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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).

Four closely related Δ baryons exist: Δ++ (constituent quarks: uuu), Δ+ (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, a spin of ​3⁄2, and an isospin of ​3⁄2. Ordinary protons and neutrons (nucleons (symbol N)), by contrast, have a mass of about 939 MeV/c2, a spin of ​1⁄2, and an isospin of ​1⁄2. The Δ+ (uud) and Δ0 (udd) particles are higher-mass excitations of the proton (N+ , uud) and neutron ( N0, udd), respectively. However, the Δ++ and Δ−
have no direct nucleon analogues.

The states were established experimentally at the University of Chicago cyclotron[1][2] and the Carnegie Institute of Technology synchro-cyclotron[3] in the mid-1950s using accelerated positive pions on hydrogen targets. The existence of the Δ++ , with its unusual +2 charge, was a crucial clue in the development of the quark model.

The Delta states discussed here are only the lowest-mass quantum excitations of the proton and neutron. At higher masses, additional Delta states appear, all defined by having ​3⁄2 units of isospin, but with a spin quantum numbers including ​1⁄2, ​3⁄2, ​5⁄2, ... ​11⁄2. A complete listing of all properties of all these states can be found in Beringer et al. (2013).[4]

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

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 1232 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.

List

Delta baryons
Particle
name
Symbol Quark
content
Mass
(MeV/c2)
I−3 JP Q
(e)
S C B′ T Mean lifetime
(s)
Commonly
decays to
Delta[4]
Δ++
(1232)

u

u

u
1232±2 +​32 32+ +2 0 0 0 0 (5.63±0.14)×10−24[a]
p+
+
π+
Delta[4]
Δ+
(1232)

u

u

d
1232±2 +​12 32+ +1 0 0 0 0 (5.63±0.14)×10−24[a]
π+
+
n0
, or

π0
+
p+
Delta[4]
Δ0
(1232)

u

d

d
1232±2 −​12 32+ 0 0 0 0 0 (5.63±0.14)×10−24[a]
π0
+
n0
, or

π
+
p+
Delta[4]
Δ
(1232)

d

d

d
1232±2 −​32 32+ −1 0 0 0 0 (5.63±0.14)×10−24[a]
π
+
n0

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

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. Bibcode:1952PhRv...85..936A. doi:10.1103/PhysRev.85.936.
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. Bibcode:1952PhRv...85..934H. doi:10.1103/PhysRev.85.934.
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. Bibcode:1956PhRv..101.1149A. doi:10.1103/PhysRev.101.1149. hdl:2027/mdp.39015095214600.

J. Beringer et al. (2013): Particle listings –
Δ
(1232)

Bibliography

C. Amsler et al. (Particle Data Group) (2008). "Review of Particle Physics" (PDF). Physics Letters B. 667 (1): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018.

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