Abstract
Polarization measurements in overline{B}to {D}^{left(ast right)}tau overline{nu} are useful to check consistency in new physics explanations for the RD and {R}_{D^{*}} anomalies. In this paper, we investigate the D* and τ polarizations and focus on the new physics contributions to the fraction of a longitudinal D* polarization (FLD *), which is recently measured by the Belle collaboration FLD * = 0.60 ± 0.09, in model-independent manner and in each single leptoquark model (R2, S1 and U1) that can naturally explain the {R}_{D^{left(ast right)}} anomalies. It is found that ℬ(Bc+ → τ+ν) severely restricts deviation from the Standard Model (SM) prediction of FL,SMD * = 0.46±0.04 in the leptoquark models: [0.43, 0.44], [0.42, 0.48], and [0.43, 0.47] are predicted as a range of FLD * for the R2, S1, and U1 leptoquark models, respectively, where the current data of {R}_{D^{left(ast right)}} is satisfied at 1σ level. It is also shown that the τ polarization observables can much deviate from the SM predictions. The Belle II experiment, therefore, can check such correlations between {R}_{D^{left(ast right)}} and the polarization observables, and discriminate among the leptoquark models.
Highlights
Amplitude in the Standard Model (SM) and such a large discrepancy implies large unknown effects in the processes
We investigate the D∗ and τ polarizations and focus on the new physics contributions to the fraction of a longitudinal D∗ polarization (FLD∗), which is recently measured by the Belle collaboration FLD∗ = 0.60 ± 0.09, in model-independent manner and in each single leptoquark model (R2, S1 and U1) that can naturally explain the RD(∗) anomalies
It is found that the direct search for τ ν resonance at the LHC gives a bound which could be more stringent depending on the mass and the branching ratio of the charged scalar boson [39]
Summary
We describe general NP contributions in terms of the effective Hamiltonian. We follow analytic forms for the decay rates obtained in refs. [12], we have evaluated observables at the scale μ = μb, as defined in the effective Hamiltonian of eq (2.1). We obtained the SM predictions as RDSM = 0.300 and RDSM∗ = 0.256, which are well consistent with ref. We emphasize that we have taken care of the scale for the Wilson coefficients and that for the HQET expansion to be μ = μb = 4.2 GeV. [26, 35, 37], the constraint on the Bc+ lifetime can be translated to that on B(Bc+ → τ +ν) and one finds that a large scalar NP effect is disfavored We take this bound into account by using the analytic formula shown in ref.
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