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Gravitons and pions

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Abstract

Both gravitons and pions are described by non-linear and non-renormalizable actions at low energies. These are most usefully treated by effective field theory, which is a full quantum field theoretic approach that relies only on the low-energy degrees of freedom and their interactions. The gravitational case is particularly clean because of the masslessness of the graviton and the wide separation of scales. This essay provides an overview of this approach.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This paper describes theoretical research and there is no data associated with this research.]

Notes

  1. I am being somewhat unfair here. There was also a tradition of using dispersive techniques which in principle are fully rigorous. But in practice one had to make various approximations in applying dispersion relations to complex problems, and so also here the reliability was suspect. Dispersive techniques have been married to effective field theory successfully enhancing the power of both.

  2. Of course, effective field theory can also be used as a simplification of a known theory. The same rules apply, but the coefficients in this case can be known from matching to the full theory.

  3. For pedagogic treatments of this I recommend my lecture notes written up in Ref. [6] and those of Veltman [7].

  4. As a sociological observation related to the BJ story at the start of this essay, I would also note that the differences between these variants of nuclear EFTs seemed to bring out the religious fervor of many participants.

  5. The gravitational effective field theory has fewer parameters than the pionic one, because gravitons couple to the energy momentum tensor, which is independently known.

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Acknowledgements

I would like to thank the organizers and participants at the workshop “The tower of the effective field theories and the emergence of the nuclear phenomena” (January 2017, CEA Saclay) for lively discussions, most particularly U. Meissner, U. van Kolck and P. Vanhove. I also thank J. Bjorken for confirming the story used in the introduction. This work has been supported in part by the National Science Foundation under grant NSF PHY15-20292 and PHY18-20675

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  1. Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, Amherst, Amherst, MA, 01003, USA

    John F. Donoghue

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Communicated by T. Duguet

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Donoghue, J.F. Gravitons and pions. Eur. Phys. J. A 56, 86 (2020). https://doi.org/10.1140/epja/s10050-020-00091-2

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