For simplifying terms, following algebra is applied:
let:$$A=A$$ $$B=2\pi\sigma m\Omega\ell_{0}R$$and$$\Omega\left(z-t\right)=\tau$$
Equations you posted can be wirtten as:
$$\bar{h}_{xx}^{TT}=A \cos\tau$$
$$\delta\bar{h}_{xx}^{TT}=B \sin \left(\tau-\phi\right)$$
Then...