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Recently an `outliers' track of radio-X-ray correlation was found, which ismuch steeper than the former universal correlation, where dual tracks werespeculated to be triggered by different accretion processes. In this work, wetest this issue by exploring hard X-ray spectral evolution in four black-holeX-ray binaries (XRBs) with multiple, quasi-simultaneous radio and X-rayobservations. Firstly, we find that hard X-ray photon indices, $\Gamma$, areanti- and positively correlated to X-ray fluxes when the X-ray flux, $F_{\rm3-9keV}$, is below and above a critical flux, $F_{\rm X,crit}$, which areconsistent with prediction of advection dominated accretion flow (ADAF) anddisk-corona model respectively. Secondly and most importantly, we find that theradio-X-ray correlations are also clearly different when the X-ray fluxes arehigher and lower than the critical flux that defined by X-ray spectralevolution. The data points with $F_{\rm 3-9keV}\gtrsim F_{\rm X,crit}$ have asteeper radio-X-ray correlation ($F_{\rm X}\propto F_{\rm R}^{b}$ and $b\sim1.1-1.4$), which roughly form the `outliers' track. However, the data pointswith anti-correlation of $\Gamma-F_{\rm 3-9keV}$ either stay in the universaltrack with $b\sim0.61$ or stay in transition track (from the universal to`outliers' tracks or vice versa). Therefore, our results support that theuniversal and `outliers' tracks of radio-X-ray correlations are regulated byradiatively inefficient and radiatively efficient accretion model respectively.

Different X-ray spectral evolution for black hole X-ray binaries in dual tracks of radio-X-ray correlation