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