Determinations of the form factors of semileptonic $$D→ K$$ D→K decays and leptoquark constraints - Jian Zhang; Chong-Xing Yue; Chun-Hua Li (European Physical Journal C: Particles and Fields, 2018)
Abstract By analyzing all existing measurements for $$ D→ K \ell ^+ ν _{\ell } $$ D→Kℓ+νℓ ($$\ell =e,\ μ $$ ℓ=e,μ ) decays, we find that the determinations of both the vector form factor $$f_+^K(q^2)$$ f+K(q2) and scalar form factor $$f_0^K(q^2)$$ f0K(q2) for semileptonic $$D→ K$$ D→K decays from these measurements are feasible. By taking the parameterization of the one order series expansion of the $$f_+^K(q^2)$$ f+K(q2) and $$f_0^K(q^2)$$ f0K(q2) , $$f_+^K(0)|V_{cs}|$$ f+K(0)|Vcs| is determined to be $$0.7182± 0.0029$$ 0.7182±0.0029 , and the shape parameters of $$f_+^K(q^2)$$ f+K(q2) and $$f_0^K(q^2)$$ f0K(q2) are $$r_{+1}=-2.16± 0.007$$ r+1=-2.16±0.007 and $$r_{01}=0.89± 3.27$$ r01=0.89±3.27 , respectively. Combining with the average $$f_+^K(0)$$ f+K(0) of $$N_f=2+1$$ Nf=2+1 and $$N_f=2+1+1$$ Nf=2+1+1 lattice calculaltion, the $$|V_{cs}|$$ |Vcs| is extracted to be $$0.964± 0.004± 0.019$$ 0.964±0.004±0.019 where the first error is experimental and the second theoretical. Alternatively, the $$f_+^K(0)$$ f+K(0) is extracted to be $$0.7377± 0.003± 0.000$$ 0.7377±0.003±0.000 by taking the $$|V_{cs}|$$ |Vcs| as the value from the global fit with the unitarity constraint of the CKM matrix. Moreover, using the obtained form factors by $$N_f=2+1+1$$ 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 $$D → K$$ D→K decays.