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Different decompositions (sum rules) for the proton mass have been proposed in the literature. All of them are related to the energy-momentum tensor in quantum chromodynamics. We review and revisit these decompositions by paying special attention to recent developments with regard to the renormalization of the energy-momentum tensor. The connection between the sum rules is discussed as well. We present numerical results for the various terms of the mass decompositions up to 3 loops in the strong coupling, and consider their scheme dependence. We also elaborate on the role played by the trace anomaly and the sigma terms., 28 pages; V2: some discussion added, matches PRD version

We calculate the single spin asymmetry for the $e p \to e \Delta(1232)$ process, for an electron beam polarized normal to the scattering plane. Such single spin asymmetries vanish in the one-photon exchange approximation, and are directly proportional to the absorptive part of a two-photon exchange amplitude. As the intermediate state in such two-photon exchange process is on its mass shell, the asymmetry allows one to access for the first time the on-shell $\Delta \to \Delta$ as well as $N^\ast \to \Delta$ electromagnetic transitions. We present the general formalism to describe the $e p \to e \Delta$ beam normal spin asymmetry, and provide a numerical estimate of its value using the nucleon, $\Delta(1232)$, $S_{11}(1535)$, and $D_{13}(1520)$ intermediate states. We compare our results with the first data from the Qweak@JLab experiment and give predictions for the A4@MAMI experiment.

We evaluate the two-photon exchange correction to the elastic electron-proton scattering cross section within a dispersive framework. Besides the elastic contribution, we account for all $\ensuremath{\pi}N$ intermediate state contributions using the phenomenological MAID fit as an input. We develop a novel method for the analytical continuation of the two-photon exchange amplitudes into the unphysical region and generalize our previous work to the momentum transfer region $0.064\text{ }\text{ }{\mathrm{GeV}}^{2}\ensuremath{\lesssim}{Q}^{2}\ensuremath{\lesssim}1\text{ }\text{ }{\mathrm{GeV}}^{2}$. We compare our results with recent OLYMPUS, CLAS and VEPP-3 data as well as with empirical fits and estimates in the forward angular region.

We evaluate the pion-nucleon intermediate-state contribution to the two-photon exchange (TPE) correction in the elastic electron-nucleon scattering within a dispersive framework. We calculate the contribution from all $\ensuremath{\pi}N$ partial waves using the MAID parametrization. We provide the corresponding TPE correction to the unpolarized $ep$ scattering cross section in the region of low momentum transfer ${Q}^{2}\ensuremath{\lesssim}0.064\text{ }\text{ }{\mathrm{GeV}}^{2}$, where no analytical continuation into the unphysical region of the TPE scattering amplitudes is required. We compare our result in the forward angular region with an alternative TPE calculation, in terms of structure functions, and find a good agreement, indicating a small contribution at low ${Q}^{2}$ due to discontinuities beyond $\ensuremath{\pi}N$. We also compare our results with empirical fits.

Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpolarized and helicity PDFs. In the future, the method can be used to produce PDFs entirely based on lattice QCD results., Comment: 12 pages, 7 double-panel figures in pdf, RevTeX4-1

We study the electron as a system composed by an electron and a photon, using lowest order perturbation theory. We derive the leading-twist transverse-momentum-dependent distribution functions for both the electron and photon in the dressed electron, thereby offering a three-dimensional description of the dressed electron in momentum space. To obtain the distribution functions, we apply both the formalism of light-front wave function overlap representation and the diagrammatic approach. We perform the calculations both in light-cone gauge and Feynman gauge, and we present a detailed discussion of the role of the Wilson lines to obtain gauge-independent results. We provide numerical results and plots for many of the computed distributions., 25 pages, 14 figures

At leading twist the transverse momentum dependent parton distributions of the pion consist of two functions, the unpolarized ${f}_{1,\ensuremath{\pi}}(x,{\mathbit{k}}_{\ensuremath{\perp}}^{2})$ and the Boer-Mulders function ${h}_{1,\ensuremath{\pi}}^{\ensuremath{\perp}}(x,{\mathbit{k}}_{\ensuremath{\perp}}^{2})$. We study both functions within a light-front constituent model of the pion, comparing the results with different pion models and the corresponding nucleon distributions from a light-front constituent model. After evolution from the model scale to the relevant experimental scales, the results for the collinear pion valence parton distribution function ${f}_{1,\ensuremath{\pi}}(x)$ are in very good agreement with available parametrizations. Using the light-front constituent model results for the Boer-Mulders functions of the pion and nucleon, we calculate the coefficient $\ensuremath{\nu}$ in the angular distribution of Drell-Yan dileptons produced in pion-nucleus scattering, which is responsible for the violation of the Lam-Tung relation. We find a good agreement with the data, and carefully discuss the range of applicability of our approach.

Virtual Compton Scattering (VCS) on the proton has been studied at Jefferson Lab using the exclusive photon electroproduction reaction (e p --> e p gamma). This paper gives a detailed account of the analysis which has led to the determination of the structure functions P{sub LL}-P{sub TT}/epsilon and P{sub LT}, and the electric and magnetic generalized polarizabilities (GPs) alpha{sub E}(Q{sup 2}) and beta{sub M}(Q{sup 2}) at values of the four-momentum transfer squared Q{sup 2} = 0.92 and 1.76 GeV{sup 2}. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q{sup 2}-range, and point to their non-trivial behavior.

We report on new H(e,e{sup '}p){gamma} measurements in the {delta}(1232) resonance at Q{sup 2}=0.06 (GeV/c){sup 2} carried out simultaneously with H(e,e{sup '}p){pi}{sup 0}. It is the lowest Q{sup 2} for which the virtual Compton scattering (VCS) reaction has been studied in the first resonance region. The VCS measured cross sections are well described by dispersion-relation calculations in which the multipole amplitudes derived from H(e,e{sup '}p){pi}{sup 0} data are used as input, thus confirming the compatibility of the results. The derived resonant magnetic dipole amplitude M{sub 1+}{sup 3/2}=(40.60{+-}0.70{sub stat+sys})(10{sup -3}/m{sub {pi}{sup +}}) at W=1232 MeV is in excellent agreement with the value extracted from H(e,e{sup '}p){pi}{sup 0} measurements.

We have performed numerical simulations of the unpolarized e{sup +}e{sup -}{yields}pp process in kinematic conditions under discussion for a possible upgrade of the existing DAFNE facility. By fitting the cross section angular distribution with a typical Born expression, we can extract information on the ratio G{sub E}/G{sub M} of the proton electromagnetic form factors in the timelike region within a 5%-10% uncertainty. We have explored also non-Born contributions to the cross section by introducing a further component in the angular fit, which is related to two-photon exchange diagrams. We show that these corrections can be identified if larger than 5% of the Born contribution, and if relative phases of the complex form factors do not produce severe cancellations.

Light-front Hamiltonian dynamics is used to relate low-energy constituent quark models to deep inelastic unpolarized structure functions of the nucleon. The approach incorporates the correct Pauli principle prescription consistently and it allows a transparent investigation of the effects due to the spin-dependent SU(6)-breaking terms in the quark model Hamiltonian. Both Goldstone-boson-exchange interaction and hyperfine-potential models are discussed in a unified scheme and a detailed comparison, between the two(apparently) different potential prescriptions, is presented.