Scalar and vector form factors of D→π(K)ℓν decays with Nf=2+

Abstract

We present a lattice determination of the vector and scalar form factors of the D → π ν and D → K ν semileptonic decays, which are relevant for the extraction of the CKM matrix elements |V cd | and |V cs | from experimental data. 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 (a 0.062, 0.082, 0.089 fm) and with pion masses as small as 210 MeV. Quark momenta are injected on the lattice using non-periodic boundary conditions. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. 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. After the extrapolations to the physical pion mass and to the continuum limit we determine the vector and scalar form factors in the whole kinematical region from q 2 = 0 up to q2 accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of q 2 where some deviations are visible. A set of synthetic data points, representing our results for f(q 2 ) for several selected values of q 2 , is provided and also the corresponding covariance matrix is available. At zero 4-momentum transfer we get: f

Tensor form factor for the D → π(K) transitions with Twisted Mass fermions.

“…The presence of these effects has already been observed in Ref. [1] for the vector and scalar form factors, and in that paper we presented a method to subtract the hypercubic artefacts and recover the Lorentz-invariant form factors in the continuum limit. Apart from Ref.…”

“…Apart from Ref. [1], hypercubic effects have never been observed in the context of the D → π(K) transitions. Previous lattice calculations, however, used only a limited number of kinematical conditions (typically the D-meson at rest).…”

“…[1], we presented the first N f = 2 + 1 + 1 lattice QCD (LQCD) calculation of the vector and scalar form factors f D→π(K) + (q 2 ) and f D→π(K) 0 (q 2 ) governing the semileptonic D → π(K) ν decays, using the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light massdegenerate quarks, also the strange and charm quarks with masses close to their physical values [2,3].…”

“…In [1] the subtraction of the observed hypercubic effects was achieved by considering a more general decomposition of the matrix element, which contains, beside the usual Lorentz-covariant part, additional hypercubic form factors proportional to a 2 . The form of this decomposition is related to the Lorentz structure of the current in the matrix element.…”

“…[1], we have evaluated tensor form factor in the whole accessible range of values of q 2 in the experiments, i.e. from q 2 = 0 up to q 2 max = (M D − M π(K) ) 2 .…”