Abstract

For a long time, investigation into the weak interactions of quarks has guided us toward understanding the Standard Model we know today. Now in the era of high precision, these studies are still one of the most promising avenues for peering beyond the Standard Model. This is a large-scale endeavour with many tales and many protagonists. In these pages I follow a few threads of a complex story, those passing through the realm of lattice gauge theory.

Highlights

  • In the Standard Model (SM), flavor-changing interactions are mediated by W bosons

  • Is there a reason why electroweak symmetry breaking produces a light scalar boson with a mass just so? Is there another undiscovered source of CP violation in the quark sector which could explain why matter dominates antimatter in the universe? Is there a particle which could make up the dark matter inferred from astrophysical observations? Many of the “Beyond the Standard Model (BSM)” models addressing these questions could affect quark flavor interactions

  • By making a plethora of measurements with increasing precision, particle physicists hope to constrain the four independent CKM parameters so tightly that an inconsistency emerges, a gap that could only be explained by BSM physics

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Summary

Introduction

In the Standard Model (SM), flavor-changing interactions are mediated by W bosons. Electroweak symmetry breaking gives mass to the quarks and, in doing so, induces mixing between the SU(2)L doublets. Because experiments measure the weak interactions of hadrons, the bound states of quarks, precise QCD calculations are required to draw inferences about quark interactions from these measurements This is where lattice QCD plays an important role, one which I aim to review here. In the pages that follow, I will focus on a few stories rather than attempt an encyclopedic account In studying these stories, I was struck by the emergence of some common features, which in turn reminded me of the notion of a “monomyth” or “Hero’s Journey,” popularized by Joseph Campbell in the late 1980’s. Many of these resonate with the adventures of flavor physics heroes. For quark masses at scales where αs(mq ) is small, one can estimate the effects of heavy sea quarks perturbatively

First row unitarity
Decay constants
Semileptonic decay
Summary
Leptonic decays
Semileptonic decays
Third row
Semileptonic b → u decays
Leptonic b → u decay
Semileptonic b → c decays
Ratios
Direct CP violation in K → π π
Rare semileptonic K decays
Rare b decays
Conclusion

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