The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

3.8. Two-nucleon potential
where the Ci 's are given by
Cl ,
-4C 2 ,
- 1 -
-C7 - 2 C5 '
4C7 - 2C5 , (3 .271)
C5 -2C3 ,
C6 -C 4 + C6 ,
C7 -4C6 .
Different to the reference [78], no one-pion exchange diagrams appear at this order, since the
I
\
Figure 3.14: Next-to-next-to-leading order (NNLO) diagrams that contain vertex
corrections. The filled squares denote the 7r7r N N vertex with ßi = 1. One should
sum over all possible time orderings. Graphs resulting from time revers al operation
are not shown. For remaining notations see fig. 3.6.
7r N N vertices with three derivatives can be eliminated from the Hamiltonian or contribute at
higher orders, as pointed out in the last section.
, ,
,
,
,
,
,
,
,
1 ,
1 ,
1 ,
1 '
1 '
'
I,
"
2
"
"
" ,
, ,
, ,
, ,
, '
,
3
2
I
I
I ,
1
"
,
1 1
1
"
4
,
, I
I
I
,
,
\
\
'
"
,
,
\
,
, \
,
5
Figure 3.15: Next-to-next-to-leading order (NNLO) corrections to the NN potential.
For remaining notations see figs. 3.6, 3.14.
97