The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

124 4. The two-nuc1eon system: numerical results
LEes of the contact interactions. First, we fit to the phase shifts of the Nijmegen partial wave
analysis [33] for laboratory energies smaller than (50) 100 MeV at (NLO) NNLO. 2 Alternatively,
- -
3
we used the effective range parameters for the phases ISO, SI and EI to fix ClSO ' ClSO ' C3Sp C3Sp
and C3Dl -3Sl ' This is completely analogous to the fitting procedure in the case of the effective
1 5
5
-5
�
-1 5 0.7 0.8 0.9
1 5
-5
r l------
-- -=-::. . -:...-= =-:::- - - ------
--- -- - - ---
-1 5 0.7 0.8 0.9
A [GeV]
Figure 4.2: Running of the four-nucleon coupling constants in the 1 So (upper panel)
and 3 SI _3 Dl (lower panel) partial waves. In the upper panel, the solid (dashed)
line refers to Cl So (C\ s o ) . In the lower panel, the solid (dashed) line refers to C3 SI
( 03 sJ . The dashed-dotted line refers to the constant in the coupled 3 SI - 3 Dl
system. The units are the same as in the table 4.1.
theory considered in section 2.2. In what follows, we will mark the corresponding potentials by a
where v( O ), V(2), VOPEP, vJlJ1P are given in eqs. (4.1), (4.2) and V:LO corresponds to the expressions (3.327)­
(3.334). Although this potential corresponds to the NLO result in the "small scale expansion" , we will consider
it merely in the context of the saturation of the NNLO Cl,3,4 corrections. Therefore, we denote it by NNLO-ß
potential.
2Note that equally weil we could fit directly to the data. However, for easier comparison with other EFT
calculations, we use the Nijmegen PSA to simulate the data.
-.
I
1
I
I