Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions

Abstract

In 2010 the first extraction of the proton charge radius from muonic hydrogen was found be be five standard deviations away form the regular hydrogen value. Eight years later, this proton radius puzzle is still unresolved. One of the most promising avenues to resolve the puzzle is by a muon-proton scattering experiment called MUSE. 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 non-relativistic. The interaction between them can be described by QED-NRQED effective field theory. In a previous paper we have shown how QED-NRQED reproduces Rosenbluth scattering up to $1/M^2$, where $M$ is the proton mass, and relativistic scattering off a static potential at $\mathcal{O}(Z^2{\alpha }^2)$ and leading power in $M$. In this paper we determine the Wilson coefficients of the four-fermion contact interactions at $\mathcal{O}(Z^2{\alpha }^2)$ and power $1/M^2$. Surprisingly, we find that the coefficient of the spin-independent interaction vanishes, implying that MUSE will be sensitive mostly to the proton charge radius and not spin-independent two-photon exchange effects.

37 pages. v2: text and references added, journal version

References in corpus (18)

• Big-Bang Nucleosynthesis
• The Proton Radius Puzzle
• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle
• Model independent extraction of the proton charge radius from electron scattering
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
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• Model independent extraction of the proton magnetic radius from electron scattering
• The NRQED lagrangian at order 1/M^4
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• Nucleon electromagnetic form factors using lattice simulations at the physical point
• Reduction of the proton radius discrepancy by 3 sigma
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory
• Proton radius from electron-proton scattering and chiral perturbation theory
• Two-photon exchange corrections in elastic muon-proton scattering
• Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state
• Technical Design Report for the Paul Scherrer Institute Experiment R-12-01.1: Studying the Proton "Radius" Puzzle with μp Elastic Scattering
• Nucleon Axial and Electromagnetic Form Factors

Cited by in corpus (6)

• The proton radius (puzzle?) and its relatives
• Treating divergence in quark matter by using energy projectors
• Disperon QED
• Instrumental uncertainties in radiative corrections for the MUSE experiment
• Resonance Contributions to Radiative Corrections in Charged-Current Elastic (Anti)Neutrino-Nucleon Scattering at GeV Energies
• Quark-quark-gluon vertex for heavy quarks up to order 1/m^5