Fermions on the Electroweak String

We construct a simple class of exact solutions of the electroweak theory including the naked $Z$--string and fermion fields. It consists in the $Z$--string configuration ($\phi,Z_\theta$), the {\it time} and $z$ components of the neutral gauge bosons ($Z_{0,3},A_{0,3}$) and a fermion condensate (lepton or quark) zero mode. The $Z$--string is not altered (no feed back from the rest of fields on the $Z$--string) while fermion condensates are zero modes of the Dirac equation in the presence of the $Z$--string background (no feed back from the {\it time} and $z$ components of the neutral gauge bosons on the fermion fields). For the case of the $n$--vortex $Z$--string the number of zero modes found for charged leptons and quarks is (according to previous results by Jackiw and Rossi) equal to $|n|$, while for (massless) neutrinos is $|n|-1$. The presence of fermion fields in its core make the obtained configuration a superconducting string, but their presence (as well as that of $Z_{0,3},A_{0,3}$) does not enhance the stability of the $Z$--string.Comment: 12 text pages (Latex) and 8 postscript figures in a uuencoded fil

Top-bottom doublet in the sphaleron background

We consider the top-bottom doublet in the background of the sphaleron for the realistic case of large non-degeneracy of fermion masses, in particular $m_b=5$ GeV and $m_t=175$ GeV. We propose an axially symmetric $(r,\theta)$-dependent ansatz for fermion fields and investigate the effects of the non-degeneracy on them. The exact solution is described, with an error less than 0.01\%, by a set of ten radial functions. We also propose an approximate solution, in the $m_b/m_t\rightarrow 0$ limit, with an error ${\cal O}(m_b/m_t)$. We have found that the effects of non-degeneracy provide a $\theta$-dependence typically $\sim 10\%$.Comment: 12 pages, latex + psfig, 4 uuencoded figure

Squarks and sphalerons

Electric charge and color breaking minima along third generation squark directions do appear in the Minimal Supersymmetric Standard Model for particular regions of the corresponding supersymmetric parameters $A_t$, $\mu$, $\tan\beta$, $m_Q^2$ and $m_U^2$. We have studied possible instabilities of electroweak sphalerons along non-trivial squark configurations. We have found that instabilities along the latter lie in the region of parameter space where the electroweak minimum is not the global one. Thus charge and color conservation imply that the standard electroweak sphaleron is not destabilized along squark directions.Comment: 11 pages, LateX + psfig.sty, 1 figur