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

Abstract

We analyze two-derivative two-nucleon interactions in a combined pionless effective field theory and large-Nc expansion. At leading order in the large-Nc expansion, relationships among lowenergy constants emerge. We find these to be consistent with experiment. However, it is critical to correctly address the subtraction-point dependence of the low-energy constants. These results provide additional confidence that the dual-expansion procedure is useful for analyzing low-energy few-body observables.

Large-$N_c$ analysis of magnetic and axial two-nucleon currents in pionless effective field theory

“…While this result holds great promise that additional calculations of LECs will be available in the future, in the meantime other theoretical constraints will be valuable, especially in cases where data may be sparse or have large uncertainties. Here we will continue previous efforts [11][12][13] to obtain such constraints by combining EFT π / with the large-N c expansion [14,15], where N c is the number of colors in QCD. These constraints arise from additional symmetries that emerge in QCD in the large-N c limit.…”

Large-$N_c$ and renormalization group constraints on parity-violating low-energy coefficients for three-derivative operators in pionless effective field theory

“…Finally, for suitably small values of µ the RG results relate LECs in different channels. However, previous results [18,20] suggest that at these small values of µ the large-N c constraints do not hold.…”

“…assume that |1/a − µ| Λ π , Refs. [18,20,[48][49][50][51] observe that the large-N c predictions do not agree with experiment unless µ m π . A power counting for these larger values of µ, including the justification for resumming the diagrams in Fig.…”

“…Combining the large-N c expansion with the EFT π / expansion puts constraints on the LECs of EFT π / . Given the success of this dual EFT π / and large-N c expansion when used to analyze parity-conserving (PC) observables [18][19][20], we have some confidence that it will be useful for analyzing PV processes as well. If the dual expansion can be used to indicate which PV terms are most important, it may help prioritize future PV experiments.…”

“…[21] found that two isoscalar PV two-nucleon LECs that are independent in the EFT π / expansion are related in the large-N c expansion, with 1/N 2 c corrections. The approach of combining EFT π / with large-N c has been applied to PC nucleon-nucleon (NN ) interactions [18][19][20], PV NN interactions [21], time-reversal violating NN interactions [22], and interactions with external currents [23].…”