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).

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 and the Carnegie Institute of Technology synchro-cyclotron 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).

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	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	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	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	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

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.