Home
Unit-4
Gell-Mann–Nishijima Scheme
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)
MCQs on Gell-Mann-Nishijima Scheme
