Hadronic matrix elements of neutral-meson mixing through lattice QCD

TL;DR

This paper reviews recent lattice QCD calculations of hadronic matrix elements crucial for understanding neutral-meson mixing, aiming to improve Standard Model predictions and explore new physics possibilities.

Contribution

It presents updated lattice QCD results for $B$ and $D$-meson mixing matrix elements, enhancing theoretical precision in flavor physics.

Findings

Improved precision in $B$-meson mixing matrix elements.

First-principles calculations for $D$-meson mixing.

Enhanced constraints on new physics models.

Abstract

Neutral-meson mixing is loop suppressed in the Standard Model, leading to the possibility of enhanced sensitivity to new physics. The uncertainty in Standard Model predictions for $B$-meson oscillation frequencies is dominated by theoretical uncertainties within the short-distance $B$-meson hadronic matrix elements, motivating the need for improved precision. In $D$-meson mixing, the Standard Model short-distance contributions are further suppressed by the GIM mechanism allowing for the possibility of large new physics enhancements. A first-principle determination of the $D$-meson short-distance hadronic matrix elements will allow for model-discrimination between the new physics theories. I review recently published and ongoing lattice calculations of hadronic matrix elements in $B$ and $D$-meson mixing with emphasis on the Fermilab lattice and MILC collaboration effort on the determination of the $B$ and $D$-meson mixing hadronic matrix elements using the methods of lattice QCD.