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Higher-Order Corrections to the Effective Field Theory of Low-Energy Axions

Abstract:

Dark matter (DM) can be composed of a collection of axions, or axion-like particles (ALPs), whose existence is due to the spontaneous breaking of the Peccei–Quinn (Formula presented.) symmetry, which is the most compelling solution of the strong (Formula presented.) -problem of quantum chromodynamics (QCD). Axions must be spin-0 particles with very small masses and extremely weak interactions with themselves as well as with the particles that constitute the Standard Model. In general, the physics of axions is detailed by a quantum field theory of a real scalar field, (Formula presented.). Nevertheless, it is more convenient to implement a nonrelativistic effective field theory with a complex scalar field, (Formula presented.), to characterize the mentioned axions in the low-energy regime. A possible application of this equivalent description is for studying the collapse of cold dark matter into more complex structures. There have been a few derivations of effective Lagrangians for the complex field (Formula presented.), which were all equivalent after a nonlocal space transformation between (Formula presented.) and (Formula presented.) was found, and some other corrections were introduced. Our contribution herein is to further provide higher-order corrections; in particular, we compute the effective field theory Lagrangian up to order (Formula presented.), also incorporating the fast-oscillating field fluctuations into the dominant slowly varying nonrelativistic field.