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Register a new userRigorous constraints on the matrix elements of the energy-momentum tensor
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The structure of the matrix elements of the energy-momentum tensor play an important role in determining the properties of the form factors $A(q^{2})$, $B(q^{2})$ and $C(q^{2})$ which appear in the Lorentz covariant decomposition of the matrix elements. In this paper we apply a rigorous frame-independent distributional-matching approach to the matrix elements of the Poincar{e} generators in order to derive constraints on these form factors as $q rightarrow 0$. In contrast to the literature, we explicitly demonstrate that the vanishing of the anomalous gravitomagnetic moment $B(0)$ and the condition $A(0)=1$ are independent of one another, and that these constraints are not related to the specific properties or conservation of the individual Poincar{e} generators themselves, but are in fact a consequence of the physical on-shell requirement of the states in the matrix elements and the manner in which these states transform under Poincar{e} transformations.
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The probably most fundamental information about a particle is contained in the matrix elements of its energy momentum tensor (EMT) which are accessible from hard-exclusive reactions via generalized parton distribution functions. The spin decomposition of the nucleon and Ji sum rule are one example. Less prominent but equally important information is encoded in the stress tensor, related to the spatial components of the EMT, which shows in detail how the strong forces inside the nucleon balance to form a bound state. This provides not only unique insights on nucleon structure. It also leads to fascinating new applications to hadron spectroscopy which allow us to formulate new interpretations of the charmonium-nucleon pentaquarks discovered by LHCb. Recent progress is reviewed in this short overview article.
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