{'fraction_non_alphanumeric': 0.0444015444015444, 'fraction_numerical': 0.0, 'mean_word_length': 5.253012048192771, '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}}
Spin dependence of three-jet and two-jet plus photon production in polarized proton-proton collisions.

Using helicity-amplitude techniques, we derive the partonic level spin-spin asymmetries {ital {cflx a}}{sub {ital L}{ital L}} for all of the processes relevant to the hadronic production of three-jet and two-jet plus photon final states. We discuss the structure of the observable asymmetries in these processes in polarized proton-proton collisions and their dependence on the spin-dependent parton distributions.