Next-to-leading order effective field theory Λ N → NN potential in coordinate space

Abstract

The potential in coordinate space for the ΛN → N N weak transition, which drives the weak decay of most hypernuclei, is derived within the effective field theory formalism up to next-to-leading order. This coordinate space potential allows us to discuss how the different contributions to the potential add up at the different scales. Explicit expressions are given for each two-pion-exchange diagram contributing to the interaction. The potential is also reorganized into spin and isospin operators, and the coefficient for each operator is given in analytical form and represented in coordinate space. The relevance of explicitly including the mass differences among the baryons appearing in the two-pion-exchange diagrams is also discussed in detail.Theoretical studies of the non-mesonic weak decay amplitude were first based on one-meson-exchange (OME) models (see for example Refs. [8,9,10,11]). These models describe the long range part of the interaction through the exchange of one pion, and the shorter ranges through the exchange of heavier mesons, the η, ρ, ω, K and K * , which allow to mediate the strangeness exchange transition through weak vertices like N N K or ΛN η. With the advent of the more systematic effective field theory (EFT) formalism, and in particular with its successful description of the NN strong interaction [12,13], first steps were done in applying EFT also to the description of the non-mesonic weak decay. The EFT for the ΛN → N N potential was first studied at leading order (LO) in Refs. [14,15,16]. In Ref.[17] the EFT was further developed up to next-to-leading order (NLO), including all the possible two-pion-exchange (TPE) diagrams contributing to the transition. The potential was calculated in momentum space, and expressions in terms of master integrals were given separately for each diagram.In the present work we provide all the needed expressions in coordinate space. The different contributions to the transition potential are written in terms of 20 operational structures. Notably, a simplified version of the transition potential, obtained neglecting the baryonic mass differences of virtual baryons, provides a compelling description of the full potential. These should be readily useful for ab-initio few-body computations of the weak decay of hypernuclei [18,19,20,21].The manuscript is organized in the following way. In the beginning of Sect. 2 we review the EFT formalism used to calculate the non-mesonic weak transition. The EFT potentials up to NLO are derived in coordinate space and presented in terms of spin and isospin operators instead of diagrams. This allows us to plot for each operator the LO and the NLO potentials, and thus evaluate the magnitude of the two-pion exchanges in the ΛN → N N amplitude. The comparison is provided for each operational structure appearing in the transition potential. For the NLO, we derive approximate potentials neglecting the mass difference among the virtual baryons and compare them with the exact ones. In Sect. 3 we discuss the properties of the obtained...

Review of the electric dipole moment of light nuclei

“…The accuracy of the contribution of the |∆S| = 1 four-quark interactions to the |∆S| = 1 interbaryon potential is expected to be improved through the phenomenological and EFT analyses of the nonleptonic weak decays of hyperons 130,[140][141][142][143] and hypernuclei. [144][145][146][147][148][149][150] The nucleon EDM contribution to the nuclear EDM is also an important source of uncertainty. The long distance effect of the nucleon EDM from the CKM CP phase was estimated to be O(10 −32 )e cm in many previous works, [151][152][153][154] an order of magnitude smaller than the EDM of light nuclei (see Table 5).…”

Electric dipole moment of the deuteron in the standard model with NN − Λ N − Σ N coupling

“…As ways to improve the Y N − N N coupling potential, we have the phenomenological derivation of the low energy constants of the nonleptonic weak decay of hypernuclei [123][124][125][126][127][128][129]. The determination of the low energy constants (|∆S| = 1 meson-baryon couplings) for |∆S| = 1 four-quark operators in the effective field theory may improve the |∆S| = 1 P-odd interbaryon potential.…”