Δ-baryon

Delta baryon (Δ ++ , Δ + , Δ 0 , Δ - )
classification
Fermion Hadron Baryon
properties
electric charge	2, 0 or ± 1  e (+3.204 · 10 −19  C , 0 or ± 1.602 · 10 −19  C )
Resting energy	≈1232  MeV
Spin parity	3/2 +
Isospin	3/2 (z component ± 3/2, ± 1/2)
Decay width	≈118  MeV
Quark composition	uuu, uud, udd, ddd

The Δ-baryons ( delta baryons ) or delta resonances are baryons , which consist of up and down quarks . They have spin and isospin 3/2.

There are four different Δ-baryons, which are usually characterized by their electrical charge: Δ ⁺⁺ , Δ ⁺ , Δ ⁰ and Δ ^- .
Δ ⁺ and Δ ⁰ consist of the same quarks as the nucleons protons and neutrons and can therefore be interpreted as their spin excitation .

It was discovered as the first pion nucleon resonance in 1951 at the cyclotron in Chicago by Herbert L. Anderson , Enrico Fermi , EA Long and Darrah E. Nagle . A resonance was observed at an energy of the pions scattered on protons of about 180 M eV . It was explained by Keith Brueckner using the isospin model of pions and nucleons.

description

The SU (3) baryon decuplet.

The four-Δ baryons include the SU (3) - decuplet on. They differ in their quark content, which can be viewed abstractly as an isospin 3/2 vector in the flavor space. The quark content of the Δ-baryons is

symbol	Curd content	Isospin -z component
Δ ++	uuu	+3/2
Δ +	uud	+1/2
Δ 0	udd	−1/2
Δ -	ddd	−3/2

Almost 100% of the Δ-baryons decay into a nucleon and a pion . A very small proportion (<1%) decays into a nucleon when a photon is emitted.

particularities

If one only considers the spin and flavor components, the Δ-baryons Δ ⁺⁺ and Δ ^- seem to be a violation of the Pauli principle . As fermions , they should have an anti-symmetrical wave function , their spin and flavor wave functions however, they are completely symmetrical, e.g. B.

${\displaystyle \Delta ^{++}=u(+)u(+)u(+)}$,

where stands for up-quark and + for the spin projection. ${\displaystyle u\,}$

This problem can be solved by postulating another degree of freedom for quarks, the so-called color charge . If you introduce this new quantum number , you get

${\displaystyle \Delta ^{++}=\Sigma \,\varepsilon _{gbr}\,u^{g}(+)u^{b}(+)u^{r}(+)}$

with the Levi-Civita symbol and the degrees of freedom and (green, blue, red). So the wave function is again anti-symmetric. ${\displaystyle \varepsilon _{gbr}}$ ${\displaystyle g,b\,}$ ${\displaystyle r\,}$

The Δ-baryons contributed to the development of quantum chromodynamics .

Today, the Δ-baryons are still of theoretical interest, since, analogous to the ρ-mesons , models of the dynamics of the strong force can be tested on them.

See also

• Ω-baryon
• List of baryons
• GZK cutoff

Individual evidence

1. ↑ The information on the particle properties (info box) are, unless otherwise stated, taken from: K. Nakamura et al. ( Particle Data Group ): Review of Particle Physics. In: Journal of Physics G , 37, 2010, 075021, lbl.gov
2. ^ HL Anderson, E. Fermi, EA Long, DE Nagle: Total Cross Sections of Positive Pions in Hydrogen . In: Phys. Rev. , Volume 85, 1952, p. 936, princeton.edu (PDF)
3. ↑ Darrah E. Nagle: The Delta - the first pion nucleon resonance , LALP 84-27. (PDF) Los Alamos National Laboratory; after a lecture in honor of Herbert Anderson at the University of Chicago in 1982.
4. ↑ N. Nakamura et al . (2010): Particle listings - Δ (PDF; 70 kB)
5. ↑ F. Yndurain: The Theory of quarks and gluon interactions . 4th edition. Springer, 2006, ISBN 3-540-64881-X .