21,200 research outputs found

    Random conformal snowflakes

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    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

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    Fermionic decays of the scalar leptoquarks S=S1(+),S1(),Sm S=S_1^{(+)}, S_1^{(-)}, S_m and of the scalar gluons F=F1,F2F=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 S1(+)tlj+,S1()νib~,Smtν~j,F1tb~,F2tt~ 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 mS,mF<1m_S, m_F<1 TeV and with the total branching ratios close to 1. In the case of mS<mtm_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(S1(+)cl+)Br(S_1^{(+)}\to cl^+) \approx Br(S1()νb~)1Br(S_1^{(-)}\to \nu\tilde b) \approx 1, Br(Smbl+)0.9Br(S_m\to bl^+) \approx 0.9 and Br(Smcν~)0.1.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