  We formulate a method for calculating the hadron-hadron scattering amplitudes
at nonzero chemical potential ($\mu$) in the hadronic phase at zero
temperature, where the baryon number symmetry remains to be violated. Although
it is widely believed that the physical quantities do not change even if we
turn on a small $\mu$ at zero temperature, the shape of correlation functions
for a single hadron depends on $\mu$. Then, the dispersion relation of the
single hadron is modified to $E({\bf p},\mu) = \sqrt{{\bf p}^2+m^2}-\mu n_{O}$.
Here, $m$ and $n_O$ denote the hadron mass at $\mu=0$ and the quantum number,
respectively. From this relation, it is possible that the effective mass of the
hadron depends on $\mu$. We extend the HAL QCD method at $\mu=0$ to the case of
$\mu \ne 0$, which allows us to extract the scattering phase shifts via the
interaction potential. We have found that the interaction potential can depend
on $\mu$ only through the effective mass while the scattering phase shifts,
obtained by solving the Schr\"{o}dinger equation with the interaction
potential, are independent of $\mu$. We also numerically analyze the S-wave
scatterings of two pions with isospin $I=2$ and two scalar diquarks within the
framework of QC$_{2}$D at nonzero quark chemical potential. While the lattice
is not exactly set to zero temperature, the $\mu$-independence can be observed.
Furthermore, we improve the results for the S-wave scatterings of two hadrons
obtained above by taking the $\mu$-independence for granted. Thanks to the
asymmetric property of the correlation functions for diquarks at $\mu\neq0$, we
can access a long-$\tau$ regime and can reduce the systematic error coming from
inelastic contributions.
