General Focus Point in the MSSM

The minimal supersymmetric extension of the Standard Model (SM) is a well motivated scenario for physics beyond the SM, which allows a perturbative description of the theory up to scales of the order of the Grand Unification scale, where gauge couplings unify. The Higgs mass parameter is insensitive to the ultraviolet physics and is only sensitive to the scale of soft supersymmetry breaking parameters. Present collider bounds suggest that the characteristic values of these parameters may be significantly larger than the weak scale. Large values of the soft breaking parameters, however, induce large radiative corrections to the Higgs mass parameter and therefore the proper electroweak scale may only be obtained by a fine tuned cancellation between the square of the holomorphic \mu-parameter and the Higgs supersymmetry breaking square mass parameter. This can only be avoided if there is a correlation between the scalar and gaugino mass parameters, such that the Higgs supersymmetry breaking parameter remains of the order of the weak scale. The scale at which this happens is dubbed as focus point. In this article, we define the general conditions required for this to happen, for different values of the messenger scale at which supersymmetry breaking is transmitted to the observable sector, and for arbitrary boundary conditions of the sfermion, gaugino, and Higgs mass parameters. Specific supersymmetry breaking scenarios in which these correlations may occur are also discussed.Comment: 19 pages, 9 figures, new refs. adde

A light complex scalar for the electron and muon anomalous magnetic moments

The anomalous magnetic moments of the electron and the muon are interesting observables, since they can be measured with great precision and their values can be computed with excellent accuracy within the Standard Model (SM). The current experimental measurement of this quantities show a deviation of a few standard deviations with respect to the SM prediction, which may be a hint of new physics. The fact that the electron and the muon masses differ by two orders of magnitude and the deviations have opposite signs makes it difficult to find a common origin of these anomalies. In this work we introduce a complex singlet scalar charged under a Peccei-Quinn-like (PQ) global symmetry together with the electron transforming chirally under the same symmetry. In this realization, the CP-odd scalar couples to electron only, while the CP-even part can couple to muons and electrons simultaneously. In addition, the CP-odd scalar can naturally be much lighter than the CP-even scalar, as a pseudo-Goldstone boson of the PQ-like symmetry, leading to an explanation of the suppression of the electron anomalous magnetic moment with respect to the SM prediction due to the CP-odd Higgs effect dominance, as well as an enhancement of the muon one induced by the CP-even component.Comment: 31 pages, 3 figures and 3 tables. v2: version matched to JHE