Delta baryon

The Delta baryons (or Template:Math 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.

Properties

Four closely related Template:Math baryons exist: Template:SubatomicParticle (constituent quarks: uuu), Template:Subatomic Particle (uud), Template:SubatomicParticle (udd), and Template:SubatomicParticle (ddd), which respectively carry an electric charge of Template:Val, Template:Val, Template:Val, and Template:Val.

The Template:Math baryons have a mass of about Template:Val; their third component of isospin $I_3=\pm \frac{1}{2}\mathsf{o}\mathsf{r}\pm \frac{3}{2};$ and they are required to have an intrinsic spin of Template:Sfrac or higher (half-integer units). Ordinary nucleons (symbol N, meaning either a proton or neutron), by contrast, have a mass of about Template:Val, and both intrinsic spin and isospin of Template:Sfrac. The Template:Math (uud) and Template:Math (udd) particles are higher-mass spin-excitations of the proton (Template:SubatomicParticle, uud) and neutron (Template:SubatomicParticle, udd), respectively. The Template:Math and Template:Math, however, have no direct nucleon analogues: For example, even though their charges are identical and their masses are similar, the Template:Math (ddd), is not closely related to the antiproton (Template:SubatomicParticle, 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 Template:Sfrac or Template:Sfrac isospin (depending on charge), but with spin Template:Sfrac, Template:Sfrac, Template:Sfrac, ..., Template:Sfrac multiplied by [[reduced Planck constant|Template:Mvar]]. 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.

Discovery

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 Template:Math, with its unusual electric charge of Template:Val, 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 Template:Val 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, the Template:SubatomicParticle can decay into a proton and a photon and the Template:SubatomicParticle can decay into a neutron and a photon.

List

Delta baryons

Particle name	Symbol	Quark content	Mass (MeV/[[speed of light|Template:Mvar]]2)	[[Isospin|Template:Mvar3]]	[[Total angular momentum|Template:Mvar]][[Parity (physics)|Template:Mvar]]	[[charge (physics)|Template:Mvar]] ([[elementary charge|Template:Mvar]])	[[strangeness|Template:Mvar]]	[[charm (quantum number)|Template:Mvar]]	[[bottomness|Template:Mvar]]	[[topness|Template:Mvar]]	Mean lifetime (s)	Commonly decays to
Delta	Template:Math(1 232)	Template:SubatomicParticleTemplate:SubatomicParticleTemplate:SubatomicParticle	Template:Val	+Template:Sfrac	Template:Sfrac+	+2	0	0	0	0	Template:Val[a]	Template:Nobr
Delta	Template:Math(1 232)	Template:SubatomicParticleTemplate:SubatomicParticleTemplate:SubatomicParticle	Template:Val	+Template:Sfrac	Template:Sfrac+	+1	0	0	0	0	Template:Val[a]	Template:Nobr Template:Nobr
Delta	Template:Math(1 232)	Template:SubatomicParticleTemplate:SubatomicParticleTemplate:SubatomicParticle	Template:Val	Template:Sfrac	Template:Sfrac+	0	0	0	0	0	Template:Val[a]	Template:Nobr Template:SubatomicParticle + Template:SubatomicParticle
Delta	Template:Math(1 232)	Template:SubatomicParticleTemplate:SubatomicParticleTemplate:SubatomicParticle	Template:Val	Template:Sfrac	Template:Sfrac+	−1	0	0	0	0	Template:Val[a]	Template:Nobr

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