Abstract
In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.
Highlights
In the past few years, the energy momentum tensor (EMT) has become a major focus of both theoretical and experimental efforts in hadron physics
Matrix elements of the EMT between plane wave states define gravitational form factors [10], which provide information about both the quarkgluon decomposition and the spatial distribution of energy, momentum, and angular momentum. These form factors are in principle accessible through high-energy reactions such as deeply virtual Compton scattering [11,12,13] at facilities such as Jefferson Lab [14,15,16] and the upcoming Electron Ion Collider [17], as well as in γγà → hadrons at Belle [18]
Investigations into both the EMT and into deeply virtual Compton scattering have led to the discovery [19] of an additional form factor DðtÞ, called the “D-term” or “Druckterm” [20], which does not encode a conserved current, but instead contains information about the spatial distribution of forces within the hadron [21,22]
Summary
In the past few years, the energy momentum tensor (EMT) has become a major focus of both theoretical and experimental efforts in hadron physics. Matrix elements of the EMT between plane wave states define gravitational form factors [10], which provide information about both the quarkgluon decomposition and the spatial distribution of energy, momentum, and angular momentum These form factors are in principle accessible through high-energy reactions such as deeply virtual Compton scattering [11,12,13] at facilities such as Jefferson Lab [14,15,16] and the upcoming Electron Ion Collider [17], as well as in γγà → hadrons at Belle [18]. II, we derive the connection between spatial densities associated with an arbitrary local operator and its matrix elements between plane wave states This is done both at fixed (instant form) time and at fixed light front time.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
