DOE OSTI · 3362682
Inverse problem in the large momentum effective theory framework
Abstract
One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of 𝑥 where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of 𝜆 = 𝑧𝑃 𝑧 ∼ 5–15, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a “direct” computation of the 𝑥-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the 𝑥-dependence.
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Dutrieux, Hervé [Aix-Marseille Université, Marseille (France); Université de Toulon, Marseille (France); Centre National de la Recherche Scientifique (CNRS), Marseille (France); Centre de Physique Théorique (CPT), Marseille (France)] (ORCID:0000000183344885), Karpie, Joe [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)] (ORCID:0000000189999014), Monahan, Christopher John [Colorado College, Colorado Springs, CO (United States)] (ORCID:0000000151423490), Orginos, Kostas [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)], Radyushkin, Anatoly [Old Dominion University, Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)] (ORCID:0000000293261300), Richards, David [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)] (ORCID:000000016971873X), Zafeiropoulos, Savvas [Aix-Marseille Université, Marseille (France); Université de Toulon, Marseille (France); Centre National de la Recherche Scientifique (CNRS), Marseille (France); Centre de Physique Théorique (CPT), Marseille (France)] (ORCID:0000000301574770). 2026-04-30. Inverse problem in the large momentum effective theory framework. https://doi.org/10.1103/4f6n-vy13
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