New explicit expressions for Dirac bilinears

We derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction $n$ in Minkowski space which specifies the form of dynamics. We argue that such a dependence is unavoidable in a relativistic theory with spin, since it originates from Wigner rotation effects. Contrary to most of the expressions found in the literature, our ones are valid for all momenta and canonical polarizations of the spinors. As a by-product, we also obtain a generic explicit expression for the covariant spin vector.Comment: 9 pages, version accepted in PR

Gauge symmetry and background independence: Should the proton spin decomposition be path independent?

Exploring the similarities between the Chen \emph{et al.} approach, where physical and gauge degrees of freedom of the gauge potential are explicitly separated, and the background field method, we provide an alternative point of view to the proton spin decomposition issue. We show in particular that the gauge symmetry can be realized in two different ways, and discuss the relations between the concepts of path dependence, Stueckelberg dependence and background dependence. Finally, we argue that path/Stueckelberg/background-dependent decompositions of the proton spin are in principle measurable and therefore physically meaningful.Comment: 10 pages, extended versio

The light-front gauge-invariant energy-momentum tensor

We provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbital angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions.Comment: 15 pages, 3 table

The nucleon spin decomposition: news and experimental implications

Recently, many nucleon spin decompositions have been proposed in the literature, creating a lot of confusion. This revived in particular old controversies regarding the measurability of theoretically defined quantities. We propose a brief overview of the different decompositions, discuss the sufficient requirements for measurability and stress the experimental implications.Comment: 4 pages, contribution to the proceedings of the 13th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2013), Sep 30-Oct 4, Rome, Ital

On the hadron mass decomposition

We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force.Comment: 21 pages, 4 figure

Quark phase-space distributions and orbital angular momentum

We discuss the Wigner functions of the nucleon which provide multi-dimensional images of the quark distributions in phase space. They combine in a single picture all the information contained in the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs). In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-cone constituent quark model. We show how quark orbital angular momentum can be extracted from these distributions and compare it with alternative definitions given in terms of the GPDs and the TMDs.Comment: 5 pages, 1 figure, 1 table, prepared for the Sixth International Conference on Quarks and Nuclear Physics, April 16-20, 2012, Ecole Polytechnique, Palaiseau, Franc

Generalized Transverse-Momentum Dependent Parton Distributions in Light-Cone Quark Models

We discuss the general formalism for the calculation in light-cone quark models of the fully unintegrated, off-diagonal quark-quark correlator of the nucleon. The corresponding distributions in impact parameter space are the Wigner or phase-space distributions. The results obtained in two different light-cone quark models in the case of unpolarized quarks in an unpolarized proton are very similar and present a non-trivial shape which can be understood as due to the orbital motion of the quarks.Comment: Proceedings for the "Light Cone 2010 Relativistic Hadronic and Particle Physics" workshop, 3 Figs, 8p