Valence quark distributions of pions: insights from Tsallis entropy*

Abstract We investigate the valence quark distributions of pions at a low initial scale ( ) using Tsallis entropy, a non-extensive measure that effectively captures long-range correlations among internal constituents. Utilizing the maximum entropy approach, we adopt two distinct functional forms and fit experimental data using the elegant GLR-MQ-ZRS evolution equation to derive the model parameters. Our findings indicate that the resulting valence quark distributions provide an optimal fit to the experimental data, with q values deviating from unity. This deviation indicates that correlations among valence quarks play a significant role in shaping understanding of the internal structures of pions. Additionally, our computations of the first three moments of the pion quark distributions at GeV 2 display consistency with other theoretical models, thereby reinforcing the importance of incorporating valence quark correlations within this analytical framework.