{'fraction_non_alphanumeric': 0.029885057471264367, 'fraction_numerical': 0.011494252873563218, 'mean_word_length': 5.2214285714285715, '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}}
UV Divergences of Scattering Amplitudes in D-dimensional Yang-Mills Theories

We consider UV divergences for the on-shell planar gluon-gluon scattering amplitudes in the gauge theory in arbitrary D-dimensions in the one-loop order. The amplitudes are evaluated using the standard Feynman diagram technique for several choices of external gluon polarizations. Using the Passarino - Veltman reduction, the expansion in terms of the scalar master integrals is constructed and their calculation is performed within dimensional regularization. The resulting expressions are confronted with existing results for various cases, including maximally supersymmetric theories in D=4, 6, 8, and 10 dimensions. One ﬁnds that, contrary to the D=4 case, in D=6 one-loop UV divergences cancel, while in D=8 and 10 the contributions of gauge, scalar and fermion loops have the same sign.