nLab hierarchy problem



Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



What is called the hierarchy problem is an issue in phenomenology and model building, notably in the standard model of particle physics, concerning discrepancies between the electroweak and Planck scale. For instance, the masses of the W and Z particles, the force carriers of the weak nuclear force, are about 10,000 trillion times smaller than the Planck mass. Thus there is a huge hierarchy in the mass scales of weak nuclear forces and gravity. See Strassler for review.

Proposed solutions

Just an artifact

In 2021, Mooij and Shaposhnikov suggested that the hierarchy problem might not have any physical meaning, rather being a mere artifact of a certain formulation of the quantum field theory and/or model of the Standard model, and that if a different formulation was chosen the hierarchy problem can be avoided entirely. See Mooij and Shaposhnikov for more details.

In M-theory on G 2G_2-manifolds

In the context of M-theory on G2-manifolds (the G2-MSSM) a generic solution to the hierarchy problem is proposed in (Acharya-Kane-Kumar 12, section V.A.2 (p. 10-11)) due to control over non-perturbative effects from membrane instantons, which due to their exponential nature, provide the exponential hierarchy.


In the context of M-theory on G2-manifolds/G2-MSSM a solution is proposed in

  • Bobby Acharya, Gordon Kane, Piyush Kumar, section V.A.2 (p. 10-11) of Compactified String Theories – Generic Predictions for Particle Physics, Int. J. Mod. Phys. A, Volume 27 (2012) 1230012 (arXiv:1204.2795)

Last revised on August 25, 2022 at 10:41:39. See the history of this page for a list of all contributions to it.