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Abstract

With the development of the Deep Underground Neutrino Experiment (DUNE) and Tokai-to-Hyper-Kamiokande (T2HK), we are entering the era of high-precision neutrino measurements. The colossal output of data from DUNE, plus the current data from several other neutrino experiments, will require a fast and efficient method of testing our BSM models in event generators. However, current methods for implementing a BSM theory in the event generators are prone to errors and time-consuming. We propose a novel program capable of automatically calculating the leptonic tensor for a given quantum field theory Lagrangian. This program is written in Python and utilizes the Universal FeynRules Output (UFO) format, the Lark package, and the Berends-Giele recursive relations to produce leptonic tensors that can be automatically implemented in several neutrino event generators, including those relevant for DUNE. For this project, we tested our algorithm with three SM processes: $e^- p^+ \rightarrow e^- p^+$, $\nu_e \bar{\nu}_\mu \rightarrow e^- \mu^+$ and $\nu_e p^+ \rightarrow \nu_e p^+$. For each process, we calculated the numerical and analytic $|\mathcal{M}|^2$ and $\sigma$ that we plotted as functions of $\cos\theta$ and $E_{CM}$, respectively. The numerical results for $e^- p^+ \rightarrow e^- p^+$ and $\nu_e p^+ \rightarrow \nu_e p^+$ show good agreement with the analytic results with a cross section numerical to analytic ratio of $\sim 1$ and $\sim 0.9$, respectively. The process $\nu_e \bar{\nu}_\mu \rightarrow e^- \mu^+$ shows deviations from the analytic values with a numerical to analytic ratio of $\sim 1.5$. We believe this deviation stems from inconsistencies in the helicity sum of our program and will investigate this effect further. In the future, we will be correcting these deviations and testing more complex SM processes as well as some BSM theories.

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