Dynamic origins of fermionic D -terms

Jonathan Hudson,Peter Schweitzer

doi:10.1103/physrevd.97.056003

Jonathan Hudson, Peter Schweitzer

Open Access

https://doi.org/10.1103/physrevd.97.056003

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Abstract

The D-term is a particle property defined, similarly to the mass and spin, through matrix elements of the energy-momentum tensor. It is currently not known experimentally for any particle, but the D-term of the nucleon can be inferred from studies of hard-exclusive reactions. In this work we show that the D-term of a spin-1/2 fermion is of dynamical origin: it vanishes for a free fermion. This is in pronounced contrast to the bosonic case where already a free spin-0 boson has a non-zero intrinsic D-term as shown in an accompanying work. We illustrate in two simple models how interactions generate the D-term of a fermion with an internal structure, the nucleon. All known matter is composed of elementary fermions. This indicates the importance to study this interesting particle property in more detail, which will provide novel insights especially on the structure of the nucleon.

Highlights

The matrix elements of the energy-momentum tensor (EMT) [1] provide most basic information: the mass and spin of a particle
The matrix elements of the EMT operator in spin-12 states are described by three form factors [1]
The form factors M2ðtÞ and JðtÞ are constrained at t 1⁄4 0 because the total energy of the fermion is equal to its mass and its spin is 1/2, see [47] for a recent rigorous discussion in an axiomatic approach

Summary

INTRODUCTION

The matrix elements of the energy-momentum tensor (EMT) [1] provide most basic information: the mass and spin of a particle. They define the D-term [2], which is far less known. The second Mellin moments of unpolarized GPDs yield EMT form factors This provides the key to access information about nucleon’s spin decomposition [4], and to its mechanical properties [15]. This prediction pertains to free pointlike bosons, interacting theories of extended bosons can be constructed where this value is preserved.

FORM FACTORS OF THE ENERGY-MOMENTUM TENSOR

EMT FORM FACTORS FOR A FREE DIRAC PARTICLE

EMERGENCE OF THE D-TERM FROM BAG BOUNDARY FORCES

CHIRAL INTERACTIONS AND THE D-TERM OF NUCLEON

CONCLUSIONS