Experimental measurements of decay branching fractions of semitaunic and semimuonic Bc into J/ψ has challenged the lepton flavor universality in standard model with about two standard deviations. In this paper, we first investigate the unitary constraint on form factors of Bc meson into S-wave and P -wave charmonium. Such constraint leads to the exploration of the R J/ψ and other ratios Rη c , R hc , and Rχ cJ in a model-independent way. These results together with future experimental measurements can be used to explore the lepton flavor universality in a more systematic way. In addition, we point out that the helicity-dependent ratios R L J/ψ and R ⊥ J/ψ can also provide complementary information.
I. INTRODUCTIONWeak decays of heavy mesons play an important role in testing the standard model (SM) precisely and probing new physics effects beyond SM. In SM, the lepton interactions are universal for all three generations. Semileptonic decays of B mesons induced by the b → c transition have revealed hints lepton flavor non-university [1], which may indicate the presence of possible new physics (NP). To probe the NP effects in a more systematic way, more accurate and solid predictions of branching fractions are highly demanded.
Ratios of semitaunic and semimuonicB decays intoD or D * , i.e. R D and R D * have been measured by many experiments such as BABAR [2], Belle [3], and LHCb [4]. These measurements indicate the data of R D and R D * deviate from the SM predictions by about 3σ. Recently, the LHCb collaboration have reported the measurement of the ratio of the semitaunic and semimuonic B + c decays into J/ψ, i.e. R J/ψ , using a sample of proton-proton collision data corresponding to 3.0f b −1 of integrated luminosity [5]. A deviation, about 2σ, from SM is found in this measurement by LHCb. On the theoretical side, a few schemes are used to study the B c decays into a charmonium, such as the perturbative QCD (PQCD) approach [6-14], QCD sum rules (QCD SR) [15-18], light-cone sum rules (LCSR) [19, 20], quark model (QM) [21-27], light-front quark model (LFQM) [28-30], nonrelativistic QCD (NRQCD) [31-41] and others [42]. Uncertainties in some of these schemes are hard to control especially in the nonperturbative region and power corrections are expected important [43]. At zero recoil, many of these theoretical investigations become less solid and the extrapolations must be used in order to access the full momentum dependence of form factors. On the lattice, HPQCD collaboration have calculated form factors for decays B c into the S-wave charmonium in the entire q 2 range, using a highly improved lattice quark action [44,45]. These works make the analysis of semileptonic B c decays sitting on a firm ground.In this paper, we will adopt a model-independent way to study the form factors of B c into the S-wave and P-wave charmonium in the entire phase space. Using the dispersion relation and crossing symmetry, we will give a new parametrization form expanded in a series of polynomials. The coefficients in the expansion can...