Higgs revised in Supersymmetric Economical 3-3-1 model with B/\mu-type terms

We re-investigate the scalar potential and the Higgs sector of the supersymmetric economical 3-3-1 model (SUSYE331) in the presence of the B/\mu type terms which has many important consequences. First, the model contains no massless Higgs fields. Second, we prove that the soft mass parameters of Higgses must be at the SU(3)_L scale. As a result, the masses of the Higgses drift toward this scale except one light real neutral Higgs with the mass of m_Z|cos(2\gamma)| at the tree level. We also show that there are some Higgses containing many properties of the Higgses in the minimal supersymmetric standard model (MSSM), especially in the neutral Higgs sector. One exact relation in the MSSM, m^2_H^{+/-}=m^2_A+m^2_W, is still true in the SUSYE331. Based on this result we make some comments on the lepton flavor violating decays of these Higgses as one of signatures of new physics in the SUSYE331 model which may be detected by present colliders.Comment: Matches version accepted for publication in EPJC. Typos are corrected. We add a new section, a new appendix, a new figure and new references to explain more clearly the properties of the lightest neutral Higgs. Results unchange

Varieties with too many rational points

We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.Comment: 23 page

Topologically protected surface Majorana arcs and bulk Weyl fermions in ferromagnetic superconductors

A number of ferromagnetic superconductors have been recently discovered which are believed to be in the so-called "equal spin pairing" (ESP) state. In the ESP state the Cooper pairs condense forming order parameters $\Delta_{\uparrow\uparrow}, \Delta_{\downarrow\downarrow}$ which are decoupled in the spin-sector. We show that these three-dimensional systems should generically support topologically protected surface Majorana arcs and bulk Weyl fermions as gapless excitations. Similar protected low-energy exotic quasiparticles should also appear in the recently discovered non-centrosymmteric superconductors in the presence of a Zeeman field. The protected surface arcs can be probed by angle-resolved photoemission (ARPES) as well as scanning tunneling microscope (STM) experiments.Comment: 5 pages and 2 figures; Figure 2 revised, typos correcte

Influence of QED Corrections on the Orientation of Chiral Symmetry Breaking in the NJL model

We study QED corrections to chiral symmetry breaking in the Nambu--Jona-Lasinio (NJL) model with two flavors of quarks. In this model, the isospin symmetry is broken by the differences between the current quark masses and the electromagnetic charges of the up and down quarks. To leading order in the 1/N expansion, we calculate the effective potential of the model with one-loop QED corrections at finite temperature. Evaluating the effective potential, we study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking. The current quark mass plays an essential role in maintaining the orientation of the chiral symmetry breaking. If the average of the up and down quark masses is small enough, we find a phase in which the pion field has non-vanishing expectation value and dynamical CP violation takes place.Comment: 22 pages, 13 figures; added discussion about pion mass differenc