D term and the structure of pointlike and composed spin-0 particles

Abstract

This work deals with form factors of the energy-momentum tensor (EMT) of spin-0 particles and the unknown particle property D-term related to the EMT, and is divided into three parts.The first part explores free, weakly and strongly interacting theories to study EMT form factors with the following findings. (i) The free Klein-Gordon theory predicts for the D-term D = −1.(ii) Even infinitesimally small interactions can drastically impact D. (iii) In strongly interacting theories one can encounter large negative D though notable exceptions exist, which includes Goldstone bosons of chiral symmetry breaking. (iv) Contrary to common belief one cannot arbitrarily add "total derivatives" to the EMT. Rather the EMT must be defined in an unambiguous way.The second part deals with the interpretation of the information content of EMT form factors in terms of 3D-densities with following results. (i) The 3D-density formalism is internally consistent.(ii) The description is subject to relativistic corrections but those are acceptably small in phenomenologically relevant situations including nucleon and nuclei. (iii) The free field result D = −1 persists when a spin-0 boson is not point-like but "heuristically given some internal structure."The third part investigates the question, whether such "giving of an extended structure" can be implemented dynamically, and has the following insights. (i) We construct a consistent microscopic theory which, in a certain parametric limit, interpolates between extended and point-like solutions.(ii) This theory is exactly solvable which is rare in 3 + 1 dimensions, admits non-topological solitons of Q-ball-type, and has a Gaussian field amplitude. (iii) The interaction of this theory belongs to a class of logarithmic potentials which were discussed in literature, albeit in different contexts including beyond standard model phenomenology, cosmology, and Higgs physics.

Energy momentum tensor and the D term in the bag model

“…Recalling that D nucleon = O(N 2 c ), cf. (39), we see that the D-term of the ρ-meson (and all mesons) is of O(N 0 c ). As there is no spin-spin interaction aqq pair with anti-aligned spins corresponding to a state with pion quantum numbers has exactly the same mass (and D-term) as the ρ-meson.…”

Forces inside hadrons: Pressure, surface tension, mechanical radius, and all that

“…(18). In the spin-0 case no such compensation occurs, and the EMT densities read [119] T 00 (r) = 2m 2…”

“…5 In most physically interesting cases such corrections are very small (see the estimates in Ref. [119]) and we shall systematically neglect them. A special case is π-meson.…”

“…A free spinless boson has a non-zero intrinsic D-term D = −1. In sharp contrast to this, the D-term of a free spin-1 2 fermion is zero, see [119,134] and references therein. This unexpected finding deserves a comment.…”

Monopole and quadrupole contributions to the angular momentum density

“…The 3D density formalism is justified for heavy particles whose Compton wave length is much smaller than the particle size [31]. This condition is very well satisfied for nuclei, and for the nucleon it is satisfied to a good approximation [32]. The formalism of 2D lightcone densities has the advantage of being rigorous and free of approximations, even for light hadrons, as the transverse coordinates b ⊥ remain invariant under boosts along the lightcone [33].…”