21,239 research outputs found

### Random conformal snowflakes

In many problems of classical analysis extremal configurations appear to
exhibit complicated fractal structure. This makes it much harder to describe
extremals and to attack such problems. Many of these problems are related to
the multifractal analysis of harmonic measure.
We argue that, searching for extremals in such problems, one should work with
random fractals rather than deterministic ones. We introduce a new class of
fractals random conformal snowflakes and investigate its properties developing
tools to estimate spectra and showing that extremals can be found in this
class. As an application we significantly improve known estimates from below on
the extremal behaviour of harmonic measure, showing how to constuct a rather
simple snowflake, which has a spectrum quite close to the conjectured extremal
value

### Fermionic decays of scalar leptoquarks and scalar gluons in the minimal four color symmetry model

Fermionic decays of the scalar leptoquarks $S=S_1^{(+)}, S_1^{(-)}, S_m$
and of the scalar gluons $F=F_1, F_2$ predicted by the four color symmetry
model with the Higgs mechanism of the quark-lepton mass splitting are
investigated. Widths and branching ratios of these decays are calculated and
analysed in dependence on coupling constants and on masses of the decaying
particles. It is shown that the decays $S_1^{(+)}\to tl^+_j, S_1^{(-)}\to
\nu_i\tilde b, S_m\to t\tilde \nu_j, F_1\to t\tilde b, F_2\to t\tilde t$ are
dominant with the widths of order of a few GeV for $m_S, m_F<1$ TeV and with
the total branching ratios close to 1. In the case of $m_S < m_t$ the dominant
scalar leptoquark decays are S_1^{(+)}\to cl_j^+, S_1^{(-)}\to \nu_i\tilde b,
S_m\to b\l_j^+, S_m\to c\tilde \nu_j with the total branching ratios
$Br(S_1^{(+)}\to cl^+) \approx$ $Br(S_1^{(-)}\to \nu\tilde b) \approx 1$,
$Br(S_m\to bl^+) \approx 0.9$ and $Br(S_m\to c\tilde \nu) \approx 0.1.$ A
search for such decays at the LHC and Tevatron may be of interest.Comment: 11 pages, 1 figure, 1 table, to be published in Modern Physics
Letters

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