  The ${}^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio is a significant indicator of
nucleosynthesis and mixing processes during hydrogen burning in stars. Its
value mainly depends on the relative rates of the
${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ and
${}^{13}\mathrm{C}(p,\gamma){}^{14}\mathrm{N}$ reactions. Both reactions have
been studied at the Laboratory for Underground Nuclear Astrophysics (LUNA) in
Italy down to the lowest energies to date ($E_\mathrm{c.m.} =
60\,\mathrm{keV}$) reaching for the first time the high energy tail of hydrogen
burning in the shell of giant stars. Our cross sections, obtained with both
prompt $\gamma$-ray detection and activation measurements, are the most precise
to date with overall systematic uncertainties of $7-8\%$. Compared with most of
the literature, our results are systematically lower, by $25\%$ for the
${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ reaction and by $30\%$ for
${}^{13}\mathrm{C}(p,\gamma){}^{14}\mathrm{N}$. We provide the most precise
value up to now of $(3.6 \pm 0.4)$ in the $20-140\,\mathrm{MK}$ range for the
lowest possible ${}^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio that can be
produced during H burning in giant stars.
