$D$ meson mixing as an inverse problem

Abstract

We calculate the parameters $x$ and $y$ for the $D$ meson mixing in the Standard Model by considering a dispersion relation between them. The dispersion relation for a fictitious charm quark of arbitrary mass squared $s$ is turned into an inverse problem, via which the mixing parameters at low $s$ are solved with the perturbative inputs $x(s)$ and $y(s)$ from large $s$. It is shown that nontrivial solutions for $x$ and $y$ exist, whose values around the physical charm scale agree with the data in both CP-conserving and CP-violating cases. We then predict the observables $|q/p|-1\approx 2\times 10^{-4}$ and $Arg(q/p)\approx 6\times 10^{-3}$ degrees associated with the coefficient ratio for the $D$ meson mixing, which can be confronted with more precise future measurements. Our work represents the first successful quantitative attempt to explain the $D$ meson mixing parameters in the Standard Model.

arXiv comment7 pages, 6 figures, v2: Version accepted in PLB. References added. Fig. 5 added

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• Quark-hadron duality for heavy meson mixings in the 't Hooft model
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• Recent advances in charm mixing and $CP$ violation at LHCb
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• Long distance contributions to neutral $D$-meson mixing from lattice QCD
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• CP violation analysis of $D^0\to M^{0}K\to M^0({\pi }^{\pm }{\ell }^{\mp }\nu )$
• Pursuit of new physics within the ${\Lambda }_c\to \Delta K$ decays
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• Baryons and baryoniums in the perspective of QCD sum rules
• A Review of $CP$ Violation Measurements in Charm at LHCb