## Abstract

We present a determination of the Cabibbo–Kobayashi–Maskawa matrix elements |V_{cd}| and |V_{cs}| obtained by combining the momentum dependence of the semileptonic vector form factors f_+^{D rightarrow pi }(q^2) and f_+^{D rightarrow K}(q^2), recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic D rightarrow pi ell nu and D rightarrow K ell nu decays. Our analysis is based on the results for the semileptonic form factors produced by the European Twisted Mass Collaboration with N_f = 2 + 1 + 1 flavors of dynamical quarks in the whole range of values of the squared 4-momentum transfer accessible in the experiments. The statistical and systematic correlations between the lattice data as well as those present in the experimental data are properly taken into account. With respect to the standard procedure based on the use of only the vector form factor at zero 4-momentum transfer, we obtain more precise and consistent results: |V_{cd} |= 0.2341 ~ (74) and |V_{cs} |= 0.970 ~ (33). The second-row CKM unitarity is fulfilled within the current uncertainties: |V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.996 ~ (64). Moreover, using for the first time hadronic inputs determined from first principles, we have calculated the ratio of the semileptonic D rightarrow pi (K) decay rates into muons and electrons, which represent a test of lepton universality within the SM, obtaining in the isospin-symmetric limit of QCD: mathcal{{R}}_{LU}^{Dpi } = 0.985~(2) and mathcal{{R}}_{LU}^{DK} = 0.975~(1).

## Highlights

The golden modes for the determination of the CKM entries |Vcd | and |Vcs| are represented by leptonic and semileptonic decays of D and Ds mesons, which are sensitive probes of the c → d and c → s quark transitions

We present a determination of the Cabibbo– Kobayashi–Maskawa matrix elements |Vcd | and |Vcs| obtained by combining the momentum dependence of the semileptonic vector form factors f+D→π (q2) and f+D→K (q2), recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic D → π ν and D → K ν decays

Our analysis is based on the results for the semileptonic form factors produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 flavors of dynamical quarks in the whole range of values of the squared 4-momentum transfer accessible in the experiments

## Summary

The golden modes for the determination of the CKM entries |Vcd | and |Vcs| are represented by leptonic and semileptonic decays of D and Ds mesons, which are sensitive probes of the c → d and c → s quark transitions. We show that a more precise and consistent determination of |Vcd | and |Vcs|, compared to the one based on the use of only the theoretical form factor values at q2 = 0, can be obtained.

## Full Text

### Topics from this Paper

- European Twisted Mass Collaboration
- Flavors Of Dynamical Quarks
- Vector Form Factor
- Lattice QCD Simulations
- Form Factors + Show 5 more

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