BMO-estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series

It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series

Proton Stability In Supersymmetric SU(5)

Within supersymmetric SU(5) GUT we suggest mechanisms for suppression of baryon number violating dimension five and six operators. The mechanism is based on the idea of split multiplets (i.e. quarks and leptons are not coming from a single GUT state) which is realized by an extension with additional vector-like matter. The construction naturally avoids wrong asymptotic relation $\hat{M}_D=\hat{M}_E$. Thus, the long standing problems of the minimal SUSY SU(5) GUT can be resolved. In a particular example of flavor structure and with additional {\cal U}(1)\tm {\cal Z}_{3N} symmetry we demonstrate how the split multiplet mechanism works out. Namely, the considered model is compatible with successful gauge coupling unification and realistic fermion mass pattern. The nucleon decay rates are relatively suppressed and can be well compatible with current experimental bounds.Comment: Discussions and some clarifications adde

Anomalous U(1)_A and Electroweak Symmetry Breaking

We suggest a new mechanism for electroweak symmetry breaking in the supersymmetric Standard Model. Our suggestion is based on the presence of an anomalous U(1)_A gauge symmetry, which naturally arises in the four dimensional superstring theory, and heavily relies on the value of the corresponding Fayet-Illiopoulos \xi-term.Comment: Latex, 11 pages, discussions and references adde

Model Building with Gauge-Yukawa Unification

In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge-Yukawa coupling unification, g_i=y_f, in the effective four dimensional theory after the initial gauge symmetry and the supersymmetry are broken upon orbifold compactification. We consider gauge-Yukawa unified models based on a variety of four dimensional symmetries, including SO(10), SU(5), Pati-Salam symmetry, trinification, and the Standard Model. Only in the case of Pati-Salam and the Standard Model symmetry, we do obtain gauge-Yukawa unification. Partial gauge-Yukawa unification is also briefly discussed.Comment: 23 page

Sparticle mass spectra from SU(5) SUSY GUT models with b−τb-\tau Yukawa coupling unification

Supersymmetric grand unified models based on the gauge group SU(5) often require in addition to gauge coupling unification, the unification of b-quark and $\tau$-lepton Yukawa couplings. We examine SU(5) SUSY GUT parameter space under the condition of $b-\tau$ Yukawa coupling unification using 2-loop MSSM RGEs including full 1-loop threshold effects. The Yukawa-unified solutions break down into two classes. Solutions with low tan\beta ~3-11 are characterized by gluino mass ~1-4 TeV and squark mass ~1-5 TeV. Many of these solutions would be beyond LHC reach, although they contain a light Higgs scalar with mass <123 GeV and so may be excluded should the LHC Higgs hint persist. The second class of solutions occurs at large tan\beta ~35-60, and are a subset of $t-b-\tau$ unified solutions. Constraining only $b-\tau$ unification to ~5% favors a rather light gluino with mass ~0.5-2 TeV, which should ultimately be accessible to LHC searches. While our $b-\tau$ unified solutions can be consistent with a picture of neutralino-only cold dark matter, invoking additional moduli or Peccei-Quinn superfields can allow for all of our Yukawa-unified solutions to be consistent with the measured dark matter abundance.Comment: 19 pages, 5 figures, 1 table, PDFLate