{'fraction_non_alphanumeric': 0.019801980198019802, 'fraction_numerical': 0.0, 'mean_word_length': 4.75, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Integral coefficients for one-loop amplitudes

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried out in generality so that it never needs to be repeated. Where the master integrals are known explicitly, the results here can be used as a black box with tree-level amplitudes as input and one-loop amplitudes as output.