The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

Appendix D
Divergent loop integrals
In this appendix we give the divergent loop integrals that enter the expressions for the NLO
potential in terms of divergent integrals Jo , J 2 and J4 defined in eq. (3.284).
h ==
J d3[ [2 1 { 2 M;
2 2 }
(27r)3 wr = 87r2 3Mn: In 4JL2 + 5Mn: + 4J 2 - 6Mn: Jo , (D.l)
(D.2)
(D.3)
(D.4)
(D.5)
with s = J4M; + q2 and w± given in eq. (3.273). All other integrals appearing in the 1�loop
NLO TPEP can be deduced from these expressions by taking proper linear combinations or
differentiation with respect to M;, as explained in the text. Note that both left� and right�hand
sides of these equations do not depend on JL. The explicit logarithmic dependence of the terms on
the right�hand side is compensated by the JL�dependence of Jo .
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