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D semi-leptonic decay form factors with HISQ charm and light quarks

We present a program to study D semi-leptonic decay form factors with HISQ charm and light quarks. In this exploratory work, we study $D_s$ to $η_s$, $lν_l$ semi-leptonic decay on MILC coarse ($20^3\times64$) gauge configurations with 2+1 dynamical flavors. We develop a new method to calculate $f_+(0)$ and $f_0(q^2)$ from scalar current matrix elements, $<π|\bar{s}c|D>$, which does not require any operator renormalization. We also determine $f_+(q^2)$ and $f_0(q^2)$ from vector currents with a fully non-perturbative renormalization method.