In this appendix we define the functions appearing in the loop integrals
used in the text.
First we define the functions needed for loops with two propagators,
mainly in the form given in Ref. [44].
We consider a loop with two masses, M and m.
All needed functions can be given
in terms of the subtracted scalar integral ,
with .
The functions used in the text are then :
In the text these are used with subscripts,
and similarly for the other symbols. The subtraction point dependent part is contained in the constant k
where is the subtraction scale.
In addition, in subsection 4 these functions and symbols appear in a summation over loops I with
and again similarly for the others.
There the combination appears as well :
The last formula to be defined is the three propagator loop integral
function
where one of the three external momenta
has zero mass and two of the propagators have the same mass M.
Here
,
and
.
where is the dilogarithm