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arXiv · 2507.09557

Off-shell modifications of the pion generalized parton distributions and transverse momentum dependent parton distributions

Jin-Li Zhang
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Abstract

The off-shell characteristics of pion generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) are examined within the framework of the Nambu-Jona-Lasinio model. In our previous papers, we separately investigated the properties of on-shell pion GPDs and light-front wave functions. It is particularly intriguing to compare the differences between on-shell and off-shell pion GPDs, which allows us to explore the effects associated with off-shellness. Due to the absence of crossing symmetry, the moments of GPDs also incorporate odd powers of the skewness parameter, resulting in new off-shell form factors. Through our calculations, we derived correction functions that account for modifications in pion GPDs due to off-shell effects. Unlike their on-shell counterparts, certain properties break down in the off-shell scenario; for instance, symmetry properties and polynomiality conditions may no longer hold. Additionally, we evaluate off-shell TMDs and compare them with their on-shell equivalents while also investigating their dependence on $\bm{k}_{\perp}$.

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Jin-Li Zhang. 2025-07-13. Off-shell modifications of the pion generalized parton distributions and transverse momentum dependent parton distributions. https://arxiv.org/abs/2507.09557

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