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 three 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.
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We analyze the structure of generalized off-diagonal and transverse-momentum dependent quark-quark and gluon-gluon correlators for a spin-1/2 hadron. Using the light-front formalism, we ...provide a parametrization in terms of the parton generalized transverse-momentum dependent distributions that emphasizes the multipole structure of the correlator. The results for the quark-quark correlation functions are consistent with an alternative parametrization given in terms of Lorentz covariant structures. The parametrization for the gluon-gluon generalized correlator is presented for the first time and allows one to introduce new correlation functions which can be relevant for phenomenological applications.
We present a dispersive representation of the D-term form factor for hard exclusive reactions, using unsubtracted t-channel dispersion relations. The t-channel unitarity relation is saturated with ...the contribution of two-pion intermediate states, using the two-pion distributions amplitude for the γ⁎γ→ππ subprocess and reconstructing the ππ→NN¯ subprocess from available information on pion-nucleon partial-wave helicity amplitudes. Results for the D-term form factor as function of t as well as at t=0 are discussed in comparison with available model predictions and phenomenological parametrizations.
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Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum ...rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this aim we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon.
We perform a fit of the real Compton scattering (RCS) data below pion-production threshold to extract the electric ( E1) and magnetic (βM1) static scalar dipole polarizabilities of the proton, using ...fixed-t subtracted dispersion relations and a bootstrap-based fitting technique. The bootstrap method provides a convenient tool for including the effects of the systematic errors on the best values of E 1 and β M 1 , and for propagating the statistical errors of the model parameters fixed by other measurements. We also implement various statistical tests to investigate the consistency of the available RCS data sets below pion-production threshold, and conclude that there are not strong motivations to exclude any data point from the global set. Our analysis yields E 1 = ( 12.03 − 0.54 + 0.48 ) × 10 − 4 fm 3 and β M 1 = ( 1.77 − 0.54 + 0.52 ) × 10 − 4 fm 3 , with p-value = 12%.
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The Drell-Yan process provides important information on the internal struc- ture of hadrons including transverse momentum dependent parton distribution functions (TMDs). In this work we ...present calculations for all leading twist structure functions de- scribing the pion induced Drell-Yan process. The non-perturbative input for the TMDs is taken from the light-front constituent quark model, the spectator model, and available parametrizations of TMDs extracted from the experimental data. TMD evolution is im- plemented at Next-to-Leading Logarithmic precision for the first time for all asymmetries. Our results are compatible with the first experimental information, help to interpret the data from ongoing experiments, and will allow one to quantitatively assess the models in future when more precise data will become available.
We present a complete study of the leading-twist quark Wigner distributions in the nucleon, discussing both the T-even and T-odd sectors, along with all the possible configurations of the quark and ...nucleon polarizations. We identify the basic multipole structures associated with each distribution in the transverse phase space, providing a transparent interpretation of the spin-spin and spin-orbit correlations of quarks and nucleons encoded in these functions. Projecting the multipole parametrization of the Wigner functions onto the transverse-position and the transverse-momentum spaces, we find a natural link with the corresponding multipole parametrizations for the generalized parton distributions and transverse-momentum dependent parton distributions, respectively. Finally, we show results for all the distributions in the transverse phase space, introducing a representation that allows one to visualize simultaneously the multipole structures in both the transverse-position and transverse-momentum spaces.
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