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
| 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 | +3⁄2 | 3⁄2+ | +2 | 0 | 0 | 0 | 0 | (5.63±0.14)×10−24[a] | p+ + π+ |
| Delta[4] | Δ+ (1232) |
u u d |
1232±2 | +1⁄2 | 3⁄2+ | +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 | −1⁄2 | 3⁄2+ | 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 | −3⁄2 | 3⁄2+ | −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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