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    Further theoretical study on the renormalization group aspect of perturbative corrections

    C.-J. Yang*

    • ELI-NP, “Horia Hulubei” National Institute for Physics and Nuclear Engineering, 30 Reactorului Street, RO-077125 Bucharest-Magurele, Romania

    • *Contact author: chieh.jen@eli-np.ro

    Phys. Rev. C 112, 014004 – Published 14 July, 2025

    DOI: https://doi.org/10.1103/fxx6-2rng

    Abstract

    I perform a further study regarding a renormalization-group (RG) issue—which concerns a wide variety of the so-called perturbative power counting under effective field theories (EFTs)—as pointed out by Gasparyan and Epelbaum [A. M. Gasparyan and E. Epelbaum, Phys. Rev. C 107, 034001 (2023)]. I show that the issue could originate from a wrong power counting, or from treating those incomplete, truncated amplitudes beyond the degree to which they should be trusted. Meanwhile, under EFT principles, one should always associate the result with an uncertainty that is adequate to its EFT order. One way to accommodate this is to encode its effect in a more general form of contact terms. In this regard, no RG issue is found in the P03 nucleon-nucleon scattering under the Long and Yang power counting. In contrast, the RG issue under Weinberg's pragmatic proposal remains a problem even with uncertainty taken into account.

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