Hypercharge

	Particle	Components	el. charge ${\displaystyle Q}$	Isospin ${\displaystyle I_{3}}$	Hyperldg. ${\displaystyle Y}$
Quarks	Up	u	+2/3	+ ½	+1/3
	Anti-up	u	−2/3	−½	−1/3
	Down	d	−1/3	−½	+1/3
	Anti-down	d	+1/3	+ ½	−1/3
Hadrons	proton	uud	+1	+ ½	+1
	neutron	udd	0	−½	+1

In particle physics , the hypercharge ( symbol to differentiate it from the weak hypercharge ) is a quantum number . It is used to describe particles that are subject to strong interaction ( quarks and the hadrons made up of them ). ${\displaystyle Y\!\,}$ ${\displaystyle Y_{W}}$

The hypercharge is:

• for up and down quark respectively: ${\displaystyle Y=+1/3\!\,}$
• for anti-up and anti-down quark: ${\displaystyle Y=-1/3\!\,}$
• for the nucleons ( protons p, neutron n) respectively: . ${\displaystyle Y=+1\!\,}$

The hypercharge of a particle is related to its electrical charge (in units of the elementary charge ) and the third component of its isospin via the Gell-Mann-Nishijima relation : ${\displaystyle Y}$ ${\displaystyle Q}$ ${\displaystyle I_{3}}$

${\displaystyle Y=2\,(Q-I_{3})\qquad \Leftrightarrow \qquad Q=I_{3}+{\frac {1}{2}}Y\,}$.

In addition: , ${\displaystyle Y=B+S+C+B\;\!'+T\!\,}$

where B stands for the baryon number , S for the strangeness , C for the charm , B ' for the bottomness and T for the topness .

When considering an isospin multiplet of baryons or mesons, the following applies:

${\displaystyle Y=2\,{\overline {Q}}}$,

where Q denotes the mean electrical charge of the particles in the multiplet.

Web links

• Wikibooks: Particle Physics: Particle Properties: Charge Multiples