Poincaré constraints on the gravitational form factors for massive states with arbitrary spin

Abstract

In this work we analyse the constraints imposed by Poincaré symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distributional approach, we prove for the first time non-perturbatively that the zero momentum transfer limit of the leading two form factors in the decomposition are completely independent of the spin of the states. It turns out that these constraints arise due to the general Poincaré transformation and on-shell properties of the states, as opposed to the specific characteristics of the individual Poincaré generators themselves. By expressing these leading form factors in terms of generalised parton distributions, we subsequently derive the linear and angular momentum sum rules for states with arbitrary spin.

arXiv comment18 pages

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Cited by in corpus (18)

• Observables and amplitudes for spinning particles and black holes
• Covariant multipole expansion of local currents for massive states of any spin
• On the Double Copy for Spinning Matter
• Energy momentum tensor and the D-term in the bag model
• Effects of long-range forces on the D-term and the energy-momentum structure
• Gravitational form factors of $\rho$ meson with a light-cone constituent quark model
• 2D energy-momentum tensor distributions of nucleon in a large-$N_c$ quark model from ultra-relativistic to non-relativistic limit
• Pion gravitational form factors in a relativistic theory of composite particles
• Relativistic spin sum rules and the role of the pivot
• Universality of the Poincaré gravitational form factor constraints
• Relativistic energy-momentum tensor distributions in a polarized nucleon
• Mapping the transverse spin sum rule in position space
• Analytic constraints on the energy-momentum tensor in conformal field theories
• Energy, angular momentum and pressure force distributions inside nucleons
• Energy-momentum tensor densities in the bag model
• Gravitational form-factors of the $\pi$ and $K$ mesons in QCD sum rules
• Transverse energy-momentum tensor distributions in polarized nucleons
• Gravitational formfactors of the $\rho$ meson in QCD sum rules