Technical-note-on-implementation.md

@@ -37,7 +37,7 @@ The phase correction used here has the form:
 
 The difference stems from the 2 points:
 1. The correction is parametrized in terms of $` A_{\alpha,eff}`$ instead of $` \lambda_{A,eff}`$
-2. The correction used in lal inference was derived using phase velocity, while this one uses group velocity, following `https://dcc.ligo.org/DocDB/0182/P2200154/001/GW_phase_degeneracies.pdf`.
+2. The correction used in lal inference was derived using phase velocity, while this one uses group velocity, following `https://arxiv.org/pdf/2203.13252.pdf`.
 
 ## Reparametrizing phase velocity correction in terms of A
 
@@ -64,12 +64,12 @@ and then follow the steps of route 1.
 
 ## Parametrization in terms of group velocity.
 
-Reference `https://dcc.ligo.org/DocDB/0182/P2200154/001/GW_phase_degeneracies.pdf` derives the LIV correction if one uses group velocity instead of phase velocity. The result is eq. 2.9:
+Reference `https://arxiv.org/pdf/2203.13252.pdf` derives the LIV correction if one uses group velocity instead of phase velocity. The result is eq. 2.9:
 
 ```math
-\delta \Phi_{\alpha}(f)= -\frac{D_\alpha [\omega(1+z)]^{\alpha-1}}{2}A_{\alpha}
+\delta \Phi_{\alpha}(f)= -\frac{D_\alpha [\omega(1+z)]^{\alpha-1}}{2c}A_{\alpha}
 ```
-The paper uses $`\hbar=1`$ and does not include $'c'$ in the definition of $`D_\alpha`$ (so it is in units of time). Accounting for these, the phase correction becomes:
+The paper uses $`\hbar=1`$ - accounting for it, the phase correction becomes:
 
 ```math
 \delta \Phi_{\alpha}(f)= -\frac{\pi D_\alpha [f(1+z)]^{\alpha-1}h^{\alpha-2}}{c}A_{\alpha}= -\frac{\pi D_L h^{\alpha-2}}{c}A_{\alpha,eff}(f )^{\alpha-1}