The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory

Abstract

We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon effective theory including the Delta particle. We compare with previous results when existing. Using these results we obtain the leading hadronic contributions, associated to the pion and Delta particles, to the Wilson coefficients of the lepton-proton four fermion operators in NRQED. The spin-independent coefficient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, $\Delta E_{\mathrm{TPE}}(\pi \&\Delta )=34(13)$ $\mu$eV. We also compute the charge, $⟨r^n⟩$, and Zemach, $⟨r^n{⟩}_{(2)}$, moments for $n\ge 3$. Finally, we discuss the spin-dependent case, for which we compute the difference between the four-fermion Wilson coefficients relevant for hydrogen and muonic hydrogen.

43 pages, 6 figures. Minor corrections, references added, misprints corrected, Eq. (3.19) added, results unchanged. To meet journal version

References in corpus (7)

• High-precision determination of the electric and magnetic form factors of the proton
• The size of the proton - closing in on the radius puzzle
• The RMS Charge Radius of the Proton and Zemach Moments
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Reduction of the proton radius discrepancy by 3 sigma
• Proton structure corrections to electronic and muonic hydrogen hyperfine splitting
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory

Cited by in corpus (10)

• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
• Proton radius from electron-proton scattering and chiral perturbation theory
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• The proton radius (puzzle?) and its relatives
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen
• Two-photon-exchange effects in the unpolarized $\mu p$ scattering within the hadronic model
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions