The Neutron Electric Dipole Moment and CP-violating Couplings in the Supersymmetric Standard Model without R-parity

We analyze the neutron electric dipole moment (EDM) in the Minimal Supersymmetric Model with explicit R-parity violating terms. The leading contribution to the EDM occurs at the 2-loop level and is dominated by the chromoelectric dipole moments of quarks, assuming there is no tree-level mixings between sleptons and Higgs bosons or between leptons and gauginos. Based on the experimental constraint on the neutron EDM, we set limits on the imaginary parts of complex couplings λijk and λijk due to the virtual b-loop or τ -loop. The minimal supersymmetric standard model (MSSM) [1] has been widely considered as a leading candidate for new physics beyond Standard Model. However, unlike in the Standard Model, an additional symmetry, called R-parity defined as (−1)3B+L+F , has to be imposed on the minimal supersymmetric extensions of Standard Model (MSSM) in order to avoid renormalizable interactions which violate the lepton or the baryon number. It is in fact one of the main theoretical weaknesses of these models because R-parity conservation of is an ad hoc imposition which may or may not have a fundamental theoretical basis. Therefore, instead of neglecting them completely, it is interesting to ask how small could these R-parity breaking (6 R) couplings be by investigating directly the phenomenological constraints imposed on them [2]. The most general renormalizable R-violating superpotential using only the MSSM superfields is W6 R = λijkLiLjE C k + λ ′ ijkLiQjD c k + λ ′′ ijkU c i D c jD c k + μjLjH2 . (1) Here, i, j, k are generation indices. The couplings λij and λ k′′ ij must be antisymmetric in flavor, λijk = −λjik and λ ijk = −λ′′ ikj. There are 36 lepton number non-conserving couplings (9 of the λ type and 27 of the λ type) and 9 baryon number non-conserving couplings (all of the λ type) in Eq.(1). To avoid rapid proton decay, it is usually assumed in the literature that λ, λ type couplings do not coexist with λ type couplings. This can be achieved easily by imposing baryon number symmetry. The bilinear terms μjLjH2 contribute to lepton flavor and number violation and could be responsible for neutrino masses. Phenomenologically, many of these couplings have been severely constrained using low-energy processes or using high energy data at the colliders [3]–[10]. In this paper, we shall not consider λ ijk and μj couplings. However, most of the bounds in the literature constrain the real part of the trilinear couplings, or the product of trilinear couplings. The exception is the bound coming from the ǫK which constrains Im(λ ′ i12λ ′∗ i21) < 8× 10 [11]. We propose to study the neutron electric dipole moment, which is tightly bound by experiment, and thus obtain limits on the imaginary parts of different products of trilinear couplings from the ones imposed by ǫK . The electric dipole moment of an elementary fermion is defined through its electro-