We compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at O(p 3 ) 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, ∆E TPE (π&∆) = 34(13) µeV. We also compute the charge, r n , and Zemach, r n (2) , moments for n ≥ 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.The spin-dependent and spin-independent structure functions of T µν , the forward virtualphoton Compton tensor of the proton, carry important information about the QCD dynamics. They test the Euclidean region of the theory since Q 2 ≡ −q 2 > 0. For Q 2 ∼ m 2 π = 0, the behavior of T µν is determined by the chiral theory, and can be obtained within a chiral expansion using Heavy Baryon Effective Theory (HBET) [1]. If one works within a large N c ideology (where N c is the number of colours) the Delta particle should be incorporated in the HBET Lagrangian [2], as the Delta and the nucleon become degenerate in the large N c limit. We use this motivation to incorporate the Delta particle in the effective Lagrangian. We do so along the lines of Refs. [3,4,5], i.e. we do not impose the large N c relations among the couplings but let them free and fit to the data. This effective field theory has a double expansion in ∼ m π /m ρ and ∼ ∆/m ρ , where ∆ = M ∆ − M N . Note that this creates a new expansion parameter m π /∆ ∼ 1/2; the associated corrections will be incorporated in our computation together with the pure chiral result.Within this framework we compute the spin-dependent and spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at O(p 3 ) in Heavy Baryon Chiral Perturbation Theory (HBχPT) including the Delta particle. T µν cannot be directly related to cross sections obtained at fixed energies, as it tests the Euclidean regime. Nevertheless, it is possible to obtain it (up to eventual subtractions) from experiment through dispersion relations, i.e., through specifically weighted averages of measured cross sections over all energies. Possible constructions are the so-called generalized sum rules, which, for large energies, can be related with the deep inelastic sum rules. These have been studied in Ref.[6] for the spin-dependent case. The spin-independent case has been briefly discussed in Ref. [7]. We will not enter into this interesting line of research in this paper.Instead, our main motivation for obtaining the chiral structure of T µν is that T µν appears in the matching computation between HBET and non-relativistic QED (NRQED) that d...

We comprehensively analyse the theoretical prediction for the Lamb shift in muonic hydrogen, and the associated determination of the proton radius. We use effective field theories. This allows us to relate the proton radius with well-defined objects in quantum field theory, eliminating unnecessary model dependence. The use of effective field theories also helps us to organize the computation so that we can clearly state the parametric accuracy of the result. In this paper we review all (and check several of) the contributions to the energy shift of order α 5 , as well as those that scales like α 6 ×logarithms in the context of non-relativistic effective field theories of QED.

Positronium and Muonium are purely leptonic atoms and hence free of an internal sub-structure. This qualifies them as potentially well suited systems to probe the existence of physics beyond the Standard Model. We hence carry out a comprehensive study of the sensitivity of current Positronium and Muonium precision spectroscopy to several new physics scenarios. By taking properly into account existing experimental and astrophysical probes, we define clear experimental targets to probe new physics via precise spectroscopy. For Positronium we find that, in order for the spectroscopy bounds to reach a sensitivity comparable to the electron gyromagnetic factor, an improvement of roughly five orders of magnitude from state-of-the-art precision is required, which would be a challenge based on current technology. More promising is instead the potential reach of Muonium spectroscopy: in the next few years experiments like Mu-MASS at PSI will probe new regions of the parameter space testing the existence of medium/short range (MeV and above) spin-dependent and spin-independent dark forces between electrons and muons.

We determine the charm and bottom quark masses using the N 3 LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and B c systems: the η b , η c and B c masses. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to the pole mass renormalon. Our result for the MS masses reads m c (m c ) = 1223(33) MeV and m b (m b ) = 4186(37) MeV. We also extract a value of α s from a renormalon-free combination of the η b , η c and B c masses: α s (M z ) = 0.1195(53). We explore the applicability of the weak coupling approximation to bottomonium n = 2 states. Finally, we consider an alternative computational scheme that treats the static potential exactly and study its convergence properties.