Short-distance matrix elements for $D^0$-meson mixing for $N_f=2+1$ lattice QCD

Abstract

We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five $\hat{I}”C=2$ four-fermion operators that contribute to neutral $D$-meson mixing both in and beyond the Standard Model. We use the MILC Collaboration's $N_f=2+1$ lattice gauge-field configurations generated with asqtad-improved staggered sea quarks. We also employ the asqtad action for the valence light quarks and use the clover action with the Fermilab interpretation for the charm quark. We analyze a large set of ensembles with pions as light as $M_{\ddot{I}}€\approx 180$ MeV and lattice spacings as fine as $a\approx 0.045$ fm, thereby enabling good control over the extrapolation to the physical pion mass and continuum limit. We obtain for the matrix elements in the $\overline{\text{MS}}$-NDR scheme using the choice of evanescent operators proposed by Beneke \emph{et al.}, evaluated at 3 GeV, $⟨D^0|{\mathcal{O}}_i|{\bar{D}}^0⟩=\{0.0805(55)(16),-0.1561(70)(31),0.0464(31)(9),0.2747(129)(55),0.1035(71)(21)\}{\text{GeV}}^4$ ($i=1$--5). The errors shown are from statistics and lattice systematics, and the omission of charmed sea quarks, respectively. To illustrate the utility of our matrix-element results, we place bounds on the scale of CP-violating new physics in $D^0$~mixing, finding lower limits of about 10--50$\times 10^3$ TeV for couplings of $\mathrm{O}(1)$. To enable our results to be employed in more sophisticated or model-specific phenomenological studies, we provide the correlations among our matrix-element results. For convenience, we also present numerical results in the other commonly-used scheme of Buras, Misiak, and Urban.

Published version, 42 pages, 18 figures