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≈2×10−4 and Arg(q/p)≈6×10−3 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.
Highlights
We calculate the parameters x and y for the D meson mixing in the Standard Model by considering a dispersion relation between them
Previous evaluations based on box diagrams [1,2,3], and on heavy quark effective field theory [4, 5] led to the mixing parameters x and/or y far below the current data
In this letter we will analyze the D meson mixing in a novel approach based on a dispersion relation, which relates x and y for a fictitious D meson of an arbitrary mass
Summary
We calculate the parameters x and y for the D meson mixing in the Standard Model by considering a dispersion relation between them. It will be demonstrated that nontrivial correlated solutions for x and y exist, whose values around the physical charm quark mass mc ≈ 1.3 GeV match the data in both cases with and without CP violation.
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