Off mass shell effects in hadron electric dipole moments

Abstract

We note that off the quark mass shell the operators (p i +p f ) µ γ 5 and iσ µν (p i − p f ) ν γ 5 , both of which reduce to − σ · 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.

K→ππand a light scalar meson

“…[6], these quantities can be obtained as solutions of the quark DSE and meson Bethe-Salpeter equation. However, the successful study of an extensive range of low-and high-energy light-and heavy-quark phenomena [5,[7][8][9][10][11][12] has led to the development of efficacious algebraic parametrisations. These were employed in Ref.…”

“…[7][8][9][10][11]. It treats mesons as bound states of a dressed-quark and -antiquark with Bethe-Salpeter amplitudes describing their internal structure, and has already been used to explore CP violation in hadrons [12]. We describe the calculation and its elements in Sect.…”

Neutron electric dipole moment: Constituent dressing and compositeness

“…If we assume that CP-violating current-quark-level interactions yield h d ≫ h u , as is the case, e.g., in Higgs boson exchange models [27], then…”

“…(30) is not satisfied by the dressed-quarks in the bound state nucleon: they are confined and may not even have a mass shell, so that in the general case the two contributions are distinguishable and must be treated separately. As an example, for the ρ-meson the different operator structures generate individual contributions that differ by < ∼ 20% from their average value [27]. In our calculations then we employ the following algebraic Ansatz for the dressed-quark-photon vertex…”

“…Hitherto, lacking a Poincaré covariant bound state picture of the neutron, these aspects of dressed-quark behaviour and hadron compositeness have only been explored in studies of the dipole moments of the ρ-meson [26,27], a bound state for which sound DSE models exist. Assuming an explicit EDM contribution to the photon-current-quark vertex:…”