# nLab D-term

Contents

### Context

#### Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks ($q$)
up-typeup quark ($u$)charm quark ($c$)top quark ($t$)
down-typedown quark ($d$)strange quark ($s$)bottom quark ($b$)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion ($u d$)
ρ-meson ($u d$)
ω-meson ($u d$)
f1-meson
a1-meson
strange-mesons:
ϕ-meson ($s \bar s$),
kaon, K*-meson ($u s$, $d s$)
eta-meson ($u u + d d + s s$)

charmed heavy mesons:
D-meson ($u c$, $d c$, $s c$)
J/ψ-meson ($c \bar c$)
bottom heavy mesons:
B-meson ($q b$)
ϒ-meson ($b \bar b$)
baryonsnucleons:
proton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## Idea

In quantum hadrodynamics, the D-term is a subtle conserved charge of hadrons (alongside the well-known charges of mass, spin and electric charge), which may be understood as a limit of a gravitational form factor. Accordingly, the most natural way to measure the D-term charge for any particle is (or would be) via scattering with gravitons and, as a result, there is currently no experimental determination of the D-term of any particle.

But more indirect measurements of the D-term may be possible (cf. BEG18), such as at a future electron-ion collider, the vague prospect of which recently led to renewed attention of the problem (see FHSU22, p. 1).

Generally, it is expected that the D-term must be negative for otherwise hadrons would seem to be unstable.

A computation of the D-term via holographic QCD is claimed in FHSU22, whose authors indeed find a (small and) negative value.

## References

Original articles:

• I Yu Kobzarev, L B Okun, On gravitational interaction of fermions, Eksp. Teor. Fiz. 43 (1962) 1904-1909 $[$osti:4744739$]$ (in Russian)

• Heinz Pagels, Energy-Momentum Structure Form Factors of Particles, Phys. Rev. 144 (1966) 1250 $[$doi:10.1103/PhysRev.144.1250$]$

• Maxim V. Polyakov, C. Weiss, Skewed and double distributions in pion and nucleon $[$arXiv:hep-ph/9902451$]$

• Maxim V. Polyakov, Peter Schweitzer, D-term, strong forces in the nucleon, and their applications $[$arXiv:1801.05858, spire:1648787$]$

Review:

Experimental measurement:

• V. D. Burkert, L. Elouadrhiri, F. X. Girod, The pressure distribution inside the proton, Nature 557 (2018) 396–399 $[$doi:10.1038/s41586-018-0060-z$]$

Computation/prediction of the D-term for hadrons via holographic QCD, specifically via D4-D8-brane bound states:

• Mitsutoshi Fujita, Yoshitaka Hatta, Shigeki Sugimoto, Takahiro Ueda, Nucleon D-term in holographic QCD $[$arXiv:2206.06578$]$

Last revised on June 15, 2022 at 09:50:51. See the history of this page for a list of all contributions to it.