Gell-Mann–Nishijima Scheme
Charge relation and classification of hadrons
Introduction
The Gell-Mann–Nishijima scheme relates the electric charge of a hadron to its internal quantum numbers like isospin and hypercharge. It was very important before the quark model.
It is a fundamental relation in particle physics that connects the quantum numbers of hadrons (such as baryons and mesons) to their electric charge.
\begin{equation}
Q = I_{3} + \dfrac{Y}{2}
\end{equation}
It is also represented by
\[Q={{I}_{3}}+\frac{\left( B+S+C+B'+T \right)}{2}\]
Where:
- Q = Electric charge
- \( I_3 \) = Third component of isospin
- Y = Hypercharge
- B= Baryon Number
- S=Strangeness
- C=Charm
- T=topness( sometimes t)
- B'=Bottomness ( sometimes b)
Where
\begin{equation}
Y = B + S
\end{equation}
- B = Baryon number
- S = Strangeness
Application to Baryons
| Particle | B | S | Y | I3 | Q |
|---|---|---|---|---|---|
| Proton (p) | 1 | 0 | 1 | +1/2 | +1 |
| Neutron (n) | 1 | 0 | 1 | −1/2 | 0 |
| Λ0 | 1 | −1 | 0 | 0 | 0 |
Worked Examples
Proton
\begin{equation}
Q = 1/2 + 1/2 = 1
\end{equation}
Neutron
\begin{equation}
Q = −1/2 + 1/2 = 0
\end{equation}
Lambda
\begin{equation}
Q = 0 + 0 = 0
\end{equation}
Application to Mesons
For mesons, \begin{equation} B = 0 \end{equation}
\begin{equation}
Y = S
\end{equation}
| Meson | \( S \) | \( Y \) | \( I3 \) | \( Q \) |
|---|---|---|---|---|
| π+ | 0 | 0 | +1 | +1 |
| π0 | 0 | 0 | 0 | 0 |
| K+ | +1 | +1 | +1/2 | +1 |
Summary
- \( Q = I_3 + Y/2 \)
- \( Y = B + S \)
- Classifies hadrons
- Foundation of SU(3)