A further study on the renormalization group aspect of perturbative corrections

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 (EFT) -- as pointed out by 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 ${}^3$P${}_0$ 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.

9 pages, 9 figures, published version

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• Perturbative chiral nucleon-nucleon potential for the ${}^3{P}_0$ partial wave
• Contact operators in renormalization of attractive singular potentials
• Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N${}^3$LO
• Effective field theory with resonant P-wave interaction
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Cited by in corpus (5)

• Reexamining the perturbative renormalizability of the coupled triplets
• Regulator constraints for the perturbative renormalizability of attractive triplets
• Perturbative renormalization of chiral nuclear forces at subleading order in 3S1-3D1 channel
• Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO
• Auxiliary counterterms and their role in effective field theory