66,426 research outputs found
Vacuum stability and supersymmetry at high scales with two Higgs doublets
We investigate the stability of the electroweak vacuum for two-Higgs doublet
models with a supersymmetric UV completion. The supersymmetry breaking scale is
taken to be of the order of the grand unification scale. We first study the
case where all superpartners decouple at this scale. We show that contrary to
the Standard Model with one Higgs doublet, matching to the supersymmetric UV
completion is possible if the low-scale model contains two Higgs doublets. In
this case vacuum stability and experimental constraints point towards low
values of tan(beta) < 2 and pseudoscalar masses of at least about a TeV. If the
higgsino superpartners of the Higgs fields are also kept light, the conclusions
are similar and essentially independent of the higgsino mass. Finally, if all
gauginos are also given electroweak-scale masses (split supersymmetry with two
Higgs doublets), the model cannot be matched to supersymmetry at very high
scales when requiring a 125 GeV Higgs. Light neutral and charged higgsinos
therefore emerge as a promising signature of a supersymmetric UV completion of
the Standard Model at the grand unification scale.Comment: 27 pages, 4 figures; v2: minor changes in references and text,
results unchange
Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry
F-theory GUTs provide a promising UV completion for models with approximate
gauge coupling unification, such as the (non-supersymmetric) Standard Model.
More specifically, if the superparters have masses well above the TeV scale,
the resulting imperfection in unification can be accounted for by the, in
principle calculable, classical F-theory correction at the high scale. In this
paper we argue for the correct form of the F-theory corrections to unification,
including KK mode loop effects. However, the price of compensating the
imprecise unification in such High Scale SUSY models with F-theory corrections
is that the GUT scale is lowered, potentially leading to a dangerously high
proton decay rate from dimension-6 operators. We analyse the possibility of
suppressing the decay rate by the localization of gauge bosons in higher
dimensions. While this effect can be very strong for the zero modes, we find
that in the simplest models of this type it is difficult to realize a
significant suppression for higher modes (Landau levels). Notably, in the
absence of substantial suppressions to the proton decay rate, the superpartners
must be lighter than 100 TeV to satisfy proton decay constraints. We highlight
that multiple correlated signals of proton decay could verify this scenario.Comment: 44 pages. v2: References adde
Towards Correctness of Program Transformations Through Unification and Critical Pair Computation
Correctness of program transformations in extended lambda calculi with a
contextual semantics is usually based on reasoning about the operational
semantics which is a rewrite semantics. A successful approach to proving
correctness is the combination of a context lemma with the computation of
overlaps between program transformations and the reduction rules, and then of
so-called complete sets of diagrams. The method is similar to the computation
of critical pairs for the completion of term rewriting systems. We explore
cases where the computation of these overlaps can be done in a first order way
by variants of critical pair computation that use unification algorithms. As a
case study we apply the method to a lambda calculus with recursive
let-expressions and describe an effective unification algorithm to determine
all overlaps of a set of transformations with all reduction rules. The
unification algorithm employs many-sorted terms, the equational theory of
left-commutativity modelling multi-sets, context variables of different kinds
and a mechanism for compactly representing binding chains in recursive
let-expressions.Comment: In Proceedings UNIF 2010, arXiv:1012.455
SU(5) Completion of the Dark Scalar Doublet Model of Radiative Neutrino Mass
Adding a second scalar doublet (eta^+,eta^0) and three neutral singlet
fermions N_{1,2,3} to the Standard Model of particle interactions with a new
Z_2 symmetry, it has been shown that eta^0_R or eta^0_I is a good dark-matter
candidate and seesaw neutrino masses are generated radiatively. A minimal
extension of this new idea is proposed to allow for its SU(5) completion.
Supersymmetric unification is then possible, and leptoquarks of a special kind
are predicted at the TeV scale.Comment: 6 pages, 2 figures, 1 tabl
Computing overlappings by unification in the deterministic lambda calculus LR with letrec, case, constructors, seq and variable chains
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules.The method is similar to the computation of critical pairs for the completion of term rewriting systems. We describe an effective unification algorithm to determine all overlaps of transformations with reduction rules for the lambda calculus LR which comprises a recursive let-expressions, constructor applications, case expressions and a seq construct for strict evaluation. The unification algorithm employs many-sorted terms, the equational theory of left-commutativity modeling multi-sets, context variables of different kinds and a mechanism for compactly representing binding chains in recursive let-expressions. As a result the algorithm computes a finite set of overlappings for the reduction rules of the calculus LR that serve as a starting point to the automatization of the analysis of program transformations
Complete Sets of Transformations for General \u3cem\u3eE\u3c/em\u3e-Unification
This paper is concerned with E-unification in arbitrary equational theories. We extend the method of transformations on systems of terms, developed by Martelli-Montanari for standard unification, to E-unification by giving two sets of transformations, BT and T, which are proved to be sound and complete in the sense that a complete set of E-unifiers for any equational theory E can be enumerated by either of these sets. The set T is an improvement of BT, in that many E-unifiers produced by BT will be weeded out by T. In addition, we show that a generalization of surreduction (also called narrowing) combined with the computation of critical pairs is complete. A new representation of equational proofs as certain kinds of trees is used to prove the completeness of the set BT in a rather direct fashion that parallels the completeness of the transformations in the case of (standard) unification. The completeness of T and the generalization of surreduction is proved by a method inspired by the concept of unfailing completion, using an abstract (and simpler) notion of the completion of a set of equations
Effective theoretical approach of Gauge-Higgs unification model and its phenomenological applications
We derive the low energy effective theory of Gauge-Higgs unification (GHU)
models in the usual four dimensional framework. We find that the theories are
described by only the zero-modes with a particular renormalization condition in
which essential informations about GHU models are included. We call this
condition ``Gauge-Higgs condition'' in this letter. In other wards, we can
describe the low energy theory as the SM with this condition if GHU is a model
as the UV completion of the Standard Model. This approach will be a powerful
tool to construct realistic models for GHU and to investigate their low energy
phenomena.Comment: 18 pages, 2 figures; Two paragraphs discussing the applicable scope
of this approach are adde
Unification of terms with exponents
In an ICALP (1991) paper, H. Chen and J. Hsiang introduced a notion that allows for a finite representation of certain infinite sets of terms. These so called w-terms find an application in logic programming, where they can serve to represent finitely an infinite number of answers or to avoid nontermination in certain cases. Another application is in the field of equational logic. Using w-terms, it is possible to avoid a certain type of divergence of ordered completion. In all cases, unification is the basic computational aspect of this notation. Chen and Hsiang give a complete and terminating unification algorithm for w-terms. Recently, H. Comon introduced terms with exponents, thus significantly extending Chen and Hsiang's notion of w-terms. He provides a fairly complicated unification algorithm. This paper introduces a further syntactic generalization of Comon's notion together with a comparatively simple inference system for unification
Perspective on completing natural inflation
We present a perspective on the inflation paths in 2-, 3-,,, N-flation models
based on the ultraviolet completion in heterotic string theory, where a number
of grand unification scale axions are used. The number of non-Abelian gauge
groups for a natural inflation is restricted in string compactification, and we
argue that the most plausible completion of natural inflation from a theory
perspective is the 2-flation.Comment: 5 pages, 1 eps figur
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