Determinations of the form factors of semileptonic D→K decays and leptoquark constraints

By analyzing all existing measurements for D→Kℓ+νℓ (ℓ=e,μ) decays, we find that the determinations of both the vector form factor f+K(q2) and scalar form factor f0K(q2) for semileptonic D→K decays from these measurements are feasible. By taking the parameterization of the one order series expansion of the f+K(q2) and f0K(q2), f+K(0)|Vcs| is determined to be 0.7182±0.0029, and the shape parameters of f+K(q2) and f0K(q2) are r+1=-2.16±0.007 and r01=0.89±3.27, respectively. Combining with the average f+K(0) of Nf=2+1 and Nf=2+1+1 lattice calculaltion, the |Vcs| is extracted to be 0.964±0.004±0.019 where the first error is experimental and the second theoretical. Alternatively, the f+K(0) is extracted to be 0.7377±0.003±0.000 by taking the |Vcs| as the value from the global fit with the unitarity constraint of the CKM matrix. Moreover, using the obtained form factors by Nf=2+1+1 lattice QCD, we re-analyze these measurements in the context of new physics. Constraints on scalar leptoquarks are obtained for different final states of semileptonic D→K decays.