Possibilities for the measurement of the longitudinal structure function in diffraction $F_{\mathrm{L}}^{\mathrm{D}}$ at the future U.S. Electron Ion Collider are investigated. The sensitivity to $F_{\mathrm{L}}^{\mathrm{D}}$ arises from the variation of the reduced diffractive cross section with center-of-mass energy. Simulations are performed with various sets of beam energy combinations and for different assumptions on the precision of the diffractive cross section measurements. Scenarios compatible with current EIC performance expectations lead to an unprecedented precision on $F_{\mathrm{L}}^{\mathrm{D}}$ at the 5–10% level in the best measured regions. While scenarios with data at a larger number of center-of-mass energies allow the extraction of $F_{\mathrm{L}}^{\mathrm{D}}$ in the widest kinematic domain and with the smallest uncertainties, even the more conservative assumptions lead to precise measurements. The ratio $R^{\mathrm{D}}$ of photoabsorption cross sections for longitudinally to transversely polarized photons can also be obtained with high precision using a separate extraction method.

• Received 14 December 2021
• Accepted 18 March 2022

DOI:https://doi.org/10.1103/PhysRevD.105.074006

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Published by the American Physical Society