Delta baryon

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.

Delta baryon

Composition	Δ^++ : u u u Δ^+ : u u d Δ^0 : u d d Δ^− : d d d
Statistics	Fermionic
Interactions	Strong, weak, electromagnetic, and gravity
Symbol	Δ
Types	4
Mass	1232±2 MeV/c^2
Spin	3 /2,  5 /2,  7 /2 ...
Strangeness	0
Charm	0
Bottomness	0
Topness	0
Isospin	3 /2

Properties

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; their third component of isospin ${\displaystyle \;I_{3}=\pm {\tfrac {1}{2}}~{\mathsf {or}}~\pm {\tfrac {3}{2}}\;;}$  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 multiplied by ħ. 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.

Discovery

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 electric charge of +2 e, was a crucial clue in the development of the quark model.

Formation and decay

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

All of the Δ baryons with mass near 1232 MeV quickly decay via the strong interaction 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/c^2)	I3	J^P	Q (e)	S	C	B′	T	Mean lifetime (s)	Commonly decays to
Delta^[1]	Δ^++ (1 232)	u u u	1232±2	+ 3 /2	3 /2^+	+2	0	0	0	0	(5.63±0.14)×10^−24^[a]	p^+ + π^+
Delta^[1]	Δ^+ (1 232)	u u d	1232±2	+1/ 2	3 /2^+	+1	0	0	0	0	(5.63±0.14)×10^−24^[a]	π^+ + n^0 , or π^0 + p^+
Delta^[1]	Δ^0 (1 232)	u d d	1232±2	−+1/ 2	3 /2^+	0	0	0	0	0	(5.63±0.14)×10^−24^[a]	π^0 + n^0 , or π^− + p^+
Delta^[1]	Δ^− (1 232)	d d d	1232±2	−+ 3 /2	3 /2^+	−1	0	0	0	0	(5.63±0.14)×10^−24^[a]	π^− + n^0

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

References

1. Beringer, J.; et al. (Particle Data Group) (2013).
   Δ
   (1 232) (PDF) (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. Bibcode:1952PhRv...85..936A. doi:10.1103/PhysRev.85.936.
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. Bibcode:1952PhRv...85..934H. doi:10.1103/PhysRev.85.934.
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. Bibcode:1956PhRv..101.1149A. doi:10.1103/PhysRev.101.1149. hdl:2027/mdp.39015095214600.

Bibliography

• Amsler, C.; et al. (Particle Data Group) (2008). (PDF). Physics Letters B. 667 (1): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789. Archived from the original (PDF) on 2020-09-07. Retrieved 2019-12-11.