Radiative Corrections to the Muonium Hyperfine Structure. I. The ${\alpha }^2(Z\alpha )$ Correction

Abstract

This is the first of a series of papers on a systematic application of the NRQED bound state theory of Caswell and Lepage to higher-order radiative corrections to the hyperfine structure of the muonium ground state. This paper describes the calculation of the ${\alpha }^2(Z\alpha )$ radiative correction. Our result for the complete ${\alpha }^2(Z\alpha )$ correction is 0.424(4) kHz, which reduces the theoretical uncertainty significantly. The remaining uncertainty is dominated by that of the numerical evaluation of the nonlogarithmic part of the $\alpha (Z\alpha {)}^2$ term and logarithmic terms of order ${\alpha }^4$.

arXiv comment56 pages, Rev.tex V3.0 and epsf.tex. 12 postscript files are called in the text. Version accepted by Phys. Rev. D. A new table is added

References in corpus (4)

• Improved Nonrelativistic QCD for Heavy Quark Physics
• CORRECTIONS OF ORDER ${\alpha }^2(Z\alpha {)}^5$ TO HYPERFINE SPLITTING AND LAMB SHIFT
• Improved Theory of the Muonium Hyperfine Structure
• Order m alpha^8 Contributions to the Decay Rate of Orthopositronium

Cited by in corpus (89)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• The Muon g-2
• Effective field theories for heavy quarkonium
• Theory of Light Hydrogenlike Atoms
• Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants
• The HQET/NRQCD Lagrangian to order alpha/m^3
• 50 Years of Quantum Chromodynamics
• Probing new light force-mediators by isotope shift spectroscopy
• Potential NRQED: The Positronium Case
• The Heavy Quarkonium Spectrum at Order $m{\alpha }_s^5\ln {\alpha }_s$
• Effective Field Theory and Matching in Non-Relativistic Gauge Theories
• Review of Heavy Quarkonium at weak coupling
• Nuclear-bound quarkonia and heavy-flavor hadrons
• Model independent analysis of proton structure for hydrogenic bound states
• Matching at one loop for the four-quark operators in NRQCD
• Effective field theories for QED bound states: extending Nonrelativistic QED to study retardation effects
• The NRQED lagrangian at order 1/M^4
• Order alpha^7 ln(1/alpha) Contribution to Positronium Hyperfine Splitting
• 2S Hyperfine splitting of muonic hydrogen
• The Born-Oppenheimer approximation in an effective field theory language
• pi(-)p atom in ChPT: strong energy-level shift
• O(alpha^3 ln alpha) corrections to muonium and positronium hyperfine splitting
• New Value of M_mu/M_e from Muonium Hyperfine Splitting
• Lorentz invariance in heavy particle effective theories
• Radiative Corrections to the Muonium Hyperfine Structure. II. The $\alpha (Z\alpha {)}^2$ Correction
• Self-interacting Dark Matter Without Direct Detection Constraints
• Zemach and magnetic radius of the proton from the hyperfine splitting in hydrogen
• Logarithms of alpha in QED bound states from the renormalization group
• QCD on a small circle
• Hilbert Series and Operator Basis for NRQED and NRQCD/HQET
• Calculation of the relativistic Bethe logarithm in the two-center problem
• Muonic hydrogen ground state hyperfine splitting
• Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level
• Muonium hyperfine structure and hadronic effects
• Calculation of the nonrelativistic Bethe logarithm in the velocity gauge
• Higher order corrections to the hydrogen spectrum from the Standard-Model Extension
• Relativistic corrections of mα^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion
• Effective Field Theory Approach to Pionium
• Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms
• An Introduction to NRQED
• One More Analytic Result for ${\alpha }^2(Z\alpha {)}^{5}m$ Correction to the Lamb Shift
• Positronium hyperfine splitting at order $m{\alpha }^7$: light-by-light scattering in the two-photon-exchange channel
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Quantum Corrections to the QED Vacuum Energy
• Non-Relativistic Pion Interactions and the Pionium Lifetime
• Accuracy of Calculations Involving ${\alpha }^3$ Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$
• Effective field theories for van der Waals interactions
• Hyperfine structure in the H${}_2^{+}$ and HD${}^{+}$ molecular ions at $m{\alpha }^6$ order
• Second Order in Mass Ratio Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• NRQED and Next-to-Leading Hyperfine Splitting in Positronium
• Radiative improvement of the lattice NRQCD action using the background field method with applications to quarkonium spectroscopy
• Universal Binding and Recoil Corrections to Bound State $g$-Factors
• Higher-order corrections to spin-spin scalar interactions in HD${}^{+}$ and H${}_2^{+}$
• The renormalization group for correlated scales: one-stage versus two-stage running
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• Hindered M1 Radiative Decay of ${\rm Y}(2S)$ from Lattice NRQCD
• Leading order relativistic corrections to the ro-vibrational spectrum of $\mbox{H}^+_2$ and $\mbox{HD}^+$ molecular ions
• Non-relativistic and potential non-relativistic effective field theories for scalar mediators
• Variational versus perturbative relativistic energies for small and light atomic and molecular systems
• Light-by-Light Scattering Nonlogarithmic Corrections to Hyperfine Splitting in Muonium
• Hadronic Atoms
• Finite Volume Corrections to the Electromagnetic Mass of Composite Particles
• Poincaré invariance in NRQCD and pNRQCD revisited
• Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H${}_2^{+}$
• Ditauonium spectroscopy
• Elements of QED-NRQED Effective Field Theory: I. NLO scattering at leading power
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Conformal Structure of the Heavy Particle EFT Operator Basis
• Recoil corrections to the energy levels of hydrogenic atoms
• Reconciling the lattice background field method with nonrelativistic QED: Spinor case
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium
• Light-by-Light Scattering Single-Logarithmic Corrections to Hyperfine Splitting in Muonium
• Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions
• Spin-orbit corrections of order $m{\alpha }^6$ to the fine structure of $(37,35)$ state in ${}^4{He}^{+}\bar{p}$ atom
• Muon Loop Light-by-Light Contribution to Hyperfine Splitting in Muonium
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Quantum field theory for multipolar composite bosons with mass defect and relativistic corrections
• Three-Loop Contribution to Hyperfine Splitting in Muonium: Polarization Corrections to Light by Light Scattering Blob
• Recoil corrections in the hydrogen isoelectronic sequence
• One-loop vacuum polarization at m$\alpha$7 and higher orders for three-body molecular systems
• Eighth-Order Foldy-Wouthuysen Transformation
• One-loop vacuum polarization at $m{\alpha }^7$ order for the two center problem
• Forbidden "ortho"--"para" electric dipole transitions in H${}_2^{+}$ ion
• Spin-orbit interaction in the HD${}^{+}$ ion
• Universality of Leading Relativistic Corrections to Bound State Gyromagnetic Ratios
• Matching the Standard Model to Heavy-Quark Effective Theory and Nonrelativistic QCD
• Matching in Nonrelativistic Effective Quantum Field Theories
• Gauge dependence and matching procedure of a nonrelativistic QED/QCD boundstate formalism
• Angular Momentum in Non-Relativistic QED and Photon Contribution to Spin of Hydrogen Atom