Supersymmetric Unification

The measured value of the weak mixing angle is, at present, the only precise experimental indication for physics beyond the Standard Model. It points in the direction of Unified Theories with Supersymmetric particles at accessible energies. We recall the ideas that led to the construction of these theories in 1981.Comment: 21 pages, latex, two figures available by snail-mail upon e-mail request; Talk presented at the International Conference on the History of Original Ideas and Basic Discoveries in Particle Physics held at Ettore Majorana Centre for Scientific Culture, Erice, Sicily, July 29-Aug.4, 199

The Supersymmetric Flavor Problem

The supersymmetric $SU(3)\times SU(2)\times U(1)$ theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes $\mu \rightarrow e + \gamma$ and $K^0 - \bar{K}^0$ mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for $\mu \rightarrow e + \gamma$ exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than $M_{\rm Planck}$.Comment: 17 pages, Latex + epsf macros, 5 postscript figures uuencoded and attached at botto

Split families unified

We present a simple supersymmetric model of split families consistent with flavor limits that preserves the successful prediction of gauge coupling unification and naturally accounts for the Higgs mass. The model provides an intricate connection between the Standard Model flavor hierarchy, supersymmetric flavor problem, unification and the Higgs mass. In particular unification favors a naturally large Higgs mass from D-term corrections to the quartic couplings in the Higgs potential. The unification scale is lowered with a stable proton that can account for the success of b-tau Yukawa coupling unification. The sparticle spectrum is similar to that of natural supersymmetry, as motivated by the supersymmetric flavor problem and recent LHC bounds, with a heavy scalar particle spectrum except for a moderately light stop required for viable electroweak symmetry breaking. Finally, Higgs production and decays, NLSP decays, and new states associated with extending the Standard Model gauge group above the TeV scale provide signatures for experimental searches at the LHC.Comment: 21 pages, 4 figure

Maximally Natural Supersymmetry

We consider 4D weak scale theories arising from 5D supersymmetric (SUSY) theories with maximal Scherk-Schwarz breaking at a Kaluza-Klein (KK) scale of several TeV. Many of the problems of conventional SUSY are avoided. Apart from 3rd family sfermions the SUSY spectrum is heavy, with only ~50% tuning at a gluino mass of ~2TeV and a stop mass of ~650 GeV. A single Higgs doublet acquires a vacuum expectation value, so the physical Higgs is automatically Standard-Model-like. A new U(1)' interaction raises the Higgs mass to 126 GeV. For minimal tuning the associated Z', as well as the 3rd family sfermions, must be accessible to LHC13. A gravitational wave signal consistent with BICEP2 is possible if inflation occurs when the extra dimensions are small.Comment: 5 pages, 4 figure

Logarithmic Unification From Symmetries Enhanced in the Sub-Millimeter Infrared

In theories with TeV string scale and sub-millimeter extra dimensions the attractive picture of logarithmic gauge coupling unification at $10^{16}$ GeV is seemingly destroyed. In this paper we argue to the contrary that logarithmic unification {\it can} occur in such theories. The rationale for unification is no longer that a gauge symmetry is restored at short distances, but rather that a geometric symmetry is restored at large distances in the bulk away from our 3-brane. The apparent `running' of the gauge couplings to energies far above the string scale actually arises from the logarithmic variation of classical fields in (sets of) two large transverse dimensions. We present a number of N=2 and N=1 supersymmetric D-brane constructions illustrating this picture for unification.Comment: 21 pages, 6 figure