D meson mixing as an inverse problem
Hsiang-nan Li, Hiroyuki Umeeda, Fanrong Xu, Fu-Sheng Yu
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.