Form factors of the $D \to \pi$ and $D \to K$ semileptonic decays with $N_f = 2$ twisted mass lattice QCD

Understand

We present lattice results for the vector and scalar form factors of the semileptonic decays D -> \pi \ell \nu_ell and D -> K \ell \nu_\ell in the physical range of values of squared four momentum transfer q^2, obtained with N_f=2 maximally twisted Wilson fermions simulated at three different lattice spacings (a ~ 0.102 fm, 0.086 fm, 0.068 fm) with pion masses as light as 270 MeV and m_\pi L \gtrsim 4.

• The form factors are extracted using a double ratios strategy, which allows a good statistical accuracy and is independent of the vector current renormalization constant.
• The chiral/continuum extrapolation is performed through a simultaneous fit in the three variables (m_\pi, q^2, a) using HMChPT formulae with additional O(a^2) terms that parametrically account for the lattice spacing dependence.
• Our results are in very good agreement with the experimental data in the full q^2 range for both D -> \pi \ell \nu_\ell and D -> K \ell \nu_\ell.