The time-reversal- and parity-violating nuclear potential in chiral effective theory

Abstract

We derive the parity-and time-reversal-violating nuclear interactions stemming from the QCDθ term and quark/gluon operators of effective dimension 6: quark electric dipole moments, quark and gluon chromo-electric dipole moments, and two four-quark operators. We work in the framework of two-flavor chiral perturbation theory, where a systematic expansion is possible. The different chiral-transformation properties of the sources of time-reversal violation lead to different hadronic interactions. For all sources considered the leading-order potential involves known one-pion exchange, but its specific form and the relative importance of short-range interactions depend on the source. For theθ term, the leading potential is solely given by one-pion exchange, which does not contribute to the deuteron electric dipole moment. In subleading order, a new two-pion-exchange potential is obtained. Its short-range component is indistinguishable from one of two undetermined contact interactions that appear at the same order and represent effects of heavier mesons and other shortrange QCD dynamics. One-pion-exchange corrections at this order are discussed as well.

Nuclear electric dipole moment of three-body systems

“…We use this general form of a leading order of TVPV potential with an assumption of naturalness of low energy constants (LECs) in the Lagrangian. However, LECs can be suppressed for some models of TRIV, which can lead to the importance of higher order contributions to the potential (see, for example [15]). …”

Time-reversal violation in the nucleon and light nuclei

“…The second term is the PVTV pion-nucleon non-derivative interactions consisting of isoscalar (ḡ 0 ) and isovector (ḡ 1 ) pieces. The operators with coefficients C 1,2 are PVTV two-nucleon contact interactions that account for heavier-meson exchange and other short-range effects [4]. These operators do not have proper chiral-transformation properties by themselves; their chiral partners are lumped in the ".…”

“…PVTV form factors involve essentially a sandwich between PCTC wavefunctions of either PVTV currents or PCTC currents together with the PVTV potential [4]. Because light nuclei are characterized by binding momenta somewhat smaller than F , pions can be treated perturbatively, with the LO consisting of only momentum-independent contact interactions.…”

“…[10]. Alternatively, one 01011-p. 4 MENU 2013 Table 3. Expected magnitudes of the neutron EDM (in units of e/m N ) and of the EDM ratios proton to neutron, deuteron to neutron, helion to neutron, and triton to helion, for the PVTV sources of dimension up to six.…”

“…At momenta below the characteristic QCD scale M QCD ∼ 1 GeV, TV can be incorporated [3][4][5] in chiral EFT [6], which generalizes chiral perturbation theory [7] to the multinucleon sector and serves as the basis for nuclear calculations consistent with the rest of the SM.…”