We propose to introduce general messenger-matter interactions in the deflected anomaly mediated supersymmetry (SUSY) breaking (AMSB) scenario to explain the $g_{\mu }-2$ anomaly. Scenarios with complete or incomplete grand unified theory (GUT) multiplet messengers are discussed, respectively. The introduction of incomplete GUT mulitiplets can be advantageous in various aspects. We found that the $g_{\mu }-2$ anomaly can be solved in both scenarios under current constraints including the gluino mass bounds, while the scenarios with incomplete GUT representation messengers are more favored by the $g_{\mu }-2$ data. We also found that the gluino is upper bounded by about 2.5 TeV (2.0 TeV) in scenario A and 3.0 TeV (2.7 TeV) in scenario B if the generalized deflected AMSB scenarios are used to fully account for the $g_{\mu }-2$ anomaly at $3\sigma$ ($2\sigma$) level. Such a gluino should be accessible in the future LHC searches. Dark matter (DM) constraints, including DM relic density and direct detection bounds, favor scenario B with incomplete GUT multiplets. Much of the allowed parameter space for scenario B could be covered by the future DM direct detection experiments.

• Received 20 June 2017

DOI:https://doi.org/10.1103/PhysRevD.96.075025