We present a supersymmetric version of a two-field relaxion model that naturalizes tuned versions of supersymmetry. This arises from a relaxion mechanism that does not depend on QCD dynamics and where the relaxion potential barrier height is controlled by a second axion-like field. During the cosmological evolution, the relaxion rolls with a nonzero value that breaks supersymmetry and scans the soft supersymmetric mass terms. Electroweak symmetry is broken after the soft masses become of order the supersymmetric Higgs mass term and causes the relaxion to stop rolling for superpartner masses up to ∼ 10 9 GeV. This can explain the tuning in supersymmetric models, including split-SUSY models, while preserving the QCD axion solution to the strong CP problem. Besides predicting two very weakly-coupled axion-like particles, the supersymmetric spectrum may contain an extra Goldstino, which could be a viable dark matter candidate.

Anomaly mediation is a ubiquitous source of supersymmetry (SUSY) breaking which appears in almost every theory of supergravity. In this paper, we show that anomaly mediation really consists of two physically distinct phenomena, which we dub "gravitino mediation" and "Kähler mediation". Gravitino mediation arises from minimally uplifting SUSY anti-de Sitter (AdS) space to Minkowski space, generating soft masses proportional to the gravitino mass. Kähler mediation arises when visible sector fields have linear couplings to SUSY breaking in the Kähler potential, generating soft masses proportional to beta function coefficients. In the literature, these two phenomena are lumped together under the name "anomaly mediation", but here we demonstrate that they can be physically disentangled by measuring associated couplings to the goldstino. In particular, we use the example of gaugino soft masses to show that gravitino mediation generates soft masses without corresponding goldstino couplings. This result naively violates the goldstino equivalence theorem but is in fact necessary for supercurrent conservation in AdS space. Since gravitino mediation persists even when the visible sector is sequestered from SUSY breaking, we can use the absence of goldstino couplings as an unambiguous definition of sequestering.

We study the phenomenology of supersymmetric models in which gauge-singlet scalars mix with the MSSM sneutrinos through weak-scale A terms. After reviewing the constraints on mixed-sneutrino dark matter from measurements of Ω CDM and from direct-detection experiments, we explore mixed-sneutrino signatures relevant to the LHC. For a mixed-sneutrino LSP and a right-handed slepton NLSP, decays of the lightest neturalino can produce opposite-sign, same-flavor (OSSF) dileptons with an invariant-mass distribution shifted away from the kinematic endpoint. In different parameter regions, the charginos and neutralinos produced in cascades all decay dominantly to the lighter sneutrinos, leading to a kinematic edge in the jet-lepton invariant-mass distribution from the decay chainq → χ − q →ν * lq, without an OSSF dilepton signature. We explore the possibility of using mass estimation methods to distinguish this mixed-sneutrino jet-lepton signature from an MSSM one. Finally, we consider signatures associated with Higgs-lepton or Z-lepton production in cascades involving the heavier sneutrinos.

When supergravity (SUGRA) is spontaneously broken, it is well known that anomaly mediation generates sparticle soft masses proportional to the gravitino mass. Recently, we showed that one-loop anomaly-mediated gaugino masses should be associated with unbroken supersymmetry (SUSY). This counterintuitive result arises because the underlying symmetry structure of (broken) SUGRA in flat space is in fact (unbroken) SUSY in antide Sitter (AdS) space. When quantum corrections are regulated in a way that preserves SUGRA, the underlying AdS curvature (proportional to the gravitino mass) necessarily appears in the regulated action, yielding soft masses without corresponding goldstino couplings. In this paper, we extend our analysis of anomaly mediation to sfermion soft masses. Already at tree-level we encounter a number of surprises, including the fact that zero soft masses correspond to broken (AdS) SUSY. At one-loop, we explain how anomaly mediation appears when regulating SUGRA in a way that preserves super-Weyl invariance. We find that recent claims in the literature about the non-existence of anomaly mediation were based on a Wilsonian effective action with residual gauge dependence, and the gauge-invariant 1PI effective action contains the expected anomaly-mediated spectrum. Finally, we calculate the sfermion spectrum to all orders, and use supertrace relations to derive the familiar two-loop soft masses from minimal anomaly mediation, as well as unfamiliar tree-level and one-loop goldstino couplings consistent with renormalization group invariance.

Supersymmetric collider phenomenology depends crucially on whether the lightest observable-sector supersymmetric particle (LOSP) decays, and if so, what the LOSP decay products are. For instance, in SUSY models where the gravitino is lighter than the LOSP, the LOSP decays to its superpartner and a longitudinal gravitino via supercurrent couplings. In this paper, we show that LOSP decays can be substantially modified when there are multiple sectors that break supersymmetry, where in addition to the gravitino there are light uneaten goldstini. As a particularly striking example, a bino-like LOSP can have a near 100% branching fraction to a higgs boson and an uneaten goldstino, even if the LOSP has negligible higgsino fraction. This occurs because the uneaten goldstino is unconstrained by the supercurrent, allowing additional operators to mediate LOSP decay. These operators can be enhanced in the presence of a U (1) R symmetry, leading to copious boosted higgs production in SUSY cascade decays.