Resummation of non-global logarithms
Creators: name: Balsiger, Marcel
Publisher: name: Universität Bern
Year: 2020
Subjects: 530 Physics

description: Most of what we know about the laws of physics at the sub-nuclear length scale is derived from analyzing the outcomes of high-energy collisions of particles. Size and sophistication of such experiments have steadily increased, producing more accurate and precise measurements. To interpret these and to understand the underlying physics we need to develop and improve state-of-the-art theoretical tools to predict collider observables in a more refined way. Such a tool is Soft-Collinear Effective Theory, which is a theoretical framework for calculations that involve particles at widely separated energy scales. In a collider experiment, such hierarchies are very common. In the analysis of detector patterns after a collision event, one observes regions where a lot of energetic particles were measured close together, and a small amount of energy that is uniformly distributed in the entire detector. This name-giving collinear and soft radiation is captured by this specific effective theory. When calculating the cross sections of such multi-scale problems, corrections that are normally suppressed by orders of the coupling constant are multiplied by a logarithm of the ratio of the scales. In the case of the interjet energy flow, for example, we have particles of high energy Ein ~ Q produced at the hard interaction inside the jets and soft particles of energy Eout ~ βQ outside the jets. If these scales are far separated, the logarithms ln(β) become big and can ruin the perturbative expansion in the coupling constants. One needs to resum these logarithmically enhanced terms to all orders. The so-called non-global logarithms that arise in the presence of hard phase-space cuts are especially difficult to resum. A simple exponentiation of the logarithmically enhanced terms is in this case not possible. Starting from a factorization theorem in Soft-Collinear Effective Theory, we derive a parton shower equation for the resummation of non-global logarithms. We implement the shower in a dedicated, easy-to-use computer code NGL_RESUM to resum such logarithms at leading logarithmic accuracy in the large-Nc limit. We use tree-level event files in the common Les Houches format as input and explicitly calculate observables such as the interjet energy flow and photon isolation cone cross sections at leading-logarithmic accuracy. Since our parton shower is derived from first principles and based on renormalization group evolution, it is clear what ingredients we have to include to perform the resummation at subleading logarithmic accuracy. After adding the observable-dependent next-to-leading order corrections for di-jet processes, we are able to take a first step towards the higher-logarithmic resummation for the interjet energy flow and the jet mass. To reach full next-to-leading logarithmic accuracy, one would also have to include the two-loop anomalous dimension. This is indeed very challenging and has not been reached thus far. In a final step, we extend the framework to get away from the high-energy limit and include massive quarks. At this point, NGL_RESUM becomes a general-purpose parton shower to resum non-global logarithms at leading logarithmic accuracy for a plethora of observables. We apply it to compute the interjet energy flow in tt̅ -production.