l\neq l',m\neq m' $) may be finite, reflecting hybridization between such states. Nevertheless in the BE limit we have$$m_{l,m,l',m'}^{b,ij}\left( \beta ,\mu \right) \rightarrow \left\{ \begin{array}{l}
2m^{*}\textrm{ if }l=l'\textrm{ and }m=m'\\
\infty \textrm{ otherwise}
\end{array}\right.$$ indicating that the tightly-bound PP propagate freely as particles of mass $ 2m^{*} $ without changing their angular momentum. This simplifies (\[Sb\]) to $$\label{Sb simpl}
S_{eff}^{(2)}\left[ \Delta ^{*},\Delta \right] =\beta \sum _{\mathbf{q}\nu }\sum _{l,m}\Delta ^{*}_{l,m,\mathbf{q}}\left( \omega _{\nu }\right) \left( -i\omega _{\nu }+\frac{\hbar ^{2}\left| \mathbf{q}\right| ^{2}}{4m^{*}}-\mu _{l}^{b}\left( \beta ,\mu \right) \right) \Delta _{l,m,\mathbf{q}}\left( \omega _{\nu }\right)$$ in that limit. The effective chemical potentials $ \mu _{l}^{b}\left( \beta ,\mu \right)  $, on the other hand, are different for bosons with different values of the angular momentum quantum number $ l $. The condition for an instability of the gas of preformed pairs to a superconducting state with angular momentum quantum number $ l $, Eq. (\[Tc eq\]), corresponds to the BE condensation of the corresponding PP: $ \mu _{l}^{b}\left( \beta _{c},\mu _{c}\right) =0 $. Typically, other PP with angular momentum quantum number $ l'\neq l $ are also present in the normal state, just above $ T_{c} $, however their chemical potential is $ \mu _{l'}^{b}\left( \beta _{c},\mu 