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We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.

 

A bstract We present the Sudakov form factor in full color $$ \mathcal{N} $$ N = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight. 

Facility with foundational practices in computer science (CS) is increasingly recognized as critical for the 21st century workforce. Developing this capacity and broadening participation in CS disciplines will require learning experiences that can engage a larger and more diverse student population (Margolis et al., 2008). One promising approach involves including CS concepts and practices in required subjects like science. Yet, research on the scalability of educational innovations consistently demonstrates that their successful uptake in formal classrooms depends on teachers’ perceived alignment of the innovations with their goals and expectations for student learning, as well as with the specific needs of their school context and culture (Blumenfeld et al., 2000; Penuel et al., 2007; Bernstein et al., 2016). Research is nascent, however, about how exactly to achieve this alignment and thereby position integrated instructional models for uptake at scale. To contribute to this understanding, we are developing and studying two units for core middle school science classrooms, known as Coding Science Internships. The units are designed to support broader participation in CS, with a particular emphasis on females, by expanding students’ perception of the nature and value of coding. CS and science learning are integrated through a simulated internship model, in which students, as interns, apply science knowledge and use computer programming as a tool to address real-world problems. In one unit, students gain first-hand experience with sequences, loops, and conditionals as they program and debug an interactive scientific model of a coral reef ecosystem under threat. The second unit engages students in learning concepts related to data analysis and visualization, abstraction, and modularity as they code data visualizations using real EPA air quality data. A core goal for both units is to provide students experience with some of the increasingly prevalent ways that computer science is integrated into the work of scientists.