  We present a preliminary study toward a lattice determination of the vector
and scalar form factors of the $B \to \pi \ell \nu$ semileptonic decays. We
compute the form factors relative to the transition between heavy-light
pseudoscalar mesons, with masses above the physical D-mass, and the pion. We
simulate heavy-quark masses in the range $m_c^{phys} < m_h < 2m_c^{phys}$.
Lorentz symmetry breaking due to hypercubic effects is clearly observed in the
data, and included in the decomposition of the current matrix elements in terms
of additional form factors. We discuss the size of this breaking as the
parent-meson mass increases. Our analysis is based on the gauge configurations
produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$
flavors of dynamical quarks at three different values of the lattice spacing
and with pion masses as small as $210$ MeV.
