We present a preliminary lattice calculation of theD→πandD→Ktensorform factorsfT(q2) as a function of the squared 4-momentum transferq2. ETMC recentlycomputed the vector and scalar form factorsf+(q2) andf0(q2) describingD→π(K)`νsemileptonic decays analyzing the vector current and the scalar density. The study ofthe weak tensor current, which is directly related to the tensor form factor, completes theset of hadronic matrix element regulating the transition between these two pseudoscalarmesons within and beyond the Standard Model where a non-zero tensor coupling is possi-ble. Our analysis is based on the gauge configurations produced by the European TwistedMass Collaboration withNf=2+1+1 flavors of dynamical quarks. We simulated atthree different values of the lattice spacing and with pion masses as small as 210 MeV andwith the valence heavy quark in the mass range from'0.7mcto'1.2mc. The matrixelement of the tensor current are determined for a plethora of kinematical conditions inwhich parent and child mesons are either moving or at rest. As for the vector and scalarform factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed inthe data. We will present preliminary results on the removal of such hypercubic latticeeffects.
Lubicz, V., Riggio, L., Salerno, G., Simula, S., Tarantino, C. (2018). Tensor form factor for the D → π(K) transitions with Twisted Mass fermions. In Tensor form factor for theD→π(K) transitions with Twisted Mass fermions (pp.13022) [10.1051/epjconf/201817513022].