Abstract
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.
Highlights
On the other hand, spin is an intrinsic property of a particle defined as one of the two Casimir invariants of the Poincare group
We provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energymomentum tensor, generalizing former works on the symmetric, local and gaugeinvariant kinetic energy-momentum tensor known as the Belinfante-Rosenfeld energymomentum tensor
Ji has shown that the kinetic OAM, which is local and gauge invariant, can be expressed in terms of Generalized Parton Distributions (GPDs) that are accessible in some exclusive experiments like e.g. Deeply Virtual Compton Scattering [9]
Summary
In order to deal most conveniently with the various gauge-invariant decompositions proposed in the literature, we consider the following five gauge-invariant energy-momentum tensors. Where n is a timelike or lightlike four-vector and d3r = αβγδ nα drβ ∧ drγ ∧ drδ is the volume element This ensures that the quark and gluon linear and angular momenta are the same in the three kinetic decompositions d3r TBneνl,a(r) = d3r JBneνlρ,a(r) =. For a given phase factor, the difference between the gauge-invariant kinetic and canonical decompositions lies in the separation of total linear and orbital angular momentum into quark and gluon contributions. Which are called potential linear and angular momentum tensors [41, 42], respectively
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