The $m_D-b_M$ Problem of Dirac Gauginos and its Solutions

Abstract

We examine the effective low-energy theory of the adjoint sector of Dirac gaugino models and its UV completions, and identify the main source of tuning. A holomorphic scalar adjoint mass square (the "$b_M$ term") is generated at the same order (1-loop) as the Dirac gaugino mass (the "$m_D$ term"), leading to the problematic relation $b_M\sim16\pi^2 m_D^2$, somewhat analogous to the $\mu-B_\mu$ problem of gauge mediation. We identify the leading operators of the low-energy effective theory contributing to the adjoint sector, and evaluate them in various UV completions, confirming the existence of this problem. We suggest a solution by introducing messenger mixing and tuning the relevant parameters. We also present a novel dynamical model for Dirac gauginos based on a strongly coupled SUSY QCD theory, where the additional adjoint $M$ is identified with a confined meson, the U(1) with a baryon-number like symmetry, and the messengers with the confined baryons. We find a SUSY breaking vacuum with a non-vanishing D-term, which after tuning the messenger mixing angles gives rise to a realistic gaugino and squark sector.