41,187 research outputs found
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
SO(10) unification in noncommutative geometry revisited
We investigate the SO(10)-unification model in a Lie algebraic formulation of
noncommutative geometry. The SO(10)-symmetry is broken by a 45-Higgs and the
Majorana mass term for the right neutrinos (126-Higgs) to the standard model
structure group. We study the case that the fermion masses are as general as
possible, which leads to two 10-multiplets, four 120-multiplets and two
additional 126-multiplets of Higgs fields. This Higgs structure differs
considerably from the two Higgs multiplets 16 \otimes 16^* and 16^c \otimes
16^* used by Chamseddine and Fr\"ohlich. We find the usual tree-level
predictions of noncommutative geometry m_W=(1/2)m_t, \sin^2\theta_W=(3/8) and
g_2=g_3 as well as m_H \leq m_t.Comment: 25 pages, LaTeX 2e. v2: typos corrected and footnote on
Super-Kamiokande results adde
Decoupling heavy sparticles in Effective SUSY scenarios: Unification, Higgs masses and tachyon bounds
Using two-loop renormalization group equations implementing the decoupling of
heavy scalars, Effective SUSY scenarios are studied in the limit in which there
is a single low energy Higgs field. Gauge coupling unification is shown to hold
with similar or better precision than in standard MSSM scenarios. b-tau
unification is examined, and Higgs masses are computed using the effective
potential, including two-loop contributions from scalars. A 125 GeV Higgs is
compatible with stops/sbottoms at around 300 GeV with non-universal boundary
conditions at the scale of the heavy sparticles if some of the trilinear
couplings at this scale take values of the order of 1-2 TeV; if more
constrained boundary conditions inspired by msugra or gauge mediation are set
at a higher scale, heavier colored sparticles are required in general. Finally,
since the decoupled RG flow for third-generation scalar masses departs very
significantly from the MSSM DR-bar one, tachyon bounds for light scalars are
revisited and shown to be relaxed by up to a TeV or more.Comment: 35 pages, 17 figures. v2: Updated some scans, allowing for changes in
sign of some parameters, minor improvements. v3: Typos corrected in formulae
in the appendices, added some clarifying remarks about flavor mixing being
ignore
SU(5)xSU(5) unification revisited
The idea of grand unification in a minimal supersymmetric SU(5)xSU(5)
framework is revisited. It is shown that the unification of gauge couplings
into a unique coupling constant can be achieved at a high-energy scale
compatible with proton decay constraints. This requires the addition of a
minimal particle content at intermediate energy scales. In particular, the
introduction of the SU(2)_L triplets belonging to the (15,1)+(\bar{15},1)
representations, as well as of the scalar triplet \Sigma_3 and octet \Sigma_8
in the (24,1) representation, turns out to be crucial for unification. The
masses of these intermediate particles can vary over a wide range, and even lie
in the TeV region. In contrast, the exotic vector-like fermions must be heavy
enough and have masses above 10^10 GeV. We also show that, if the SU(5)xSU(5)
theory is embedded into a heterotic string scenario, it is not possible to
achieve gauge coupling unification with gravity at the perturbative string
scale.Comment: 17 pages, 6 figure
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