{'fraction_non_alphanumeric': 0.01888888888888889, 'fraction_numerical': 0.0033333333333333335, 'mean_word_length': 4.596273291925466, '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}}
Twist Four Longitudinal Structure Function for a Positronium-like Bound State in Weak Coupling Light-Front QED

To have an analytic understanding of the higher-twist structure functions, we calculate twist four longitudinal structure function for a positronium-like bound state in weak coupling light-front QED. We verify a previously proposed sum rule for twist four FL in the weak coupling theory. We find that in the weakly coupled system, the fermionic part of FL, which is actually measured in DIS experiments, is related to the kinetic energy of the fermions and not to the interaction. The sum rule in this case reduces to a relation connecting the kinetic and the potential energies to the binding energy of positronium in the non-relativistic limit. Using the analytic form of the wave function of positronium in this limit, we find that FL is sharply peaked at x = 12 at fixed value of Q 2.