It has been shown recently that the anomalies observed inB → D ( * ) τν τ andB →K + − decays could be resolved with just one scalar leptoquark. Fitting to the current data on R(D ( * ) ) along with acceptable q 2 distributions inB → D ( * ) τν τ decays, four best-fit solutions for the operator coefficients have been found. In this paper, we explore the possibilities of how to discriminate these four solutions. Firstly, we find that two of them * With the discovery of heavy quark spin-flavor symmetry and the formulation of heavy quark effective theory (HQET) [1][2][3][4][5], it has become clear that the physical observables in semi-leptonic B → D ( * ) ν could be rather reliably predicted within the Standard Model (SM), especially at the zero recoil point, allowing therefore a reliable determination of the Cabibbo-Kobayashi-Maskawa (CKM) element V cb . It is also believed that the effect of New Physics (NP) beyond the SM should be tiny since these decays are induced by the tree-level charged current.However, the BaBar [6, 7], Belle [8,9] and LHCb [10] collaborations have recently observed anomalies in the ratios R(D ( * ) ) = B(B → D ( * ) τν τ ) B(B → D ( * ) ν ) , = e/µ . (1.1) The Heavy Flavor Average Group (HFAG) gives the average values [11] R(D) avg =0.397 ± 0.040 ± 0.028 , R(D * ) avg =0.316 ± 0.016 ± 0.010 , (1.2) which exceed the SM predictions [12, 13] R(D) SM =0.300 ± 0.008 , R(D * ) SM =0.252 ± 0.003 , (1.3) by 1.9σ and 3.3σ, respectively. Especially when the R(D)-R(D * ) correlation of −0.21 is taken into account, the tension with the SM predictions would be at 4.0σ level [11]. Theoretically, R(D) and R(D * ) can be rather reliably calculated, because they are independent of the CKM element |V cb | and, to a large extent, of the B → D ( * ) transition form factors.The above anomalies have been investigated extensively both within model-independent frameworks [14-35], as well as in some specific NP models where the b → cτν τ transition is mediated by leptoquarks [14, 15, 36-44], charged Higgses [14, 45-55], charged vector bosons [14, 56-58], and sparticles [ [59][60][61]. It is also interesting to point out that, besides the branching ratios, the measured differential distributions dΓ(B → D ( * ) τν)/dq 2 by BaBar [7] and Belle [8,9]