Proton number fluctuation is sensitive observable to search for the QCD critical point in heavy-ion collisions. In this paper, we studied rapidity acceptance dependence of the proton cumulants and correlation functions in most central Au+Au collisions at $sqrt{s_mathrm{NN}} = 5$ GeV from a microscopic hadronic transport model (JAM). At mid-rapidity, we found the effects of resonance weak decays and hadronic re-scattering on the proton cumulants and correlation functions are small, but those effects get larger when further increasing the rapidity acceptance. On the other hand, we found the baryon number conservation is a dominant background effect on the rapidity acceptance dependence of proton number fluctuations. It leads to a strong suppression of cumulants and cumulant ratios, as well as the negative proton correlation functions. We also studied those two effects on the energy dependence of cumulant ratios of net-proton distributions in most central Au+Au collisions at $sqrt{s_mathrm{NN}} = 5-200$ GeV from JAM model. This work can serve as a non-critical baseline for future QCD critical point search in heavy-ion collisions at high baryon density region.
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