Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elements of QED-NRQED Effective Field Theory: I. NLO scattering at
  leading power   The proton radius puzzle, i.e. the large discrepancy in the extraction of the
proton charge radius between regular and muonic hydrogen, challenges our
understanding of the structure of the proton. It can also be an indication of a
new force that couples to muons, but not to electrons. An effective field
theory analysis using Non Relativistic Quantum Electrodynamics (NRQED)
indicates that the muonic hydrogen result can be interpreted as a large,
compared to some model estimates, muon-proton spin-independent contact
interaction. The muonic hydrogen result can be tested by a muon-proton
scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in
Switzerland. The typical momenta of the muons in this experiment are of the
order of the muon mass. In this energy regime the muons are relativistic but
the protons are still non-relativistic. The interaction between the muons and
protons can be described by a hybrid QED-NRQED effective field theory. We
present some elements of this effective field theory. In particular we consider
${\cal O}(Z\alpha)$ scattering up to power $m^2/M^2$, where $m$ ($M$) is the
muon (proton) mass and $Z=1$ for a proton, and ${\cal O}(Z^2\alpha^2)$
scattering at leading power. We show how the former reproduces Rosenbluth
scattering up to power $m^2/M^2$ and the latter the relativistic scattering off
a static potential. Proton structure corrections at ${\cal O}(Z^2\alpha^2)$
will be considered in a subsequent paper.

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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: gr-qc