Physics:Delta baryon

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Delta baryon
InteractionsStrong, weak, electromagnetic, and gravity
Spin 3 /2,  5 /2,  7 /2 ...
Isospin 3 /2

The Delta baryons (or Δ baryons, also called Delta resonances) are a family of subatomic particle made of three up or down quarks (u or d quarks), the same constituent quarks that make up the more familiar protons and neutrons.


Four closely related Δ baryons exist: Δ++ (constituent quarks: uuu), Template:Subatomic Particle (uud), Δ0 (udd), and Δ (ddd), which respectively carry an electric charge of +2 e, +1 e, 0 e, and −1 e.

The Δ baryons have a mass of about 1232 MeV/c2; their third component of isospin [math]\displaystyle{ \; I_3 = \pm\tfrac{1}{2} ~\mathsf{ or }~ \pm\tfrac{3}{2}\;; }[/math] and they are required to have an intrinsic spin of  3 /2 or higher (half-integer units). Ordinary nucleons (symbol N, meaning either a proton or neutron), by contrast, have a mass of about 939 MeV/c2, and both intrinsic spin and isospin of 1/ 2 . The Δ+ (uud) and Δ0 (udd) particles are higher-mass spin-excitations of the proton (N+, uud) and neutron (N0, udd), respectively.

The Δ++ and Δ, however, have no direct nucleon analogues: For example, even though their charges are identical and their masses are similar, the Δ (ddd), is not closely related to the antiproton ( p uud).

The Delta states discussed here are only the lowest-mass quantum excitations of the proton and neutron. At higher spins, additional higher mass Delta states appear, all defined by having constant  3 /2 or  1 /2 isospin (depending on charge), but with spin  3 /2,  5 /2,  7 /2, ...  11 /2 in ħ; units. A complete listing of all properties of all these states can be found in Beringer et al. (2013).[1]

There also exist antiparticle Delta states with opposite charges, made up of the corresponding antiquarks.


The states were established experimentally at the University of Chicago cyclotron[2][3] and the Carnegie Institute of Technology synchro-cyclotron[4] in the mid-1950s using accelerated positive pions on hydrogen targets. The existence of the Δ++, with its unusual +2 electric charge, was a crucial clue in the development of the quark model.

Formation and decay

The Delta states are created when an energetic-enough probe – such as a photon, electron, neutrino, or pion – impinges upon a proton or neutron, or possibly by the collision of an energetic-enough nucleon pair.

All of the Δ baryons with mass near 1 232 MeV quickly decay via the strong force into a nucleon (proton or neutron) and a pion of appropriate charge. The relative probabilities of allowed final charge states are given by their respective isospin couplings. More rarely and more slowly, the Δ+ can decay into a proton and a photon and the Δ0 can decay into a neutron and a photon.


Delta baryons
Symbol Quark
S C B′ T Mean lifetime
decays to
Delta[1] Δ++(1 232) Up quarkUp quarkUp quark 1232±2 + 3 /2  3 /2+ +2 0 0 0 0 (5.63±0.14)×10−24[a] Proton+ + Pion+
Delta[1] Δ+(1 232) Up quarkUp quarkDown quark 1232±2 +1/ 2   3 /2+ +1 0 0 0 0 (5.63±0.14)×10−24[a] Pion+ + Neutron0, or
Pion0 + Proton+
Delta[1] Δ0(1 232) Up quarkDown quarkDown quark 1232±2 +1/ 2   3 /2+ 0 0 0 0 0 (5.63±0.14)×10−24[a] Pion0 + Neutron0, or
Pion- + Proton+
Delta[1] Δ(1 232) Down quarkDown quarkDown quark 1232±2 + 3 /2  3 /2+ −1 0 0 0 0 (5.63±0.14)×10−24[a] Pion- + Neutron0

[a] ^ PDG reports the resonance width (Γ). Here the conversion [math]\displaystyle{ \tau = \frac{\hbar}{\Gamma} }[/math] is given instead.


  1. 1.0 1.1 1.2 1.3 1.4 Beringer, J. (2013). Δ(1 232) (Report). Particle listings. 
  2. Anderson, H.L.; Fermi, E.; Long, E.A.; Nagle, D.E. (1 March 1952). "Total cross-sections of positive pions in hydrogen". Physical Review 85 (5): 936. doi:10.1103/PhysRev.85.936. Bibcode1952PhRv...85..936A. 
  3. Hahn, T.M.; Snyder, C.W.; Willard, H.B.; Bair, J.K.; Klema, E.D.; Kington, J.D.; Green, F.P. (1 March 1952). "Neutrons and gamma-rays from the proton bombardment of beryllium". Physical Review 85 (5): 934. doi:10.1103/PhysRev.85.934. Bibcode1952PhRv...85..934H. 
  4. Ashkin, J.; Blaser, J.P.; Feiner, F.; Stern, M.O. (1 February 1956). "Pion-proton scattering at 150 and 170 Mev". Physical Review 101 (3): 1149–1158. doi:10.1103/PhysRev.101.1149. Bibcode1956PhRv..101.1149A.