Electric dipole moments, new forces and dark matter

Published for SISSA by Springer Received: October 8, 2020 Revised: December 2, 2020 Accepted: February 14, 2021 Published: March 19, 2021 Pavel Fileviez Pérez and Alexis D. Plascencia Physics Department and Center for Education and Research in Cosmology and Astrophysics (CERCA), Case Western Reserve University, Cleveland, OH 44106, U.S.A. E-mail: , Abstract: New sources of CP violation beyond the Standard Model are crucial to explain the baryon asymmetry in the Universe. We discuss the impact of new CP violating interactions in theories where a dark matter candidate is predicted by the cancellation of gauge anomalies. In these theories, the constraint on the dark matter relic density implies an upper bound on the new symmetry breaking scale from which all new states acquire their masses. We investigate in detail the predictions for electric dipole moments and show that if the relevant CP-violating phase is large, experiments such as the ACME collaboration will be able to fully probe the theory. Keywords: Beyond Standard Model, CP violation ArXiv ePrint: 2008.09116 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP03(2021)185 JHEP03(2021)185 Electric dipole moments, new forces and dark matter Contents 1 2 EDMs and dark matter 2 3 Theoretical framework 3 4 Predictions for EDMs 5 5 Summary 8 A EDMs contributions 9 B Fermionic states 10 C Feynman rules 11 1 Introduction The search for violation of the CP symmetry in nature represents a powerful tool to search for physics beyond the Standard Model (SM). The existence of new large CP-violating phases beyond the SM are needed to explain the observed matter-antimatter asymmetry in the Universe. Unfortunately, the baryon asymmetry cannot be explained in the context of the SM even if CP is broken in the quark sector. An important observable that arises from the violation of the CP symmetry is the electric dipole moment (EDM) of elementary particles. Recently, the ACME collaboration has set an impressive new upper limit [1]: |de | < 1.1 × 10−29 cm, e on the electron electric dipole moment. For reviews on this subject we refer the reader to refs. [2–5]. There is a large list of studies in this field. Previous studies about CP violation and the predictions for EDMs have mostly focused in the context of the Minimal Supersymmetric Standard Model (MSSM), see e.g. [6–18], and split-SUSY [19–21]; there are a few studies in the context of dark sectors [22, 23] and see refs. [24–29] for other studies. The current experimental upper bounds on the EDMs already constrain new physics at the TeV scale if one has large CP-violating phases. The predictions for EDMs in theories for physics beyond the SM depend on two main factors: 1) the new CP-violating phases and 2) the new scale defining the mass of the fields generating the EDMs, see refs. [2–5] for more details. For example, in supersymmetric –1– JHEP03(2021)185 1 Introduction 2 EDMs and dark matter In theories beyond the SM with new gauge forces one typically needs a new sector to define an anomaly free theory. This new sector can provide new sources for CP violation and if the new particles are not very heavy then large values for the electric dipole moments can be predicted. For example, in theories based on gauging baryon U(1)B or lepton number U(1)L , the new sector must be light because one of the fields needed for anomaly cancellation is a cold dark matter candidate. The cosmological constraint on the dark matter relic density, ΩDM h2 ≤ 0.12 [33], implies that the dark matter candidate must be below the multi-TeV scale [34, 35]. In these theories, all the new fermions acquire mass from the new symmetry scale, and hence, the fields that contribute to the EDMs must also be light. –2– JHEP03(2021)185 theories there can be new CP-violating phases coming from the supersymmetry (SUSY) breaking sector and the SUSY scale defines the overall scale of all superpartner masses. However, there exist different scenarios such as split-SUSY, and in general, the SUSY scale can be high unless we are restricted to be in a low-energy SUSY scenario. Generically, the mass scale associated to the generation of the EDMs can be pushed up to very high values in many theories for physics beyond the SM and the predictions for EDMs can be far from the current experimental bounds. In this letter, we investigate the predictions for EDMs in the context of gauge theories where a dark matter candidate is predicted by the cancellation of gauge anomalies. In this context one predicts the existence of new CP-violating phases and the cosmological bounds on the dark matter relic density implies an upper bound on the new symmetry scale in the multi-TeV. We show that one can predict large values for the electron EDM in this context if the CP-violating phases are large. A dark matter candidate is predicted in simple gauge theories where the anomaly cancellation predicts a new electrically neutral field which is automatically stable after symmetry breaking. The minimal theories with this prediction correspond to promoting baryon and/or lepton number to local gauge symmetries [30, 31]. We discuss in detail the predictions for EDMs in the minimal theory that describes the spontaneous breaking of local baryon number at the low scale. In these theories, the existence of an upper bound on the dark matter mass implies an upper bound on the full theory since all particles acquire a mass from the same symmetry breaking scale. Consequently, the charged fermions responsible for the EDMs must live below the multi-TeV scale which leads to large values for the electron EDM that can be fully probed in the near future. Similar results can be obtained in other gauge theories with these features. This letter is organized as follows. In section 2, we discuss the connection to dark matter and the upper bound on the symmetry breaking scale. In section 3, we discuss the general aspects of gauge extensions of the SM that give rise to a dark matter candidate from the cancellation of gauge anomalies. In section 4, we show that CP violation is present in these theories and calculate the contribution to the electric dipole moments of SM fermions from the two-loop Barr-Zee diagrams [32] shown in figure 1. We summarize our findings in section 5. Further details are provided in the appendices A, B and C. γ Vµ h e e Figure 1. Barr-Zee contribution to the electric dipole moment of the electron. Vµ is a generic neutral gauge boson, e.g. the photon, the Z or a Z 0 . Here h corresponds to the SM Higgs boson. 3 Theoretical framework In theories for physics beyond the SM where a new gauge symmetry is spontaneously broken there can be new sources of CP-violation. In this article, we focus on extensions of the SM where the new symmetry is not anomaly free in the SM. The simplest cases correspond to the cases where B and/or L are promoted to local gauge symmetries [30, 31]. Our main re (...truncated)