Recently,an "outlier" track of radio-X-ray correlation was found,which is much steeper than the former universal correlation,where dual tracks were speculated to be triggered by different accretion processes.In this work,we test this issue by exploring hard X-ray spectral evolution in four black-hole X-ray binaries with multiple,quasi-simultaneous radio and X-ray observations.First,we find that hard X-ray photon indices,Γ,are negatively and positively correlated with X-ray fluxes when the X-ray flux,F3–9 keV,is below and above a critical flux,FX;crit,which are consistent with predictions of the advection-dominated accretion flow and the disk-corona model,respectively.Second,and most importantly,we find that the radio-X-ray correlations are also clearly different when the X-ray fluxes are higher and lower than the critical flux as defined by X-ray spectral evolution.The data points with F3–9 keV(>~)FX;crit have a steeper radio-X-ray correlation(FX∝ Fb R and b~1.1–1.4),which roughly forms the “outlier” track.However,the data points with anti-correlation of Γ–F3–9 keV either stay in the universal track with b~0.61 or stay in the transition track(from the universal to “outlier” tracks or vice versa).Therefore,our results support that the universal and “outlier” tracks of radio-X-ray correlations are regulated by radiatively inefficient and radiatively efficient accretion model,respectively.