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tokens: by the electrons in the converging flow on to a compact star and they called such Comptonization BMC, i.e. Bulk-Motion Comptonization. The BMC model has been adopted to interpret the PL component in the broad-band X-ray spectrum of BHXBs well (Shrader Titarchuk 1998 ; Titarchuk Seifina 2009 ; Titarchuk Shaposhnikov 2010 ). The BMC is one of the models of xspec and it is formulated as This expression consists of two subcomponents: one is the injected blackbody-like component ( BB ) to provide the seed photons for Comptonization, and the other is BB * G to describe the Comptonization emission, where G is the response of the Compton medium. In xspec , this model includes four parameters, i.e. kT bb , α, log ( A ), and C N , which are the seed photon temperature, spectral index (photon index Γ = α + 1), logarithm of weighting factor, and normalization, respectively. The observed fluxes of BMC are comprised of a direct emission flux and a Comptonized emission flux. The fraction of the direct emission is calculated with the factor 1/(1 + A ), whereas the fraction of Comptonized emission is inferred by a Comptonization factor f ( f = A /(1 + A )). In two cases, the BMC model is reduced to BB: one is with A ≪ 1, indicating that the value of f is very small, so the Comptonized emission is negligible; the other is with α ≫ 1, meaning that the energy for the seed photons to get from the high-energy electrons is very small, so the Comptonization is inefficient. The theoretical study of Titarchuk et al. ( 1997 ) shows that the BMC process taking place around the compact star can only result in the PL component with Γ > 1. Therefore, theoretically, the BMC model can only account for the relatively soft hard X-ray PL tail in the X-ray spectrum of XRBs. In xspec , in order to ensure Γ > 1, the spectral index α is set to be a positive parameter, i.e. α > 0. In this work, the obtained photon index of the PL hard tail spans a range of ∼(1.1–2.3) and ∼(0.7–2.1) on the HB and on the NB, respectively. Considering the error of the lower limit of NB photon index, the photon index of HB or NB satisfies the condition of Γ > 1. Assuming the hard X-ray tail in Sco X-1 to be originated from the BMC process around the NS, we form model to fit the broad-band spectra of this source. Assuming the NS to provide the seed photons for the dynamic Comptonization in the converging accretion flow on to the compact star, the BB emission of the NS as well as the outgoing PL component is included in the BMC model. Adopting that there exists an ADC in Sco X-1, the disc emission is described by a CPL (Church et al. 2012 ). Taking into consideration the iron line and the additive BB in the PCA spectrum, finally, we form a multicomponent model of BMC+LINE+CPL+BB to fit the PCA+HEXTE spectra of HB and NB in which hard X-ray PL tails are detected. The fitting results are listed in Table 4 and four unfolded spectra are shown in Fig. 9 . As listed in Table 4 , the values of the reduced