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We note that off the quark mass shell the operators $(p_i+p_f)_mugamma_5$ and $isigma_{mu u}(p_i -p_f)^ ugamma_5$, both of which reduce to $-vec{sigma}cdotvec{E}$ in the non-relativistic limit, are no longer identical. In this paper we explore the effects of this difference in the contribution of these quark electric moments to hadronic electric moments.
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For a bound state internal wave function respecting parity symmetry, it can be rigorously argued that the mean electric dipole moment must be strictly zero. Thus, both the neutron, viewed as a bound state of three quarks, and the water molecule, viewed as a bound state of ten electrons two protons and an oxygen nucleus, both have zero mean electric dipole moments. Yet, the water molecule is said to have a nonzero dipole moment strength $d=eLambda $ with $Lambda_{H_2O} approx 0.385 dot{A}$. The neutron may also be said to have an electric dipole moment strength with $Lambda_{neutron} approx 0.612 fm$. The neutron analysis can be made experimentally consistent, if one employs a quark-diquark model of neutron structure.
The off-shell anomalous chromomagnetic dipole moment of the standard model quarks ($u$, $d$, $s$, $c$ and $b$), at the $Z$ gauge boson mass scale, is computed by using the $overline{textrm{MS}}$ scheme. The numerical results disagree with all the previous predictions reported in the literature and show a discrepancy of up to two orders of magnitude in certain situations.
Searches for permanent electric dipole moments of fundamental particles and systems with spin are the experiments most sensitive to new CP violating physics and a top priority of a growing international community. We briefly review the current status of the field emphasizing on the charged leptons and lightest baryons.
We examine the sensitivity of electric dipole moments (EDMs) to new $CP$-violating physics in a hidden (or dark) sector, neutral under the Standard Model (SM) gauge groups, and coupled via renormalizable portals. In the absence of weak sector interactions, we show that the electron EDM can be induced purely through the gauge kinetic mixing portal, but requires five loops, and four powers of the kinetic mixing parameter $epsilon$. Allowing weak interactions, and incorporating the Higgs and neutrino portals, we show that the leading contributions to $d_e$ arise at two-loop order, with the main source of $CP$-violating being in the interaction of dark Higgs and heavy singlet neutrinos. In such models, EDMs can provide new sensitivity to portal couplings that is complementary to direct probes at the intensity frontier or high energy colliders.
We consider a model in which baryogenesis occurs at low scale, at a temperature below the electroweak phase transition. This model involves new diquark-type scalars which carry baryon number. Baryon number violation is introduced in the scalar potential, permitting $Delta B=2$ violating process involving Standard Model quarks while avoiding stringent proton decay constraints. Depending on their quantum number assignment, the diquark-type scalars can couple to either right or left handed quarks, or to both. We show that this model can provide a viable explanation of the baryon asymmetry of the universe provided that the coupling to left handed quarks are present. However, the coexistence of couplings to left and right handed quarks introduces important phenomenological constraints on the model, such as radiative contributions to quark masses and the generation of electric dipole moments for nuclei, which probe the CP even and CP odd products of the relevant couplings constants, respectively. We demonstrate that the strongest such constraints arise from electric dipole moment measurements of the neutron and $^{199}$Hg. These constraints are sufficiently strong that, in the absence of an intricate flavor structure, baryogenesis must be dominated by the couplings of the new scalars to left handed quarks.
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