README:
NLO thermal corrections to chi chi \to f fbar using Grammer and
Yennie technique

Prabhat Butola, D. Indumathi, Pritam Sen, 2024

The nondynamical results (for all diagrams, both photon and fermion) are
in total_rot_nondyn.nb . The results for the non-relativistic case are
the last entries, namely, Totala and Totalb for the a and b terms.

The dynamical (expanded scalar propagator) results for the various
diagrams (both photon and fermion) are in the following:
diagram1_rot_dyn_expand.nb
diagram2_rot_dyn_expand.nb
diagram3_rot_dyn_expand.nb
diagram4_rot_dyn_expand.nb
diagram5_rot_dyn_expand.nb

1. The total results when the photon is thermal (t + u - tu channels)
are called Int_j_totgamma for _j_ = 1, 5.

2. Int_j_totgammas substitutes for p', p, and mcfp = \Sqrt(mc^2 + mf^2-
mh^2)$, with $c,f,h$ standing for \chi, f and \phi respectively.

3. Int_j_totgammaexpand expands the log terms in the small momentum
limit, preparatory to calculating the non-relativistic terms a and b.

4. Int_j_totgammaNRe1 is the a term and
Int_j_totgammaNRe4 is the b term (actually coefficient of p^2, not v^2).

5. Analogous results for the case when the fermion (or antifermion) is
thermal are called Int_j_fermion, etc.

6. The total result is integrated over (omega, omega_t) and then summed.

7. The general result in the relativistic case is expressed in terms of
H = \sqrt{s}/2; that for the NR case in terms of p = mc v.

8. A factor of 32 . (e^2 pi lambda^4) (pi^2 T^2/6) must be removed from these
expressions to match the expressions in Table 1 of the paper.