L. Colzi, O. Sipilä, I. Jiménez-Serra, V. M. Rivilla, M. Sanz-Novo, S. Martín, S. Zeng

Isotopic ratios are key tracers of Galactic chemical evolution because different isotopes are synthesized through distinct stellar nucleosynthesis processes. While the $^{12}$C/$^{13}$C ratio increases with galactocentric distance across the Galactic disc, measurements in the Central Molecular Zone (CMZ) have historically yielded low values ($\sim$3-30), often affected by high optical depths. We aim to determine the initial $^{12}$C/$^{13}$C ratio of the parent material of the CMZ molecular cloud G+0.693$-$0.027 using optically thin molecular tracers and correcting for isotopic fractionation. We analyzed an ultra-high-sensitivity spectral survey obtained with the IRAM 30m and Yebes 40m telescopes, detecting single and double $^{13}$C isotopologues of HC$_3$N and HC$_5$N. Column densities and isotopic ratios were derived and compared with astrochemical models including $^{13}$C- and $^{15}$N-isotopologues to quantify isotopic fractionation. We derive $^{12}$C/$^{13}$C ratios of $36.7\pm1.0$ for HC$_3$N (using double $^{13}$C isotopologues) and $38.8\pm1.5$ for HC$_5$N, significantly higher than previous CMZ estimates based on simpler molecules. The models indicate low to intermediate isotopic fractionation at early times ($<3\times10^4$ yr), implying an initial $^{12}$C/$^{13}$C ratio of $\sim$48 for the gas from which present-day CMZ molecular clouds formed. The inferred range (37-48) is consistent with values observed at Galactocentric distances of 3-5 kpc, supporting a scenario in which the CMZ is replenished by gas inflows from the Galactic disc driven by the Galactic bar, with a possible contribution from less chemically processed material accreted from external systems such as dwarf galaxies.