Hadronic EDMs, the Weinberg Operator, and Light Gluinos

TL;DR

The paper analyzes the neutron EDM from the Weinberg operator in SUSY, obtaining $d_n(w) \sim e\,(10-30)~{\rm MeV}~w(1~{\rm GeV})$, about a factor of two smaller than naive dimensional analysis. It then shows that in a regime with light gluinos, the gluino color EDM enhances the Weinberg operator with a $1/(m_\lambda \Lambda_W)$ scaling, potentially pushing $d_n$ above the experimental bound unless the CP-odd phase is tuned. The work emphasizes that even when one suppresses one-loop EDMs by a hierarchical gluino mass, the Weinberg operator remains a crucial constraint on MSSM CP violation and provides a framework for interpreting EDM measurements across SUSY parameter space. Overall, the results quantify the interplay between quark (C)EDMs and the Weinberg operator and highlight the importance of gluonic CP-violating operators in EDM phenomenology.

Abstract

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.

Figures (3)

• Figure 1: Schematic behavior of the neutron EDM $d_n$ as a function of the gluino mass. Lowering $m_\lambda$ from the SUSY threshold there is an initial suppression of $d_n$ due to the decrease of $d_i(m_\lambda)$ as $m_\lambda$ decreases from $\Lambda_W$ to the intermediate value $m_\lambda^{\rm int}$. A further decrease of $m_\lambda$ in the interval from $m_\lambda^{\rm int}$ to $\Lambda_{ {\rm hadr}}$ leads to the increase of $d_n$ due to the contribution of the Weinberg operator, induced by the gluino CEDM. When $m_\lambda$ is smaller than $\Lambda_{\rm hadr}$, $d_n$ receives a linear suppression by $m_\lambda$.
• Figure 2: Perturbative insertion of the Weinberg operator into a quark line. The resulting correction to the propagator is proportional to $w\gamma_5\langle \bar{q} g_s(G\sigma)q\rangle$.
• Figure 3: The $\delta_t$ dependence of the gluino contribution to $d_{n}$ for $m_{\lambda}=1\ {\rm GeV}$ (solid), $m_{\lambda}=m_b$ (dashed), and $m_{\lambda}=20\ {\rm GeV}$ (dot--dashed).