Leptons and Quarks

Subject: Physics

Overview

The leptons are the lightweight elementary particles which do not have strong interactions.This note provides us an information about leptons and quarks.

Note
Things to remember

Leptons and Quarks

Leptons

The leptons are the lightweight elementary particles which do not have strong interactions. There are six types of leptons. They are electron (e^-), the muon(µ^-), the tau particle (τ^-), electron neutrino (v_e), muons neutrino (v_µ) and tau neutrino (v_τ). Each of the six particles has a distinct antiparticle. All leptons have spin and thus are fermions.

The types of leptons are shown in the table

Particle Name	Symbol	Anti-particle	Mass (MeV/c²)	Lifetime (s)
Electron Electron neutrino	e^- v_e	e^-	0.511< 3× 10^-6	Stable Stable
Muon Muon neutrino	µ^- v_µ	µ⁺	105.7<0.19	2.20 ×10^-6 Stable
Tau Tau neutrino	τ^-v_τ	τ⁺	1777<18.2	2.9 ×10^-13 Stable

Hadrons

Hadrons are the strongly interacting particles. Each hadron has an antiparticle. There are two subclasses of hadrons: mesons and baryons. Properties of some hadrons are shown in the table below.

Hadrons and their proporties

Particle	Mass (MeV/c²)	Charge Ratio Q/e	Spin	Mean Lifetime (s)	Quark Content
Mesons
π⁰	135.0	0	0	8.4 × 10^-17	u \(\overline{u}\), d\(\overline{d}\)
π⁺	139.6	+1	0	2.60 × 10^-8	u\(\overline{d}\)
π^-	139.6	-1	0	2.60 × 10^-8	d \(\overline{u}\)
K⁺	493.7	+1	0	1.24 × 10^-8	u \(\overline{s}\)
K^-	493.7	-1	0	1.24 × 10^-8	s\(\overline{u}\)
^\(\eta\)0	547.3	0	0	=10^-18	u\(\overline{u}\), d\(\overline{d}\), u\(\overline{s}\)
Baryons
P	938.6	+1	½	-	uud
n	939.6	0	½	pe^-	udd
\(\Lambda\)	1116	0	½	pπ^- or n π⁰	uds
^\(\sum\)+	1189	+1	½	pπ⁰ or n π^-	uus
^\(\sum\)0	1193	0	½	Ù⁰Æ³	uds
^\(\sum\)-	1197	-1	½	nπ^-	dds
^\(\Xi\)0	1315	0	½	Ù⁰ π⁰	uss
^\(\Xi\)-	1321	-1	½	Ù⁰ π^-	dss
\(\Delta\)⁺⁺	1232	+2	½	pπ⁺	uuu
^\(\Omega\)-	1672	--1	½	Ù⁰ π^-	sss
^\(\wedge\)+	2285	+1	½	pK^- π^-	udc

Mesons

Mesons are intermediate mass particles. They are heavier than leptons but lighter than baryons. Mesons include pions, kaons, eta particles etc. They are all bosons with spin 0 and 1. There are no stable mesons.

Baryons

Baryons include nucleons and hyperons. They are heavy particles and they have half-integer spin and, therefore, all are fermions. The only stable baryon is a proton.

Quarks

Quarks are fundamental constituents of all the hadrons. They are strongly interacting particles. No isolated existence of quark is discovered so far.

Original Quark Model

According to this model all hadrons are a composite system of two or here fundamental constituents called quark. There are three types of quarks up, down and strange. Each quark has anti-quark of opposite charge, baryon number and strangeness.

Main properties of quarks and anti quarks are given in the table:

Name	Symbol	Spin	Charge	Baryon Number	Strangeness
Quarks
Up	u	½	+2e/3	1/3	0
Down	d	½	-e/3	1/3	0
Strange	s	½	-e/3	1/3	-1
Anti Quarks
Anti-up	\(\overline {u}\)	½	-2e/3	-1/3	0
Anti-down	\(\overline{d}\)	½	+e/3	-1/3	0
Anti-strange	\(\overline{s}\)	½	+e/3	-1/3	-1

The composition of all hadrons could be completely specified by three simple rules.

Mesons consist of one quark and one anti-quark.
Baryons consist of three quarks.
Antibaryons consist of three antiquarks.

Composition of several baryons and mesons are given below

Baryons	Quarks composition
P	uud
n	udd
\(\lambda\)₀	uds
^\(\sum\)+	uus
^\(\sum\)-	dds
^\(\sum\)0	uds
^\(\Xi\)0	uss
^\(\Xi\)-	dss
^\(\Omega\)-	sss
^\(\Delta\)-	ddd
^\(\Delta\)++	uuu

Mesons	Quarks composition
π⁰	u
π⁺	u
π^-	d
K⁺	u
K^-	s
K⁰	u

The third quark is needed only to construct charged particle with strangeness.

Charm and Other Recent Development

Consequently, fourth quark was proposed by several physicists in 1967. The fourth quark was given the new property or quantum number called charm.

In 1975 researcher at SU reported strong evidence of the τ lepton. This discovery led to the more elaborate quark model and purposed of new quarks called top (t) and bottom (b)

The properties of overall quark with additional quark.

Name	Symbol	Spin	Charge	Baryon Number	Strangeness	Charm ness	Bottom ness	Top ness
Quarks
Up	u	½	+2e/3	1/3	0
Down	d	½	-e/3	1/3	0
Strange	s	½	-e/3	1/3	1
Charm	c	½	+2e/3	1/3		1	0	0
Bottom	b	½	-e/3	1/3		0	1	0
Top	t	½	+2e/3	1/3		0	0	1
Anti Quarks
Anti-up	\(\overline{u}\)	½	-2e/3	-1/3	0
Anti-down	\(\overline{d}\)	½	+e/3	-1/3	0
Anti-strange	\(\overline {s}\)	½	+e/3	-1/3	-1
Anti-charm	\(\overline{c}\)	½	-2e/3	-1/3		-1	0	0
Anti-bottom	\(\overline {t}\)	½	+e/3	-1/3		0	-1	0
Anti-top	\(\ overline{b}\)	½	-2e/3	-1/3		0	0	-1

After the discovery of top quark according to the standard model all the matter is composed of six strongly interacting particles the quarks (u, d, s, c, b, t) and six weakly interacting particles the leptons (e, µ, τ, n_e, n_µ, n_τ) together with their antiparticles.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, et.al.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

Things to remember

The leptons are the lightweight elementary particles which do not have strong interactions.

Quarks are fundamental constituents of all the hadrons.

According to original quark model all hadrons are a composite system of two or here fundamental constituents called quark.

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