Effective theory for the two-nucleon system

Abstract

We apply the method of unitary transformations to a model two-nucleon potential and construct from it an effective potential in a subspace of momenta below a given cut-off Λ. The S-matrices in the full space and in the subspace are shown to be identical. We solve numerically the Schrödinger equation in the small momentum space and recover exactly the bound and scattering states of the full theory. We then expand the heavy repulsive meson exchange of the effective potential in a series of local contact terms and discuss the question of naturalness of the corresponding coupling constants. Using our exact effective theory we address further issues related to the chiral perturbation theory approach of the two-nucleon system. The coordinate space representation of the effective potential is also considered.

Hyperon–nucleon interactions—a chiral effective field theory approach

“…A comparison between the experimental scattering data considered and the values found in the fitting procedure is given in Table 4 Figure 4.1b shows that the predicted Λp cross section at higher energies is too large, which is related to the problem that some LO partial waves are too large at higher energies. Note that this was also the case for the NN interaction [15]. In a NLO calculation this problem will probably vanish.…”

“…We emphasize that the empirical data, considered in the fitting procedure, are at lower energies. Also for the NN interaction in leading order these partial waves were much larger than the Nijmegen phase shift analysis, see [15]. It is expected that this prob- lem for the Y N interaction can be solved by the derivative contact terms in a NLO calculation, just like in the NN case.…”

“…We remark that in LO only the S-waves contain contact terms, the other partial waves are parameter free. The 1 S 0 and 3 P 0 partial waves are too large at higher energies, this was also a problem in the LO NN study [15]. Probably this shortcoming will not occur in a NLO study, where derivative four-body contact terms may solve this problem.…”

“…These 5 contact terms need to be determined by a fit to the experimental data. Since the NN data can not be described with a LO EFT, see [1,15], we will not consider the NN interaction explicitly. Therefore, we consider the Y N partial wave potentials…”

Similarity renormalization group for nucleon-nucleon interactions

“…This leads to strongly correlated many-body wave functions and highly nonperturbative few-and many-body systems. But recent work shows how a cutoff on relative momentum can be imposed and evolved to lower values using renormalization group (RG) methods, thus eliminating the troublesome highmomentum modes [1,2]. The evolved NN potentials are energy-independent and preserve two-nucleon observables for relative momenta up to the cutoff.…”