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Naturalness in nuclear effective field theories

  • Regular Article -Theoretical Physics
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Abstract

Nuclear effective field theories (EFTs) have been developed over the last quarter-century with considerable impact on the description of light and even medium-mass nuclei. At the core of any EFT is a systematic expansion of observables, which is usually obtained from a rule based on an assumption of naturalness. I discuss naturalness in the context of the relatively weak binding of nuclei, where discrete scale invariance plays a role in the emergence of complexity.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theory paper and has no experimental data (duh!).]

Notes

  1. Just so the true believers burn me at the stake for the right reason: I ain’t saying the tower never ends, only that we’ll not know for sure.

  2. In the particle physics literature, where dimensional regularization is almost exclusively used, the physical breakdown scale is normally referred to as the “cutoff” of the theory. Unfortunately dimensional regularization is not well adapted to nonperturbative problems where loops do not factorize, as in nuclear physics (except for a very specific situation mentioned below). Here I reserve “cutoff” to the arbitrary momentum (or coordinate) cutoff introduced by the regularization procedure.

  3. This estimate gives the correct position of the T-matrix pole for \(A=2\) and ensures that all nucleons contribute equally to the binding energy when \(A\gg 2\).

  4. When nonperturbative physics is involved, the calculation of quantum corrections is often limited to numerics and one cannot write a simple analytical formula for the renormalized LEC. In nuclear physics, this limitation causes an inordinate amount of confusion.

  5. “Naive” perhaps due to the modesty of the authors of Ref. [5].

  6. Note that this is not the only possible fine tuning in this toy model. One can also make \(-r_0/R\) large by fine tuning \(a_2/R\) to be small, that is, dialing a zero of the amplitude to the threshold region. The low-energy EFT for this situation is a Pionless EFT with a different scaling of \(C_{n}\) [15] than discussed in the following.

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Acknowledgements

I thank Matt Baumgart, Ozan Erdogan, and Jaber Balal Habashi for useful discussions. This material is based upon work supported in part by the US Department of Energy, Office of Science, Office of Nuclear Physics, under award DE-FG02-04ER41338 and by the European Union Research and Innovation program Horizon 2020 under Grant No. 654002.

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  1. Institut de Physique Nucléaire, CNRS/IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406, Orsay, France

    U. van Kolck

  2. Department of Physics, University of Arizona, Tucson, AZ, 85721, USA

    U. van Kolck

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van Kolck, U. Naturalness in nuclear effective field theories. Eur. Phys. J. A 56, 97 (2020). https://doi.org/10.1140/epja/s10050-020-00092-1

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