109,187 research outputs found
Undecidability of the unification and admissibility problems for modal and description logics
We show that the unification problem `is there a substitution instance of a
given formula that is provable in a given logic?' is undecidable for basic
modal logics K and K4 extended with the universal modality. It follows that the
admissibility problem for inference rules is undecidable for these logics as
well. These are the first examples of standard decidable modal logics for which
the unification and admissibility problems are undecidable. We also prove
undecidability of the unification and admissibility problems for K and K4 with
at least two modal operators and nominals (instead of the universal modality),
thereby showing that these problems are undecidable for basic hybrid logics.
Recently, unification has been introduced as an important reasoning service for
description logics. The undecidability proof for K with nominals can be used to
show the undecidability of unification for boolean description logics with
nominals (such as ALCO and SHIQO). The undecidability proof for K with the
universal modality can be used to show that the unification problem relative to
role boxes is undecidable for Boolean description logic with transitive roles,
inverse roles, and role hierarchies (such as SHI and SHIQ)
Implications of Canonical Gauge Coupling Unification in High-Scale Supersymmetry Breaking
We systematically construct two kinds of models with canonical gauge coupling
unification and universal high-scale supersymmetry breaking. In the first we
introduce standard vector-like particles while in the second we also include
non-standard vector-like particles. We require that the gauge coupling
unification scale is from 5 x 10^{15} GeV to the Planck scale, that the
universal supersymmetry breaking scale is from 10 TeV to the unification scale,
and that the masses of the vector-like particles (M_V) are universal and in the
range from 200 GeV to 1 TeV. Using two-loop renormalization group equation
(RGE) running for the gauge couplings and one-loop RGE running for Yukawa
couplings and the Higgs quartic coupling, we calculate the supersymmetry
breaking scales, the gauge coupling unification scales, and the corresponding
Higgs mass ranges. When the vector-like particle masses are less than 1 TeV,
these models can be tested at the LHC.Comment: 25 pages, 4 figure
Yukawa coupling unification and non-universal gaugino mediation of supersymmetry breaking
The requirement of Yukawa coupling unification highly constrains the SUSY
parameter space. In several SUSY breaking scenarios it is hard to reconcile
Yukawa coupling unification with experimental constraints from B(b->s gamma)
and the muon anomalous magnetic moment a_mu. We show that b-tau or even t-b-tau
Yukawa unification can be satisfied simultaneously with b->s gamma and a_mu in
the non-universal gaugino mediation scenario. Non-universal gaugino masses
naturally appear in higher dimensional grand unified models in which gauge
symmetry is broken by orbifold compactification. Relations between SUSY
contributions to fermion masses, b->s gamma and a_mu which are typical for
models with universal gaugino masses are relaxed. Consequently, these
phenomenological constraints can be satisfied simultaneously with a relatively
light SUSY spectrum, compared to models with universal gaugino masses.Comment: 20 pages, 8 figures. References added. A copy of the paper with
better resolution figures can be found at
http://www.hep.fsu.edu/~balazs/Physics/Papers/2003
Gauge Coupling Unification due to Non-universal Soft Supersymmetry Breaking
Gauge coupling unification is studied in the MSSM with non-universal soft
supersymmetry breaking terms. If gaugino masses are sufficiently smaller than
scalar soft masses and the scalar soft masses have also certain types of
non-universality, gauge coupling unification scale can be larger than ~GeV even within the MSSM contents. String unification may not need a
large threshold correction or a large modulus value. We also discuss the
relation to the string model building.Comment: 14 pages,LaTeX file included 1 compressed and uuencoded figure,
KANAZAWA-94-0
SO(10) Yukawa Unification with mu < 0
We consider the low energy implications including particle spectroscopy of
SO(10) inspired t-b-tau Yukawa coupling unification with mu < 0, where mu is
the coefficient of the bilinear Higgs mixing term of the minimal supersymmetric
standard model (MSSM). We imploy non-universal MSSM gaugino masses induced by
SO(10) invariant dimension five operators, such that the total number of
fundamental parameters is precisely the same as in Yukawa unified
supersymmetric SO(10) models with universal gaugino masses and mu > 0. We find
that t-b-tau Yukawa unification with mu < 0 is compatible with the current
experimental bounds, including the WMAP bound on neutralino dark matter and the
measured value of the muon anomalous magnetic moment. We present a variety of
benchmark points which include relatively light squarks (~ TeV) of the first
two families and an example in which the bottom and top squarks are lighter
than the gluino. This is quite distinct from Yukawa unification with mu > 0 and
universal gaugino masses in which the gluino is the lightest colored sparticle
and the sqaurks of the first two families have masses in the multi-TeV range.Comment: 13 pages, 2 figures, 1 tabl
Yukawa Unification as a Window into the Soft Supersymmetry Breaking Lagrangian
We study Yukawa unification, including the effects of a physical neutrino
mass consistent with the Superkamiokande observations, in a string/-brane
inspired Pati-Salam model which allows the most general non-universal scalar
and gaugino masses, including the usual -term contributions which arise in
SO(10). We investigate how the tight constraints from rare decays such as and can provide information about the
family dependent supersymmetry breaking soft Lagrangian, for example the
trilinears associated with the second and third family. Many of our results
also apply to SO(10) to which the model approximately reduces in a limiting
case. In both models we find that Yukawa unification is perfectly viable
providing the non-universal soft masses have particular patterns. In this sense
Yukawa unification acts as a window into the soft supersymmetry breaking
Lagrangian.Comment: References added. 82 pages, 57 figures, Late
Running of Soft Parameters in Extra Space-Time Dimensions
The evolution of the parameters including those in the soft
supersymmetry-breaking (SSB) sector is studied in the minimal supersymmetric
standard model (MSSM) with a certain set of Kaluza-Klein towers which has been
recently considered by Dienes et al. We use the continuous Wilson
renormalizaion group technique to derive the matching condition between the
effective, renormalizable and original, unrenormalizable theories. We
investigate whether the assumption on a large compactification radius in the
model is consistent with the gauge coupling unification, the
unification and the radiative breaking of the electroweak gauge symmetry with
the universal SSB terms. We calculate the superpartner spectrum under the
assumption of the universal SSB parameters to find differences between the
model and the MSSM.Comment: 32 pages, latex, 14 figure
Grand unification through gravitational effects
We systematically study the unification of gauge couplings in the presence of
(one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand
unified theory by gravitational interactions at the Planck scale MPl. These
operators alter the usual condition for gauge coupling unification, which can,
depending on the Higgs content H and vacuum expectation value, result in
unification at scales MX significantly different than naively expected. We find
non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson
coefficients c, that easily satisfy the constraints from proton decay.
Furthermore, gauge coupling unification at scales as high as the Planck scale
seems feasible, possibly hinting at simultaneous unification of gauge and
gravitational interactions. In the Appendix we work out the group theoretical
aspects of this scenario for SU(5) and SO(10) unified groups in detail; this
material is also relevant in the analysis of non-universal gaugino masses
obtained from supergravity.Comment: 27 pages, 5 figures, 8 tables, 1 appendix, revtex; v2: introduction
and conclusion expanded, references added, minor changes, version published
in PR
Phenomenology of non-universal gaugino masses and implications for the Higgs boson decay
Grand unified theories (GUTs) can lead to non-universal gaugino masses at the
unification scale. We study the implications of such non-universal gaugino
masses for the composition of the lightest neutralino in supersymmetric (SUSY)
theories based on SU(5) gauge group. We also consider the phenomenological
implications of non-universal gaugino masses for the phenomenology of Higgs
bosons in the context of Large Hadron Collider.Comment: 4 pages, 8 eps figures, style files included, Talk at LCWS06,
Bangalore, India; typos correcte
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