Lecture notes, lecture Particle Physics PDF

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Chapter Four Introduction to Particle Physics 4.1. Four basic questions The development of particle physics is mainly dedicated to find the answers to the following 4 basic questions: Q1. What holds matter together? Four forces responsible for all phenomena and they have different strength. a) Strong force: inside a nucleus, exists between nucleons, or between quarks. If we set the strong force between two particles is 1, then: b) Electromagnetic force is 10-2, and restricted to electrically charged particles and holds atoms/molecules together. c) Weak force is 10-8 , exists in radioactive decay and nuclear fusion of subatomic particles. d) Gravitational force is 10-45 , exists between particles of mass (all particles). Q2. How is a force transmitted between particles without direct physical contact with each other? In classical physics, the concept of ‘field’ is used, resulting in action at distance. A particle, by virtue of its presence somewhere, modifies the physical properties of the space around it, i.e. it ‘creates a field, a second particle, at distance r away, is embedded in this field. The field ‘acts’ on this second particle. The second particle experiences the force acted on it by the first particle. However, when investigating the interaction between particles inside a nucleus, for example, continuous field theory doesn’t work, because the elementary particle world is governed by Quantum Mechanics. In 20th century, particle physicists (quantum mechanics) use the concept of ‘exchange force’: two particles interact with each other by exchanging a (virtual) particle between them. An exchange particle (‘field quantum’) is created (and emitted) by one of the interacting particles, is absorbed by the other. This process produces the interaction specific to an interaction (different exchange particle is for different interaction). 1

As shown in the following figure: Two ice skaters can push each other apart by throwing a ball between them. The person on the left is pushed back when he throws it. The other on the right is pushed back when he catches it. This exchange particle is called a “ virtual “ particle (we may not see it)! How can energy be conserved during this creation? In Quantum theory: The uncertainty in energy measurement E is related to the uncertainty in time measurement t is by Heisenberg uncertainty Principle (HUP):

h   2 No extra energy is needed to create it! It is from one particle to another particle and may exist for short enough t between creation and absorption, for its energy E to obey HUP and thus not violate energy conservation. E t 

Q3. How do we describe the physical properties of a particle? The world of elementary particles is governed by quantum mechanics in which the physical state of a particle is specified by Quantum numbers. They are quantised properties of particles that are subject to constraints: --electric charge: in unit of e; --energy: quantised by an integer n, E(n); --angular momentu

it of  

h , which 2

is called Plank constant

=1.05457172 × 10 --spin of a Bosons: S = Fermions:

cle (angular momentum of self rotation): 2 ,

3 ,

,…

………………

,

… … ….

There are many more quantised quantities we will know later to describe different physical properties of elementary particles. 2

Q4. Is matter infinitely dividable? For over 2000 years, people have thought about the fundamental particles from which all matter is made, starting with gradual development of atomic theory, followed by a deeper understanding of the quantized atom, leading to the recent theory of the standard model. The answer to this question is limited by our knowledge about elementary particles at different period of time. In 1920s, we thought p, n, e- are elementary particles, which are undividable. We now follow the steps of the historical development of particle physics, to explore the structure and physical features of the elementary particles.

4.2. Neutron Beta decay  discovery of Neutrinos In 1920s, the reaction was found to occur under a certain physical condition.

as shown by the vertical line in the figure.

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The energy spectrum of the electrons was expected to be a line spectrum. However the observed is a continuum spectrum, shown by the black solid curve. Some amount of the energy got lost! The observed continuous energy spectrum of the electrons appeared to violate E&P conservation laws, or which inferred unseen product particle. Then it was suggested that a particle called electron anti-neutrino must be produced to carry the lost energy, Now rewrite the reaction equation:

The kinetic energy of electrons: KEe = m c2 – Ev(neutrino) Since the anti-neutrinos can carry different amounts of energy (Ev ), the kinetic energy carried by different electrons is different. Therefore the kinetic energy KEe of the electrons shows a continuous distribution . Neutrino is a type of elementary particle much smaller than a neutron, without carrying charges. It is a fermion particles of spin S number of ½. It was originally thought to be mass less, but it is now known that it carries a very small amount of mass: ~ 0.1 eV/c2 . Later on, it is found that there were three different types of neutrinos, i.e., e,  and  . 4.3 Atomic stability—> discovery of photons Why are atoms stable? –

q1 q 2

F  4

0r

2

Electrostatic force between a nucleus (+ve) and electrons(- ve). If we further ask: How is this force transmitted between two charged particles not in direct physical contact with each other? For this electromagnetic interaction field, the predicted exchange particle is called photon – another elementary particle! In Quantum Electrodynamics, charged particles interact by the exchange of virtual photons, photons that do not exist outside of the interaction and only 4

serve as carriers of momentum/force. Photon is a boson with spin number |S|= 1, massless and zero charge. 4.4 Nuclear stability  discovery of pions If we consider in a nucleus, there are only positive charges, protons, according to the EM theory, the field of a positive charge exerts a repulsive force to another positive charge, but why is the nucleus is stable? Why doesn’t it fly apart?

Yukawa potential ( in 1935) suggested a form of the relevant potential function r

A V (r)   e R r R: the range of the nuclear force, A: constant, which is of the same form as coulomb potential.

The question raised was what is the quantum particle of the nuclear force field? Prediction of the exchange particle for nuclear strong force starts from work on what is the quantised energy of the particle for the strong nuclear force? 5

Use the range of nuclear force: 1.5fm=1.5*10-15m . The longest time t a particle could exist, if moving with speed of light c, and a

x 1.5 1015 m t    5 10 24 s 8 c 3 10 m / s The corresponding energy E related to t by the HUP, would be:  1.05 1034 J .s 1 E    131MeV  24 13 t 5 10 s 1.6 10 J / MeV

This predicted (in 1935, by Hideki Yukawa) a new particle of 131MeV rest energy. In 1947, a new particle called pion is discovered and the measured rest energy

Therefore Pion was thought as another type of “elementary particle” ! Later on, it was found that there were three types pions:

m(  )  m(  )  140MeV / c 2 ; m( 0 )  135MeV / c2 Pions have different charges, e, and 0. ---They are all bosons, have spin number 0. 4.5 The decaying of pions  Muons

The muon is produced in the upper atmosphere by the decay of pions produced by cosmic rays. With a lifetime: 2.20x10-6s; m(+)=m( -)=105.7MeV/c2 6

They are unstable and decay into electrons and neutrinos:

v and ve are different particles, v are associated with muons and ve are associated with electrons in reactions. 4.6 Weak Interaction  W+, W-, and Z particles Let’s go back to the beta decay, which led to the discovery of neutrinos.

Question: what interaction causes beta decay? The decay Involves neutrinos, but neutrinos experience neither strong nor electromagnetic interactions. Also more such decays were discovered:

But everything that happens, every reaction and decay, is caused by something ‘interacting’ with something else. There must be a new type of interaction, the so-called weak interaction, which exists between muons, electrons and neutrinos, and causes beta decay and some other types of decay processes. Later, it was found that the carrier particles of the weak interactions are the W+, W-, and the Z particles. --The W's are electrically charged () and the Z is neutral. -- They are bosons with spin number |S|=1. -- heavy particles, with masses of m(W+) = m( W-)=80GeV/c2, m(Z)=91GeV/c2.

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After that, a lot of new particles appear in pairs, they are called particles and antiparticles. 4.7. Particles and Antiparticles Since the first positive electron (position) discovered by Carl Anderson in 1932, From observations and lab experiments, it is found that particles come in pairs. Antiparticle has the same mass and spin number as its opposite particle, but opposite charge, and other charge-like quantities: Particles ----------------- Antiparticles proton p ---------------- antiproton Neutron n

---------------- antineutron

Electron e-

----------------- positron e+

Electron neutrino e

----------------- electron antineutrino

Muon minus -

------------------ muon plus +

Muon neutrino 

------------------ muon antineutrino

Pi minus -

----------------- pi plus +

Pi zero 0

----------------- pi zero 0

Photon 

----------------- photon 

Parti. + anti.parti. - annihilates  produce other kind of particles. It is interesting to see that a neutron has an antiparticle too, the difference in their sub-structure will be known later after standard model of particles physics is introduced. 4.8. Discovery of Strange Particles In 1947, Rochester and Butler reported so called V0 events in cloud chamber experiment with charged cosmic particles hitting a lead target plate, many different new particles were produced. -

+ p+ 

+ K0 8

These produced new particles were called hadr hadrons ons and were classified as two groups: Ba Baryo ryo ryons ns ns: particles with half-integer spin number; Me Meson son sonss: particles with zero or integer spin number;

Theoretical calculation showed that the neutral particles were produced with large reaction cross-section area, so this reaction is via strong force interaction.  particle has a short half-life time 1/2 = 2.6*10-10s,

 p+ +  -

K0 particle has a shorter half-life time 1/2=0.9*10-10s, K0   + +  Theoretical calculation showed that the cross section area for these decaying processes was very small, so they were via weak force interaction. These particles are called strange particle because their formation (, K0 etc) is via strong interaction but their decaying via weak interaction. Abraham Pais in 1952 suggested introducing a new quantum number called Strangeness S for all of these found strange particles, with the following rules: a) every of strange particle is offered a quantum number called Strangeness quantum number, e.g., +, -, 0,: S = 0 p, n,: S=0 : K:

S = -1 S=1

b) In the strong interaction, S is conserved, S = 0. In weak interaction, S is not conserved, S  0 .

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K and  are not the only strange particles. By 1960s, more strange particles were discovered as listed in the following:

--8 (at the time) particles with strong interaction and spin (1/2) (baryons); and

--9 strongly interacting particles with spin 0 (mesons) .

In 1960s, more than 200 new particles were discovered. Physicist realized that a more important issue was actually:

Q: are they ALL elementary ? A physicist called Murray Gell-Mann (at the same time also Yuvan Ne’eman) observed patterns of symmetry in the discovered mesons and baryons.

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He plotted the spin ½ baryons and spin 0 mesons in so-called octets. There is a similarity between Mendeleev’s periodic table of elements and the super multiples of particles of Gell Mann. Both pointed out a deeper structure of matter. The strangeness QN is plotted vertically and decreases from 0 to -2. The red parallel lines are for charges of baryons.

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4.9 Quark model: To explain the structures of baryons & mesons: 3 quarks called ‘up’, ‘down’, ‘strange’, and three of their ‘anti-’s were suggested. All of quarks are Fermions (with spin number: ½)

-- A baryon consists of 3 quarks: (q1q2q3), while a meson consists of ( Because 2 quarks cannot make baryon of 2, so a set of three quarks have to be used. --Mesons can be their own anti-particle (

baryon cannot.

Now let’s how these strange particles can be combined: For a neutron n: strangeness Quantum Number (QN): S = 0 , Q =0, it is composed of three quarks (udd): S=0+2*0=0, Q=2/3 +(-1/3) +(-1/3)=0. For a proton: p: strangeness QN: S=0, Q=1, It is composed of three quarks (uud): S= 0+2*0 =0, Q=2*2/3-1/3 = 1. Now we can explain the question why a neutron has its anti-particle, which is different from n.

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For Mesons: Ko: S=1, Q=0, (d, S=0+1=1, Q=-1/3 +1/3=0. We now can deduce the t according to the defaulted

of mesons and baryons there should be binations.

For mesons’ structure is ( e different quarks and anti-quarks can be arranged in two positions, there should be 3*3= 9 different combinations. Therefore we have found 9 mesons.

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However for baryons, (q1q2q3), there should be 3*3*3 different combinations, which means there should be 27 baryons, why there were only 8+9=17? It turned out that the other 10 baryons were found later. Now we can construct a picture of particle hierarchy.

We are in place to understand the so-called standard model of particles. 4.10. Standard model-- elementary particles We now know that the structure of newly discovered hadrons are composite particles by using 3 quarks and their anti-quarks. The investigation of particle physics revealed that In order to explain all of the structure of known particles, another 3 quarks and their anti-quarks has to be introduced, together with 6 leptons (means ‘small mass’ in Greek) particles. Everything in the universe is made from quarks and leptons. The following table shows a summary of the properties of these quarks and leptons.

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-- All quarks and leptons have antiparticle partners with all of the quantum numbers reversed, but with the same masses. Quarks behave differently from leptons. Let’s first discuss the properties of a) Leptons – small mass particles: L

Le

L

L

M (MeV/c2)

e-

1

1

0

0

0.5



1

0

1

0

106



1

0

0

1

1784

e

1

1

0

0

0.1-a few 10-6



1

0

1

0

0.1-a few 10-6



1

0

0

1

0.1-a few 10-6

It is worth noting that decay.

nd

re not elementary particles, because they can

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Charge: three of leptons have electrical charge and three of which do not. Decay: The heavier leptons,  and , are not found in ordinary matter at all, for when they are produced they very quickly decay, or transform, into lighter leptons. All anti-leptons have negative sign for all of the 4 lepton numbers. When heavy leptons decay into lighter lepton: --L, Le, Lu, L QNs must be conserved; --A particle and an antiparticle in the same family "cancel out" to make the total of them equal to zero. Which of the following lepton decaying is possible (assuming decaying particle is initially motionless, v =0) ?

Therefore this decaying is possible.

Because L: 0 1+0; and L : 1 2; Now try a tricky one:

L, L, Le, momentum are all conserved, Energy: m(e)...