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Abstract
We propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around $2~\mathrm{GeV}$. We demonstrate that systematic errors for the Wilson coefficients $C_1$ and $C_2$, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.
Highlights
IntroductionThe large scale separation between the mesons, strongly bounded particles with masses of order ΛQCD, and the weak mediators with masses around 100 GeV, is used to simplify theoretical predictions of these processes in the framework of effective field theories
Weak decays of hadrons, and in particular of mesons, play an important role in our understanding of the fundamental forces and having precise theoretical predictions to compare against the experimental results can either strengthen the solidity of the Standard Model or lead to discoveries of new physics [1].The large scale separation between the mesons, strongly bounded particles with masses of order ΛQCD, and the weak mediators with masses around 100 GeV, is used to simplify theoretical predictions of these processes in the framework of effective field theories
The coefficients capture the effect of the weak bosons and heavy quarks that are absent from the effective field theory (EFT), making them well suited for a perturbative calculation
Summary
The large scale separation between the mesons, strongly bounded particles with masses of order ΛQCD, and the weak mediators with masses around 100 GeV, is used to simplify theoretical predictions of these processes in the framework of effective field theories. By integrating out the heavier degrees of freedom, the weak bosons and heavy quarks, from the Standard Model, it is possible to define a new effective Hamiltonian with new operators and new coupling constants usually called the Wilson coefficients. The coefficients capture the effect of the weak bosons and heavy quarks that are absent from the effective field theory (EFT), making them well suited for a perturbative calculation. Thanks to algorithmic and computational advances, the Lattice QCD community has been able to cover a wide range of processes involving two mesons (see e.g. Ref. [2]) and to complete the first two-body final state decays of K → ππ [3,4,5,6]
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