Determine the Origin of Very-high-energy Gamma Rays from Galactic Sources by the Prospect of Observing Neutrinos

Recently, the Large High Altitude Air Shower Observatory (LHAASO) identified 12 $\gamma$-ray sources emitting above 100 TeV gamma rays, making them potential PeV cosmic-ray accelerators (PeVatrons). Neutrino observations are crucial in determining whether the gamma-ray radiation process is due to hadronic or leptonic origin. In this paper, we study three detected sources, LHAASO J1908+0621, LHAASO J2018+3651, and LHAASO J2032+4102, which are also the most promising galactic high-energy neutrino candidate sources with the lowest pre-trial p-value based on the stacking searches testing for excess neutrino emission by IceCube Neutrino Observatory. We study the lepto-hadronic scenario for the observed multiband spectra of these LHAASO sources considering the possible counterpart source of the LHAASO sources. The very-high-energy gamma rays are entirely attributed to the hadronic contribution, therefore the most optimistic neutrino flux can be derived. Then, we evaluate the statistical significance (p-value) as the observational time of the IceCube and next-generation IceCube-Gen2 neutrino observatory respectively. We find that the origin of gamma rays totally from the hadronic process or at most partially from the hadronic process can be determined by IceCube-Gen2 for LHAASO J1908+0621 at a $5\sigma$ significance level with a running time of $\sim 10$ months. For LHAASO J2018+3651 and LHAASO J2032+4102, the required running time is $\sim 10$ years ($3\sigma$) and $\sim 4$ years ($5\sigma$), respectively. The future confirmation by the next-generation neutrino telescope will be crucial to understanding the particle acceleration and the radiation processes inside the sources.