Abstract
We calculate in three-flavor lattice QCD the short-distance hadronic matrix elements of all five $\Delta C=2$ 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 $M_\pi \approx 180$ 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, $\langle D^0|\mathcal{O}_i|\bar{D}^0 \rangle = \{0.0805(55)(16), -0.1561(70)(31), 0.0464(31)(9), 0.2747(129)(55), 0.1035(71)(21)\}~\text{GeV}^4$ ($i=1$--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.
Highlights
The mixing between neutral K, D, B, and Bs mesons and their antiparticles is loop suppressed in the Standard Model and, provides a window into new physics
It provides unique information on new-physics contributions to the down-quark sector that is complementary to that provided by kaons and BðsÞ mesons, in which mixing is mediated by up-type quarks
Eq (2.22) can be used to test models in which new physics does not change the phase of Γ12.2 A convenient way to do so is illustrated in Fig. 2, which plots jx12jeiφ12 as a complex number
Summary
The mixing between neutral K, D, B, and Bs mesons and their antiparticles is loop suppressed in the Standard Model and, provides a window into new physics. Still not as precise as experiment, the Standard Model theory for kaon and BðsÞ-meson mixing is under good control, owing to recent lattice-QCD calculations of the relevant hadronic matrix elements for kaons [3,4,5] and for neutral BðsÞ mesons [6]. Final results are provided in double-precision as Supplemental Material [12]
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