Renormalization of CP -violating nuclear forces

Jordy De Vries,Alex Gnech,Sachin Shain

doi:10.1103/physrevc.103.l012501

Abstract

Electric dipole moments of nuclei, diamagnetic atoms, and certain molecules are induced by CP-violating nuclear forces. Naive dimensional analysis predicts these forces to be dominated by long-range one-pion-exchange processes, with short-range forces entering only at next-to-next-to-leading order in the chiral expansion. Based on renormalization arguments we argue that a consistent picture of CP-violating nuclear forces requires a leading-order short-distance operator contributing to ${}^1S_0$-${}^3P_0$ transitions, due to the attractive and singular nature of the strong tensor force in the ${}^3P_0$ channel. The short-distance operator leads to $\mathcal O(1)$ corrections to static and oscillating, relevant for axion searches, electric dipole moments. We discuss strategies how the finite part of the associated low-energy constant can be determined in the case of CP violation from the QCD theta term by the connection to charge-symmetry violation in nuclear systems.

Highlights

Electric dipole moments (EDMs) of nuclei, atoms, and molecules are excellent probes of new sources of CP violation [1,2]
We investigate CP-violating OPE potentials and use cutoff dependence of observables as a diagnostic tool to demonstrate that a LO short-distance operator for 1S0 - 3P0 transitions is required. This directly affects the interpretation of EDM experiments and other time-reversalodd observables, such as magnetic quadrupole moments or neutron-nucleus scattering
We have argued the need for a leading-order short-range CP-violating counterterm in 1S0 - 3P0 transitions that affects calculations of EDMs and CP violation in nucleonnucleon and neutron-nucleus scatterings at the O(1) level

Summary

Introduction

Electric dipole moments (EDMs) of nuclei, atoms, and molecules are excellent probes of new sources of CP violation [1,2]. In the framework of the SM effective field theory (SMEFT), EDM limits constrain a large set of CP-odd dimension-six operators at the multi-TeV scale, well above limits from collider experiments [9]. Nuclear EDMs require the derivation of CP-violating forces and currents. Is based on Weinberg’s power-counting scheme [29] In this scheme, the CP-odd potential arises from one-pion-exchange (OPE) diagrams, whose LECs can be fixed from processes involving just nucleons and pions (only in principle as π Nscattering experiments are not sufficiently accurate). In the CP-violating case, NN interactions require, at least, one space-time derivative, and Weinberg’s power-counting scheme predicts short-distance operators to enter at N 2LO.

Published by the American Physical Society

Nτ σN

Ct Pt

Conclusion