Quarks

Fundamental constituents of hadrons

Introduction to Quarks

Quarks are elementary fermions that interact through the strong force described by quantum chromodynamics (QCD). They combine to form hadrons such as baryons and mesons.

General Properties

Property	Description
Spin	\( \frac{1}{2} \)
Statistics	Fermi–Dirac
Color Charge	Red, Green, Blue
Isolation	Not observed freely (confinement)

Properties of Quarks

Flavor	Symbol	Charge	Mass (approx.)	Charm (C)	Colour	Beauty (B′)	Strangeness (S)	Baryon Number (B)
Up	u	+2/3	2.2 MeV	0	Red / Green / Blue	0	0	+1/3
Down	d	−1/3	4.7 MeV	0	Red / Green / Blue	0	0	+1/3
Strange	s	−1/3	96 MeV	0	Red / Green / Blue	0	−1	+1/3
Charm	c	+2/3	1.27 GeV	+1	Red / Green / Blue	0	0	+1/3
Bottom	b	−1/3	4.18 GeV	0	Red / Green / Blue	−1	0	+1/3
Top	t	+2/3	173 GeV	0	Red / Green / Blue	0	0	+1/3

Color Confinement

The force between quarks increases with separation distance. This leads to color confinement, preventing free quarks.

\[ V(r) \approx kr \]

Quark Composition of Various Particles

All hadrons are made of quarks. There are two main categories:

Baryons → Made of 3 quarks (qqq)
Mesons → Made of 1 quark + 1 antiquark (q q̄)

1️⃣ Baryons (Three Quark States)

Particle	Symbol	Quark Composition	Charge
Proton	p	u u d	+1
Neutron	n	u d d	0
Lambda	Λ⁰	u d s	0
Sigma Plus	Σ⁺	u u s	+1
Sigma Zero	Σ⁰	u d s	0
Sigma Minus	Σ⁻	d d s	−1
Xi Zero	Ξ⁰	u s s	0
Xi Minus	Ξ⁻	d s s	−1
Omega Minus	Ω⁻	s s s	−1

2️⃣ Mesons (Quark–Antiquark States)

Particle	Symbol	Quark Composition	Charge
Positive Pion	π⁺	u d̄	+1
Negative Pion	π⁻	d ū	−1
Neutral Pion	π⁰	(u ū − d d̄)/√2	0
Positive Kaon	K⁺	u s̄	+1
Negative Kaon	K⁻	s ū	−1
Neutral Kaon	K⁰	d s̄	0
Anti-Kaon	K̄⁰	s d̄	0

3️⃣ Heavy Quark Hadrons

Particle	Quark Composition	Type
J/ψ	c c̄	Charmonium (Meson)
Υ	b b̄	Bottomonium (Meson)
Lambda_c	u d c	Charmed Baryon
Lambda_b	u d b	Bottom Baryon

Important Points

All baryons have baryon number = +1
All mesons have baryon number = 0
Quark charges: u, c, t → +2/3 ; d, s, b → −1/3
Antiquarks have opposite charge and quantum numbers

Quark Composition – MCQ Quiz

The quark composition of a proton is:

u d d
u u d
d d u
s u d

The neutron consists of:

u d d
u u d
d d s
u s s

How many quarks are present in a baryon?

2
3
4
6

Mesons are made of:

One quark and one antiquark
Three quarks
Two quarks
Three antiquarks

The quark content of π⁺ is:

u d̄
d ū
u ū
d d̄

The baryon number of a meson is:

+1
0
−1
+1/3

The Ω⁻ particle is composed of:

u u s
d d s
s s s
u s s

The electric charge of the up quark is:

+2/3
−1/3
+1
0

Which quark carries strangeness −1?

Up
Down
Strange
Charm

The quark content of K⁺ is:

u s̄
s ū
d s̄
u d̄

Which of the following is a charmonium state?

c c̄
b b̄
u d̄
s s s

The baryon number of a quark is:

1
0
+1/3
−1/3

The Λ⁰ particle contains which quarks?

u d s
u u d
d d s
u s s

The bottom quark has electric charge:

+2/3
−1/3
+1
0

Which of the following is a baryon?

π⁺
Proton
K⁺
J/ψ