We analyze non-minimally coupled scalar field theories in metric (second-order) and Palatini (first-order) formalisms in a comparative fashion. After contrasting them in a general setup, we specialize to inflation and find that the two formalisms differ in their predictions for various cosmological parameters. The main reason is that dependencies on the non-minimal coupling parameter are different in the two formalisms. For successful inflation, the Palatini approach prefers a much larger value for the non-minimal coupling parameter than the Metric approach. Unlike the Metric formalism, in Palatini, the inflaton stays well below the Planck scale whereby providing a natural inflationary epoch.

We report an error in the renormalization group equations ͑RGE's͒ ͑A13͒-͑A21͒. The normalization of the U͑1͒ gauge couplings requires that in Eqs. ͑A13͒-͑A21͒ and ͑B18͒-͑B19͒, g 1 2 should be replaced by 3 5 g 1 2 , and g 1 Ј 2 should be replaced by.47 m 2 02 Ϫ0.12 m 1 02 Ϫ0.12 m S 02 Ϫ0.41 m U 02 Ϫ0.41 m Q 02 Ϫ0.031 A 02 Ϫ0.039 A Q 02 Ϫ3.21͑ M 1/2 ͒ 2 ϩ0.034 A 0 A Q 0 ϩ0.035 A 0 M 1/2 Ϫ0.18 A Q 0 M 1/2 , ͑6͒ m S 2 ͑ M Z ͒ϭϪ0.25 m 2 02 Ϫ0.38 m 1 02 ϩ0.62 m S 02 ϩ0.12 m U 02 ϩ0.12 m Q 02 Ϫ0.11 A 02 ϩ0.017 A Q 02 ϩ0.42͑ M 1/2 ͒ 2 ϩ0.068 A 0 A Q 0 Ϫ0.1 A 0 M 1/2 ϩ0.087A Q 0 M 1/2 , ͑7͒ m U 2 ͑ M Z ͒ϭϪ0.27 m 2 02 ϩ0.05 m 1 02 ϩ0.05 m S 02 ϩ0.68 m U 02 Ϫ0.32 m Q 02 ϩ0.017 A 02 Ϫ0.032 A Q 02 ϩ4.1͑ M 1/2 ͒ 2 ϩ0.00 A 0 A Q 0 ϩ0.06 A 0 M 1/2 Ϫ0.15 A Q 0 M 1/2 , ͑8͒

We consider electroweak symmetry breaking in supersymmetric models with an extra nonanomalous U͑1͒Ј gauge symmetry and an extra standard-model singlet scalar S. For appropriate charges the U͑1͒Ј forbids an elementary term, but an effective is generated by the VEV of S, leading to a natural solution to the problem. There are a variety of scenarios leading to acceptably small Z-ZЈ mixing and other phenomenological consequences, all of which involve some but not excessive fine-tuning. One class, driven by a large trilinear soft supersymmetry-breaking term, implies small mixing, a light ZЈ ͑e.g., 200 GeV͒, and an electroweak phase transition that may be first order at the tree level. In another class, with m S 2 Ͻ0 ͑radiative breaking͒, the typical scale of dimensional parameters, including M Z Ј and the effective , is ϳ1TeV, but the electroweak scale is smaller due to cancellations. We relate the soft supersymmetry-breaking parameters at the electroweak scale to those at the string scale, choosing Yukawa couplings as determined within a class of string models. We find that one does not obtain either scenario for universal soft supersymmetry-breaking mass parameters at the string scale and no exotic multiplets contributing to the renormalization group equations. However, either scenario is possible when the assumption of universal soft breaking is relaxed. Radiative breaking can also be generated by exotics, which are expected in most string models.

The explicit CP violation in the MSSM radiatively induces a finite unremovable alignment between the Higgs doublets. This additinal phase can be as large as the original CP phases in certain portions of the MSSM parameter space. Considering the specific case of the charginos, this additional phase is shown to induce a conceivable amount of CP violation near the would-be CP conserving points. Moreover, the CP violation in the absence of this phase is smaller than the one in the presence of it, and the former can never compete with the latter, however large tan β is.

Within the minimal supersymmetric standard model (MSSM), the large tan β regime can lead to important modifications in the pattern of CP-violating sources contributing to low energy electric dipole moments (EDMs). In particular, four-fermion CP-violating interactions induced by Higgs exchange should be accounted for alongside the constituent EDMs of quarks and electrons. To this end, we present a comprehensive analysis of three low energy EDM observables -namely the EDMs of thallium, mercury and the neutronat large tan β, in terms of one-and two-loop contributions to the constituent EDMs and four-fermion interactions. We concentrate on the constrained MSSM as well as the MSSM with non-universal Higgs masses, and include the CP-violating phases of µ and A. Our results indicate that the atomic EDMs receive significant corrections from four-fermion operators, especially when Im(A) is the only CP-violating source, whereas the neutron EDM remains relatively insensitive to these effects. As a consequence, in a large portion of the parameter space, one cannot infer a separate bound on the electron EDM via the experimental constraint on the thallium EDM. Furthermore, we find that the electron EDM can be greatly reduced due to the destructive interference of one-and two-loop contributions with the latter being dominated by virtual staus.

We re-examine questions concerning the contribution of the three-gluon Weinberg operator to the electric dipole moment of the neutron, and provide several QCD sum rule-based arguments that the result is smaller than -but nevertheless consistent with -estimates which invoke naive dimensional analysis. We also point out a regime of the MSSM parameter space with light gluinos for which this operator provides the dominant contribution to the neutron electric dipole moment due to enhancement via the dimension five color electric dipole moment of the gluino.

In the Higgs inflation scenario the Higgs field is strongly coupled to the Ricci scalar in order to drive primordial inflation. However, in its original form in pure metric formulation of gravity, the ultraviolet (UV) cutoff of the Higgs interactions and the Hubble rate are of the same magnitude, and this makes the whole inflationary evolution dependent of the unknown UV completion of the Higgs sector. This problem, the unitarity violation, plagues the Higgs inflation scenario. In this Letter we show that, in the Palatini formulation of gravitation, Higgs inflation does not suffer from unitarity violation since the UV cutoff lies parametrically much higher than the Hubble rate so that unknown UV physics does not disrupt the inflationary dynamics. Higgs-Palatini inflation, as we call it, is, therefore, UV-safe, minimal and endowed with predictive power.

Motivated by the apparent need for extending the MSSM and perhaps mitigating naturalness problems associated with the µ parameter and fine-tuning of the soft masses, we augment the MSSM spectrum by a SM gauge singlet chiral superfield, and enlarge the gauge structure by an additional U(1) ′ invariance, so that the gauge and Higgs sectors are relatively secluded. One crucial aspect of U(1) ′ models is the existence of anomalies, cancellation of which may require the inclusion of exotic matter which in turn disrupts the unification of the gauge couplings. In this work we pursue the question of canceling the anomalies with a minimal matter spectrum and no exotics. This can indeed be realized provided that U(1) ′ charges are family-dependent and the soft-breaking sector includes non-holomorphic operators for generating the fermion masses. We provide the most general solutions for U(1) ′ charges by taking into account all constraints from gauge invariance and anomaly cancellation. We analyze various laboratory and astrophysical bounds ranging from fermion masses to relic density, for an illustrative set of parameters. The U(1) ′ charges admit patterns of values for which family nonuniversality resides solely in the lepton sector, though this does not generate leptonic FCNCs due to the U(1) ′ gauge invariance. *