Heavy particle effective field theory: formalism, dark matter and the proton size puzzle

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particle expansions, familiar from heavy quark physics, have found important
applications in the analysis of dark matter candidates and their interactions
with the Standard Model. From a different direction, precision
spectroscopy of muonic hydrogen has challenged QED and required more precise
knowledge of proton structure. These problems have forced a closer
examination of the construction of general heavy particle lagrangians at high
orders in the 1/M expansion, and in the absence of known ultraviolet
completions. Key aspects of this formalism, including the emergence of
Lorentz invariance from "nonrelativistic" lagrangians, are reviewed,
and several applications are presented. A status report on the
proton radius puzzle is given.