An Improved General E-unification Method

A generalization of Paramodulation is defined and shown to lead to a complete E-Unification method for arbitrary equational theories E. The method is defined in term of transformations on systems, building upon and refining results of Gallier and Snyder

A refined version of general E-unification

Transformation--based systems for general E-unification were first investigated by Gallier and Snyder. Their system extends the well--known rules for syntactic unification by Lazy Paramodulation, thus coping with the equational theory. More recently, Dougherty and Johann improved on this method by giving a restriction of the Lazy Paramodulation inferences. In this paper, we show that their system can be further improved by a stronger restriction on the applicability of Lazy Paramodulation. It turns out that the framework of proof transformations provides an elegant and natural means for proving completeness of the inference system

Reduction of Couplings in Quantum Field Theories with applications in Finite Theories and the MSSM

We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. It has a remarkable predictive power since, at the unification scale, it leads to relations between gauge and Yukawa couplings in the dimensionless sectors and relations involving the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the unified gaugino mass in the soft breaking sector. In both the MSSM and the FUT model we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Furthermore we also predict the masses of the other Higgses, as well as the supersymmetric spectrum, both being in very confortable agreement with the LHC bounds on Higgs and supersymmetric particles.Comment: 18 pages, 4 figures. To appear in the proceedings of LT-10, Varna. Based on invited talks given at: LT-10, Varna; PACT-2013, Madrid; SQS'2013, Dubna; CORFU 2013, Corfu, and in several invited seminar

Removing the gauge parameter dependence of the effective potential by a field redefinition

The gauge parameter dependence of the effective potential is determined by partial differential equations involving also the Higgs boson field expectation value. Solving these equations by the method of characteristics leads to complete elimination of the gauge parameter dependence of the effective potential. The construction is carried out in the case of the standard model of electroweak unification for the renormalization group improved effective potential up to the next-leading logarithmic order.Comment: 17 page

Focus Point Supersymmetry: Proton Decay, Flavor and CP Violation, and the Higgs Boson Mass

In focus point supersymmetry, all squarks and sleptons, including those of the third generation, have multi-TeV masses without sacrificing naturalness. We examine the implications of this framework for low energy constraints and the light Higgs boson mass. Undesirable contributions to proton decay and electric dipole moments, generic in many supersymmetric models, are strongly suppressed. As a result, the prediction for alpha_s in simple grand unified theories is 3 to 5 standard deviations closer to the experimental value, and the allowed CP-violating phases are larger by one to two orders of magnitude. In addition, the very heavy top and bottom squarks of focus point supersymmetry naturally produce a Higgs boson mass at or above 115 GeV without requiring heavy gauginos. We conclude with an extended discussion of issues related to the definition of naturalness and comment on several other prescriptions given in the literature.Comment: 31 pages, 10 figures, references added, version to appear in Phys. Rev.

Yukawa Quasi-Unification

We construct concrete supersymmetric grand unified theories based on the Pati-Salam gauge group SU(4)_c x SU(2)_L x SU(2)_R which naturally lead to a moderate violation of "asymptotic" Yukawa unification and thus can allow an acceptable b-quark mass even with universal boundary conditions. We consider the constrained minimal supersymmetric standard model which emerges from one of these theories with a deviation from Yukawa unification which is adequate for mu>0. We show that this model possesses a wide and natural range of parameters which is consistent with the data on b --> s gamma, the muon anomalous magnetic moment, the cold dark matter abundance in the universe, and the Higgs boson masses. The lightest supersymmetric particle can be as light as about 107 GeV.Comment: 27 pages including 10 figures, Revtex, minor corrections, version to appear in Nucl. Phys.

A note on the RG flow in (N=1, D=4) Supergravity and applications to Z_3 orbifold/orientifold compactification

We apply the standard approach of RG flow for the gauge couplings in N=1 D=4 Supergravity to show how to match its results with the heterotic $Z_3$ orbifold and Type IIB ${Z_3}$ orientifold-based models. Using only supergravity, anomaly cancellation and the requirement of unification we determine the part of the K\"ahler potential of the model invariant under the symmetries of the model. For heterotic orbifolds/type IIB orientifolds, this shows that the lowest order K\"ahler term of the dilaton has the structure $-\ln(S+{\bar S})$ in agreement with string calculations. The structure of the holomorphic coupling is also found from arguments of unification and anomaly cancellation under the conjectured $SL(2,Z)_{T_i}$ symmetries of the models. A consequence of the latter is that in the case of the $Z_3$ orientifold the holomorphic coupling necessarily contains a part with coefficient proportional to the one loop beta function, in agreement with string calculations which do not however assume this symmetry. This gives circumstantial evidence for the existence of this symmetry at string level in $Z_3$ orientifold. Finally, we comment on the values of the unification scale and examine the possibility of mirage unification in which the effective unification scale may be situated far above the string scale.Comment: 17 pages, LaTe