Partonic functions in Minkowski space – a Schwinger model study with tensor networks

Mari Carmen Bañuls¹, Krzysztof Cichy², C.-J. David Lin^3,4,5, Manuel Schneider^3,4*

¹Max Planck Institute of Quantum Optics, Garching, Germany
²Faculty of Physics and Astronomy, Adam Mickiewicz University, Poznań, Poland
³Institute of Physics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
⁴Center for Theoretical and Computational Physics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
⁵Centre for High Energy Physics, Chung-Yuan Christian University, Taoyuan, Taiwan

* Presenter:Manuel Schneider, email:manuel.schneider@nycu.edu.tw

The rich internal structure of hadrons is encoded in partonic functions, such as parton distribution functions (PDFs) and light-cone distribution amplitudes (LCDAs), which are crucial in collider experiments and decay processes. Calculating them from first principles remains a major challenge: they require matrix elements with a Wilson line along a light-like direction, which is not directly accessible in the Euclidean lattice formulation underlying conventional Monte Carlo simulations. In contrast, the Hamiltonian formalism allows for a direct treatment of light-cone dynamics. We developed a framework to extract light-cone matrix elements in Minkowski space and demonstrate the approach in the Schwinger model. We present updated PDFs and LCDAs for different fermion masses with controlled uncertainties, demonstrating the feasibility of tensor networks for dynamical calculations in gauge theories.

Keywords: Hadron Structure, Parton Distribution Functions, Schwinger Model, Tensor Networks, Quantum Algorithm