Collider physics is one of the foremost methods to learn about the fundamental laws of nature. Modern collider physics experiments such as the LHC span a huge range of scales from the TeV scale of the collisions down to the roughly 1 GeV scale at which hadrons are formed. The main theoretical tools which describe strong interaction physics over such disparate scales are parton showers, which are indispensable for collider discoveries. In spite of decades of development their accuracy has been difficult to quantify and is commonly understood to be limited to a basic level known as "leading logarithmic (LL) order".
In this talk we identify for the first time a simple set of criteria to assess the accuracy of parton showers. We then introduce new parton showers which satisfy these criteria and demonstrate that they achieve next-to--leading logarithmic (NLL) accuracy for a wide range of observables, something never achieved so far for any parton shower.