial expansion and of rotation invariance about the star axis, the effective density has been evaluated in space as a function of star coordinates. Evidence is found for an enhancement of the effective density in the northern hemisphere of the star at angular distances in excess of ~3" and covering the whole longitudinal range. The peak velocity of the narrow component is observed to vary slightly with position on the sky, a variation consistent with the model and understood as the effect of the inclination of the star axis with respect to the line of sight. While the phenomenological model presented here reproduces well the general features of the observations, significant differences are also revealed, which would require a better spatial resolution to be properly described.Comment: accepted for publication in Astronomy & Astrophysic