We present the first lattice Nf=2+1+1 determination of the tensor form factor
\$f\_T^D \pi(K)(q^2)\$ corresponding to the semileptonic and rare \$D \pi(K)\$
decays as a function of the squared 4-momentum transfer \$q^2\$. Together with
our recent determination of the vector and scalar form factors we complete the
set of hadronic matrix elements regulating the semileptonic and rare \$D \to
\pi(K)\$ transitions within and beyond the Standard Model, when a non-zero
tensor coupling is possible. Our analysis is based on the gauge configurations
produced by ETMC with Nf=2+1+1 flavors of dynamical quarks, which include in
the sea, besides two light mass-degenerate quarks, also the strange and charm
quarks with masses close to their physical values. We simulated at three
different values of the lattice spacing and with pion masses as small as 220
MeV. The matrix elements of the tensor current are determined for plenty of
kinematical conditions in which parent and child mesons are either moving or at
rest. As in the case of the vector and scalar form factors, Lorentz symmetry
breaking due to hypercubic effects is clearly observed also in the data for the
tensor form factor 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 and infinite volume limits we determine
the tensor form factor in the whole kinematical region accessible in the
experiments. A set of synthetic data points, representing our results for
\$f\_T^D \pi(K)(q^2)\$ for several selected values of \$q^2\$, is provided and the
corresponding covariance matrix is also available. At zero four-momentum
transfer we get \$f\_T^D \pi(0) = 0.506 (79)\$ and \$f\_T^D K(0) = 0.687 (54)\$,
which correspond to \$f\_T^D \pi(0)/f\_+^D \pi(0) = 0.827 (114)\$ and \$f\_T^D
K(0)/f\_+^D K(0)= 0.898 (50)\$.
%0 Journal Article
%1 Lubicz2018Tensor
%A Lubicz, V.
%A Riggio, L.
%A Salerno, G.
%A Simula, S.
%A Tarantino, C.
%D 2018
%J Physical Review D
%K ddecay
%N 1
%R 10.1103/physrevd.98.014516
%T Tensor form factor of \$D \pi(K) \nu\$ and \$D \pi(K) \ell\$ decays with \$N\_f=2+1+1\$ twisted-mass fermions
%U http://dx.doi.org/10.1103/physrevd.98.014516
%V 98
%X We present the first lattice Nf=2+1+1 determination of the tensor form factor
\$f\_T^D \pi(K)(q^2)\$ corresponding to the semileptonic and rare \$D \pi(K)\$
decays as a function of the squared 4-momentum transfer \$q^2\$. Together with
our recent determination of the vector and scalar form factors we complete the
set of hadronic matrix elements regulating the semileptonic and rare \$D \to
\pi(K)\$ transitions within and beyond the Standard Model, when a non-zero
tensor coupling is possible. Our analysis is based on the gauge configurations
produced by ETMC with Nf=2+1+1 flavors of dynamical quarks, which include in
the sea, besides two light mass-degenerate quarks, also the strange and charm
quarks with masses close to their physical values. We simulated at three
different values of the lattice spacing and with pion masses as small as 220
MeV. The matrix elements of the tensor current are determined for plenty of
kinematical conditions in which parent and child mesons are either moving or at
rest. As in the case of the vector and scalar form factors, Lorentz symmetry
breaking due to hypercubic effects is clearly observed also in the data for the
tensor form factor 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 and infinite volume limits we determine
the tensor form factor in the whole kinematical region accessible in the
experiments. A set of synthetic data points, representing our results for
\$f\_T^D \pi(K)(q^2)\$ for several selected values of \$q^2\$, is provided and the
corresponding covariance matrix is also available. At zero four-momentum
transfer we get \$f\_T^D \pi(0) = 0.506 (79)\$ and \$f\_T^D K(0) = 0.687 (54)\$,
which correspond to \$f\_T^D \pi(0)/f\_+^D \pi(0) = 0.827 (114)\$ and \$f\_T^D
K(0)/f\_+^D K(0)= 0.898 (50)\$.
@article{Lubicz2018Tensor,
abstract = { We present the first lattice Nf=2+1+1 determination of the tensor form factor
\$f\_T^{D \pi(K)}(q^2)\$ corresponding to the semileptonic and rare \$D \to \pi(K)\$
decays as a function of the squared 4-momentum transfer \$q^2\$. Together with
our recent determination of the vector and scalar form factors we complete the
set of hadronic matrix elements regulating the semileptonic and rare \$D \to
\pi(K)\$ transitions within and beyond the Standard Model, when a non-zero
tensor coupling is possible. Our analysis is based on the gauge configurations
produced by ETMC with Nf=2+1+1 flavors of dynamical quarks, which include in
the sea, besides two light mass-degenerate quarks, also the strange and charm
quarks with masses close to their physical values. We simulated at three
different values of the lattice spacing and with pion masses as small as 220
MeV. The matrix elements of the tensor current are determined for plenty of
kinematical conditions in which parent and child mesons are either moving or at
rest. As in the case of the vector and scalar form factors, Lorentz symmetry
breaking due to hypercubic effects is clearly observed also in the data for the
tensor form factor 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 and infinite volume limits we determine
the tensor form factor in the whole kinematical region accessible in the
experiments. A set of synthetic data points, representing our results for
\$f\_T^{D \pi(K)}(q^2)\$ for several selected values of \$q^2\$, is provided and the
corresponding covariance matrix is also available. At zero four-momentum
transfer we get \$f\_T^{D \pi}(0) = 0.506 (79)\$ and \$f\_T^{D K}(0) = 0.687 (54)\$,
which correspond to \$f\_T^{D \pi}(0)/f\_+^{D \pi}(0) = 0.827 (114)\$ and \$f\_T^{D
K}(0)/f\_+^{D K}(0)= 0.898 (50)\$.},
added-at = {2019-02-23T22:09:48.000+0100},
archiveprefix = {arXiv},
author = {Lubicz, V. and Riggio, L. and Salerno, G. and Simula, S. and Tarantino, C.},
biburl = {https://www.bibsonomy.org/bibtex/249cbd4709ad65b849da296214bfc5c9b/cmcneile},
citeulike-article-id = {14684634},
citeulike-linkout-0 = {http://arxiv.org/abs/1803.04807},
citeulike-linkout-1 = {http://arxiv.org/pdf/1803.04807},
citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevd.98.014516},
day = 17,
doi = {10.1103/physrevd.98.014516},
eprint = {1803.04807},
interhash = {f4ea6e2c83596e058a380c1462430e42},
intrahash = {49cbd4709ad65b849da296214bfc5c9b},
issn = {2470-0010},
journal = {Physical Review D},
keywords = {ddecay},
month = jul,
number = 1,
posted-at = {2019-02-01 09:39:13},
priority = {2},
timestamp = {2019-02-23T22:15:27.000+0100},
title = {{Tensor form factor of \$D \to \pi(K) \ell \nu\$ and \$D \to \pi(K) \ell \ell\$ decays with \$N\_f=2+1+1\$ twisted-mass fermions}},
url = {http://dx.doi.org/10.1103/physrevd.98.014516},
volume = 98,
year = 2018
}