Understanding Angular Momentum in Hadrons

Kathuria, Kunal, Physics - Graduate School of Arts and Sciences, University of Virginia
Liuti, Department of Physics, University of Virginia

The spin puzzle has been a relatively long-standing unresolved issue in hadron physics. We review and derive, using a wave-packet formalism, the first step preceding all spin sum rules: the connection of the angular momentum operator to the gravitomagnetic form factors of the energy-momentum tensor (EMT). We present our spin sum rule for spin one hadrons and comment on why the deuteron is an important system to study in an effort to understanding hadron spin and interactions better. We will visit a number of illuminating properties of spin seen from the wave packet approach (e.g. consequences/promotion of azimuthal symmetry in momentum space as the general rule for origin independence of angular momentum, merits of the different decompositions in the literature, a brand new way to express angular momentum, common ``accepted'' mistakes associated with the derivation etc) and will also say why this approach is the necessary starting point for all treatments. Additionally, we will attempt to clear a number of misconceptions surrounding the operators entering the sum rule (what the different relevant operators are, what the decompositions are, the merits of a partonic decomposition, the EMT in the free vs interacting theory, it being canonical vs Belinfante vs symmetric vs conserved etc) with simple and pertinent observations.

PHD (Doctor of Philosophy)
angular momentum, spin, proton, deuteron, boosts, translation, spin crisis, sum rule, GPD, spin sum rule
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