# nLab quark

Contents

### Context

#### Fields and quanta

field (physics)

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:
mesonspion ($u d$)
rho-meson ($u d$)
omega-meson ($u d$)
kaon ($q_{u/d} s$)
eta-meson (u u + d d + s s)
B-meson ($q b$)
baryonsproton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)

solitons

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## Idea

Quarks (Gell-Mann 64, Zweig 64) are one of the fundamental particles/matter fields in the standard model of particle physics. Quarks couple to the Yang-Mills theory given by QCD.

Quarks come in three generations of fermions:

flavors of fundamental particles – table

flavors of fermions in the
standard model of particle physics
generation of fermions1st generation2nd generation3d generation
quarks
up-typeup quarkcharm quarktop quark
down-typedown quarkstrange quarkbottom quark
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino

At room-temperature quarks always form bound states to hadrons. This phenomenon of confinement is quantitatively well-reproduced by lattice QCD computations (see Fodor-Hoelbling 12) and qualitatively well reproduced by conceptual arguments such as the AdS/QCD correspondence, but a full analytic proof of confinement from a rigorous AQFT-like foundation of QCD remains open, see the mass gap problem.

However, at high temperature QCD goes through a deconfinement phase transition and enters another phase of matter known as the quark-gluon plasma. As the name suggests, here quarks and gluons are free.

## References

Textbooks:

### History

The quark model was proposed independently in 1964 by

• Murray Gell-Mann, A Schematic Model of Baryons and Mesons, Phys.Lett. 8 (1964) 214-215 (spire:11880, doi:10.1016/S0031-9163(64)92001-3)

• George Zweig, An SU(3) model for strong interaction symmetry and its breaking, version 1 is CERN preprint 8182/TH.401, Jan. 17, 1964, version 2 in Developments in the Quark Theory of Hadrons Volume 1. Edited by D. Lichtenberg and S. Rosen. Nonantum, Mass., Hadronic Press, 1980. pp. 22-101 (spire:4674)

Review of this history:

### Ab-initio lattice computation

Due to confinement, before the quark-gluon plasma was seen in experiment it was a logical possibility that the quark-model of QCD is not actually correct. But more recend ab-initio computation in lattice QCD show that starting with the quark model, at least the light hadron bound states observes in experiment are reproduced by these ab-initio computations. This is discussed in the following references, see the good review Fodor-Hoelbling 12

• S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoffmann, S.D. Katz, S. Krieg, T. Kurth, L. Lellouch, T. Lippert, K.K. Szabo, G. Vulvert,

Ab-initio Determination of Light Hadron Masses,

Science 322:1224-1227,2008 (arXiv:0906.3599)

• Zoltan Fodor, Christian Hoelbling, Light Hadron Masses from Lattice QCD, Rev. Mod. Phys. 84, 449, (arXiv:1203.4789)

• S. Aoki et. al. Review of lattice results concerning low-energy particle physics (arXiv:1607.00299)