Large-Nclimit reduces the number of independent few-body parity-violating low-energy constants in pionless effective field theory

Abstract

The symmetries of the Standard Model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory (EFT(/ π)), the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors N c becomes large reduces the number of independent LECs to two at leading order in the combined EFT(/ π) and large-N c expansions. We also find a relation between the two isoscalar LECs in the large-N c limit. This has important implications for the number of experiments and/or lattice calculations necessary to confirm this description of physics. In particular, we find that a future measurement of the PV asymmetry in γd → np together with the existing result for PV pp scattering would constrain all leading-order (in the combined expansion) LECs. This is considerably improved from the previous understanding of the system.

A New Paradigm for Hadronic Parity Nonconservation and Its Experimental Implications

“…First, it was discovered that the agreement between past experiments was better than had been recognized [5]: most of the tension that had existed was induced by flaws in global analyses of PNC. Second, a new proposal emerged for organizing the low-energy constants (LECs) that characterize hadronic PNC, based on large-N c QCD [6,7]. We show here that this proposal accounts simply for all existing data -while illustrating that some of our past prejudices about hadronic PNC patterns were not justified.…”

“…Similarly, the EFT potentials of Girlanda et al [24] and Zhu et al [23] must also be equivalent to Eq. (7). The translation between the various formulations is given in the "Rosetta stone" Table 2 in [5].…”

“…Table 2 is a large-N c version of the "Rosetta stone" table of [5]. For the Girlanda coefficients, the key relationships are G 1 ∼G 1 ∼ N c and G 1 + 2G 1 ∼ 1/N c [7]. The relationships to the Table 2: A large-N c hadronic PNC "Rosetta stone": The LECs for the S-P PNC potential of Eq.…”

“…The relationships to the Table 2: A large-N c hadronic PNC "Rosetta stone": The LECs for the S-P PNC potential of Eq. (7) are organized according to the large-N c classification of [7]. The relationships to the DDH potential and to the coefficients of Girlanda's EFT potential are shown.…”

Large- Nc relationships among two-derivative pionless effective field theory couplings

“…In Ref. [17] some of us applied the dual EFT π / and large-N c expansions to low-energy two-nucleon parity-violating interactions. Since there is not enough data to confirm (although current data is not in contradiction with) those results, we want to test the formalism on a system where more data are available.…”