Fundamental Particles Notes

Fundamental Particles Elementary or fundamental particles are microscopic constituents of the matter out of which all matter of the universe is considered to be made up of. Until 1930 only protons, neutrons, and electrons are considered as elementary particles. But as years passed, more and more particles were discovered. At present there are more than 200 elementary particles. Characteristics : • Rest Mass : It is the basic characteristic of a particle. Each particle has definite rest mass. It is the mass of the particle in its minimum energy. If two particles are identical in all respect, but slightly different rest mass, then they are considered as different particles. Rest mass of photon is zero. The mass of particles is usually expressed in terms of electron mass. For example, mass of a proton is 1836 me , where me is the mass of electron. Mass of proton is 1838 me. Electron mass is 0.00055 atomic mass unit (amu). • •

Charge : Except quarks, all other elementary particles may have a charge +e , – e or zero. Here e is the electron charge,1.6x10-19coulomb. Spin : Particles may be having intrinsic spin. Spin is either or zero. Spin give

1 2 rise to spin angular momentum given by

where s is even or half integral.

s The particles of half integral spin obey Fermi Dirac statistics and are called Fermions. Electron, proton, neutron, neutrino and their antiparticles are Fermions. Particles having zero or integral spin obey Bose Einstein statistics. They are known as Bosons. Examples: mesons, photons. •

Average life : Particle may be stable or unstable. If it is unstable, that particle may emit another elementary particle and decays. Therefore particles are specified in terms of life time. It is the average time for which it exists. The life time of proton and electron is infinity (stable ). Life time of neutron is 920s, that of meson is 2.6x10-6 s.

µ

Antiparticles : The electron for which the detailed theory was developed by British Physicist Paul AM Dirac who obtained the relativistically correct equation. According to Dirac’s relativistic theory of electron, the free electron has not only positive energy states, it has negative energy state also. Classically this is not possible. The negative energy state has no physical meaning. Dirac introduced a new concept of antiparticle in 1924.

0 ositron energy states of pNegative E electrons

According to this, for electron there exist different energy states with positive and negative values. The electron in the negative energy state moves to positive energy state by absorbing a photon of energy , that is 1.02 MeV energy, This

hν  2m0 C 2 process leaves behind a hole in the negative energy state, just like a hole in a semiconductor energy band, behaves as if it is a particle of positive charge. This positively charged particle is called a positron. Positron is like electron in all respect except the charge. Its charge is +e. Other elementary particles also have antiparticles. The antiparticle of a particle has the same mass, spin, life time if unstable, but its charge (if any) has the opposite sign. The alignment or antialignment between its spin and magnetic moment is also opposite to that of the particle. Whenever a particle and antiparticle interact together radiation with two photons are created, having specific energy depend on the mass of the particles. Suppose electron and positron collide, two photons each with energy 0.51 MeV will be created. This is referred as annihilation. The process of creation of particle-antiparticle pair is called pair production. The energy required for pair production for electron-positron pair is 1.02 MeV. On the other hand, if electron and positron is combined then the energy liberated is 1.02 MeV. positrons were discovered (1932) in cosmic rays by American Physicist Carl David Anderson.

Different Particles : (1) Electron – Positron : Electron was discovered by JJ Thomson (1897). Its mass is 0.00055amu. charge is negative and it is 1.6x10-19coulomb. Spin is and spin angular

1 2 momentum is

. It is stable particle. Anti particle of electron is positron. Concept was

1  2 given by Dirac and discovered by Anderson(1932). .

(2) Proton- Antiproton : Proton was discovered by Rutherford. Its mass is 1836me. Charge is +e, spin is and spin angular momentum is . Anti proton was

1 2

1  2

discovered by Emileo Segre and Chembarline(1955). (3)Neutron – Antineutron : Neutron was discovered by James Chadwik (1932). Its mass is 1838me. Electrically neutral. But it has the negative magnetic moment. Charge is and angular momentum is . In free state neutron is unstable and it decays.

1 2

1  2 (T=920s) 1 0

n→

1 1

p+

0 −1

−

e+ ν

Anti neutron is same in all respect, except the anomalous magnetic moment, which is positive here. Anti neutron was discovered by American physicists Cork, Lamberston, Piccioni and Wentzel. (1956). (4) Neutrino – antineutrino : Neutrino is very lightly interacting particle with matter. The concept of neutrino was due to Pauli to explain paradoxes in beta decay. It has zero mass, no charge, and spin is and spin angular momentum is

1 2

1  2

Anti particle of neutrino is antineutrino. While antineutrino is emitted in -

decay,

β neutrino is emitted in +

decay.

β −

A Z

X → Z +A1Y + −10 e + ν

A Z

X → Z +A1Y + +10 e + ν

(5) Mesons : Proposed by Yukawa to explain nuclear forces. Theoretically he showed that these are the particles continuously exchanged between protons and neutrons. Mass of mesons is 273me. Life time is of the order of 10-8s. Three types of mesons are

π + , π −, π 0

There are other types of mesons. For example,

µ

- mesons or muons.

µ

-mesons have

mass 206me. They are discovered by Anderson and Naddermayer (1937) and Pions (Yukawa particles) were discovered by Powell (1942). In 1952 new types of mesons were discovered. Their mass is greater than mass of pions (273me) but less than mass of nucleons (proton and neutron). These particles are called K-meson (Kaeons). Kaeons are having mass in the range 900me. Then came

η

meson. (1073me) (6) Hyperons : These are massive particles. Their mass is greater than mass of nucleons. Some of the hyperons mass is as high as 4000me. Examples are,

λ, ∑ , Ξ , Ω (7) Field Particles : These are the quantum of the force field. Photon is the field particle of electromagnetic field. Its rest mass is zero, charge is zero, spin is 1. Graviton is the quantum particle of gravitational field, no charge, spin is assumed to be 2. Classification of particles : 1. Based on Spin : Based on spin particles are classified into following two classes. Fermions : Fermions are having half integral spin (1/2. 3/2, 5/2). They obey Fermi Dirac statistics. Example : electrons, neutrons, protons, neutrino Bosons : Bosons are having zero or integer spin. They obey Bose Einstein statistics. Example : pions, kaeones, photon and graviton. 2. Based on Mass : • •

Zero rest mass particles : Photons Leptons : Mass is less than 250me, neutrino, electron,

•

particles or tauons. Mesons : Intermediate mass particles – mass is greater than that of leptons, but less than mass of nucleons, mesons with mass 270me, Kaeons (900me)

µ

-meson (206me),

τ

π

and •

η

-mesons (1100me)

Baryons : Mass equal or greater than that of nucleons. There are further two classes. One is nucleon (proton and neutron), other one is hyperons (mass greater than nucleons)

3. Based on interaction with matter Particles which are strongly interact with the matter is called Hadrons. Baryons and mesons are very strongly interact with matter and they come under the class hadrons.

PhotonPions LEPTONS BARYONS(heavier Mesons(intermediate CLASSIFICATION Electron NUCLEONS Proton OF FUNDAMENTAL (lighterKaons particles, mass HYPERONS PARTICLES Graviton particles Electron mass , Neutron mass less greater particles), (BOSONS) Etons than neutriono tham BOSONS 250me, (mass 250m (integral ) Muon spin, zero) greater than FERMIONS e Muon(half neutrino that of FERNIONS Tau nucleons) integral spin, ½) Tau neutrino

….

FIELD PARTICLES

Fundamental Interactions (forces of nature) There are four kind of interactions which govern almost all phenomena of nature. They are, 1. Gravitational Interaction : It is the weakest interaction in the nature. Its range is infinity. Gravitational interaction predominates in macroscopic scale. Planets revolving round the sun, structure of galaxy etc., are due to gravitational interaction. Theoretical prediction is that the graviton is quantum or the field particle. This particle is not yet discovered. Efforts are going on to detect gravity waves and gravitons. 2. Weak Interaction : Strength wise the next interaction is the weak interaction. It causes the radioactive or particle decay. Its range is of the order of 10 -17 m The field particle is called W & Z -particles. 3. Electromagnetic Interaction : Exist between the charges. The range is infinity. Either repulsive or attractive depend on the nature of charges. Field particle is photon. 4. Strong Interaction : One of the strongest force in the nature. It is responsible for holding nucleons together to make the nucleus. If we say the strength of the gravitational force as 1, then strength of the strong interaction is 1040 Comparison of the Interactions Interaction Range Gravitational

∞

Weak Nuclear

10-17m

Electromagnetic

∞

Strong Nuclear

10-15m

Nature

Always attractive , depends on the mass and distance between masses. Attractive at larger distance and repulsive at very short distance If charges are unlike, it is attractive. Between like charges it is repulsive. Attractive in the Fermi range, if distance is less than 0.25 fermi, it becomes repulsive.

Relative strength 1

Field particle

103

1013

Intermediate vector boson W&Z particles Photon

1040

Pions

Graviton (G)

Note : Leptons which do not interact strongly with matter. Each lepton is assigned with lepton number (quantum number) 1 and -1 for their antiparticle.

Lepton electron ( ) e

Lepton number (L) 1

muon ( ) µ

1

tauon ( ) τ

1

electron neutrino ( ) νe

1

muon neutrino (

1

)

νµ tau –neutrino (

)

1

ντ In all interactions lepton number is conserved. Baryons are assigned with Baryon Number B. Baryon number is zero for mesons 1 for nucleons and hyperons. -1 for anti Baryons. Baryons Mesons (

,

π , π 0

and

η

Baryon number (B) 0

±

K

)

Nucleons (n,p) Hyperons ( ) Λ, Σ , Ξ & Ω

1 1

In all interactions Baryon number is conserved. Example 1

n+p  n+p+p+ −

p

In the above interaction, not only the atomic and mass number, but also the Baryon number is conserved.

Example 2.

p  n + e+ + neutrino . ν

To find the nature of emitted neutrino we can apply the conservation of lepton number. Lp= Ln + Le + Lν

0 = 0 + (-1) + 1

To conserve the lepton number,

should be +1. This is for electron neutrino. Hence the Lν

interaction can be written as

p  n+ e+

. νe

➢

n  p + eLn= Lp + Le + Lν

0 = 0 + (+1) + (-1) To conserve the lepton number,

should be -1. This is for anti electron neutrino. Hence the Lν

interaction can be written as

n  p + e- + −

νe Some of the particles are having strange properties and they are called strange particles. Kmesons and all hyperons are strange particles and they are assigned with strangeness number S (as lepton or baryon numbers). All K-mesons are having strangeness number +1, have -1, has -2 and hass -3. Ξ Λ, Σ & Ω In all interaction strangeness number S is also conserved.

Standard Model or Quark Model In 1964 American Physicists Murray Gellman and George Zweig proposed a Standard model of particles. According to this model there are six leptons which are having no substructure. They have only point like structure. These leptons are

e

νe

µ

νµ

τ

ντ

According to Gellman, strongly interacting particles – Baryons and Mesons (collectively called hadrons)- are made up of still smaller entity. ie., they have sub structure. These structures are called “Quarks”. There are six types of quarks. u – quark (up ) d – quark (down)

c – quark (charm)

t – quark (top)

s – quark (strange) b – quark (bottom)

Quark u (up)

Charge

spin

2 + e 3

1 2

2 + e 3

1 2

2 + e 3

1 2

d (down)

1 − e 3

1 2

s (strange)

1 − e 3

1 2

b (bottom)

1 − e 3

1 2

c (charm)

t (top)

Here “up”, “down”,“strange” do not have any physical meaning as such. Among these u, c, t have charge

& d,s,b have the charge

2 + e 3

1 − e 3

Each quark has spin ½ or spin angular momentum

, so they are fermions.

1  2 Each quark has anti quark and it has opposite charge. Baryons are composed of three quarks (u,d, or s), while mesons are combinations of a quark and anti quark. The combination of u, d, s and also their anti quarks create a proton, neutron and other baryon particles. For example proton is the combination of 2up quarks and a down quark (uud) Creation of a proton.

ud 2/ 3e 1/3e

===== PPP ppp Proton

charge of proton.

2  1 2 e +  − e = + e 3  3 Neutron is the combination of a u-quark and two d-quark. (udd) dud -2/ 3e 1/3e

===== PPP ppp Neutron

, charge of neutron.

 1 2 2 − e +  e = 0  3 3

Quark structure of some hadrons Baryonns with S =

Mesons with S =0

1 2 (uud) +

p

(u )

π

+

π

0

π

−

(ddu) n

0

(u

(uus)

Σ+

−

d

Σ Σ

−

(

) −

u d

(u )

K

+

K

0

(dds)

Λ

−

s

(d )

(uds) 0

−

u +d d

(uds) 0

) −

−

s

(u

η

0

) −

−

u −d d

Glouons : It is theoretically predicted that that the strong interaction between quarks is due to particles called “Gluons” (like photons in electromagnetic field and gravitons in gravitational field). Gluons do not have mass, electrically neutral, having spin 1, and also carry “colour charge”. The strong interaction takes place due to eight colored gluons. The theory which deals with these cololoured gluons is called “Quantum Chromo Dynamics” (QCD) and interaction between different elementary particles along with electromagnetic field is called “Quantum Electro Dynamics” (QED). Both these fields are frontier areas of Nuclear Physics and exciting prospects are there for young brilliant minds to solve the secret of the nature.