LUẬN VĂN Introduction to Particle physics

K54-H.P.HUS Page 1 Introduction The history of the physics of the infinitely small is largely the history of the uncovering of successive layers of structure, from big to small and smal

Acknowledgment

I am very glad and fortunate that I had Prf Dr Ha Huy Bang as my supervisor During the process in writing this thesis, I received a lot of his kindness and help He taught me almost everything, how to compute an interaction process both in general and detail, how to display a thesis or simply, how to search necessary documents He also gave many useful documents which I could not find by myself I am very thanks his about that

I also send my thanks to Asso Prf Dr Nguyen Anh Ky who taught me about cosmology and inspired me to Dark Matter which is the soul of this thesis Cosmology is really an interesting field and it owns have many mysterious things And, he lead me step by step how to understand universe

In addition, in the past time, I do not know how I could go on smoothly without advices of Mrs Huong Thanks for her time that she spent with me in the department lab, her guides, her encourages and her enthusiasm

I want to send my big thanks to all teachers in the department of theoretical physics who made the good conditions for finishing my thesis

Finally, I really thank you all my friends, especial my best friends who side by side me and help me pass over the past hard time

Due to the limit of time, knowledge, this thesis cannot avoid some mistakes I hope to receive your comments for the perfect complete of this work Thanks all so much

August 26, 2013 Student Nguyen Thi Hien

Contents

Introduction 1

Chapter 1: Introduction to Particle physics 3

1.1 What is particles physics? 3

1.2 Discovering the particle world 4

1.3 The Standard Model 5

Chapter 2: Dark Matter 7

2.1 A brief understanding about Dark Matter 7

2.1.1 What is dark matter? 7

2.1.2 The evidence for dark matter 8

2.1.3 Type of dark matter 9

2.1.4 Particles candidate for dark matter 9

2.1.5 Detecting for dark matter 10

2.2 Neutrinos 11

2.2.1 Neutrinos – What are they? 11

2.2.2 Where are they coming from? 12

2.2.3 Interactions and properties 12

2.2.5 Direct searches for neutrino mass 15

2.2.6 Neutrino oscillation experimental techniques 18

Chapter 3: Some interactions of neutrinos 20

3.1 Neutrino – Electron scattering 20

3.2 Neutrino-electron scattering with U-particle 8

Conclusion 13

Appendix 14

Appendix A Dirac matrices 14

Appendix B Trace of the product of matrices 14

References 16

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Introduction

The history of the physics of the infinitely small is largely the history of the uncovering of successive layers of structure, from big to small and smaller The question of what constitutes an elementary particle in fact is not static but evolves with time, changing in step with technological advances, or precisely with the growth in the power of the sources of energy that become available to the experimenter The higher the energy of the particle beam used

to illuminate or probe the object under study is, the shorter are the wavelengths associated with the incoming particles and the finer the resolutions obtained in the measure Thus, it is successively discovered that matter is built up from molecules; that the molecules are composed of atoms; the atoms of electrons and nuclei; the nuclei of protons and neutrons[3]; and the protons and neutrons of quarks As the power of the modern particle accelerators keeps on increasing, it has become possible to accelerate particles

to higher and higher velocities, to attain resolutions surpassing 10-6centimeters and to observe more violent, collisions between particles, which have revealed all the wonders of the subatomic universe, not only the presence of ever finer structure levels, but also in the existence at every level

of new particles of ever grater masses Particle physics has now become synonymous with high-energy physics[3]

Electron was discovered in 1895 opening the beginning of seeking fundamental particles era Or by theory, the physicist Dirac predicted the existence of positron in 1928 and in the 1932, it was detected In addition, in

1932, the first time, by experiment, Chadwick observed neutron directly[4] And over many years later, a numerous particles were predicted by theory and demonstrated by evidence All of it creates a whole picture of particle physics

Life is searches and in the infinite universe the knowledge of human about it just like a drop in the whole huge sea Over many years, human still

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keeps looking for and finding out the universe But, we just understood a mini part of it We just “see” about 4 percent of matter in the universe, the rest…stills in the “dark”, so we count it as dark matter(96 percent!)

In fact, theory is a useful method to predict new particles and is the theoretical basic to set up the experiment for demonstrating the true of prediction or not Neutrino electron, for example, it was predicted by theory

in 1930 by Wolfgang Pauli and was demonstrated in 1956 by Reins[5] By this way, in this thesis, I’ll postulate some interaction process of neutrinos with hoping to understand more about dark matter which is a mysterious issue

in cosmology

This thesis includes three main parts:

*Introduction: introduce to a preview of particle physics and propose of this thesis

*Three chapters:

- Chapter 1: Introduction to particle physics

- Chapter 2: A brief understanding about Dark Matter

- Chapter 3: Neutrino-Electron scattering

*Conclusion: Summary some result of computing process and comments

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Chapter 1: Introduction to Particle

physics

The physics term which deals with the interactions of elementary articles at high energies, is an important component of cosmological models

of the early universe, when the universe was dominated by radiation and its average energy density was very high Because of this, pair production, scattering processes and decay of unstable particles are important in cosmology

As a thumb rule, a scattering or a decay process is cosmologically important in a certain cosmological epoch if its relevant time scale is smaller

or even to the time scale of the universe expansion, which is 1/H with H being the Hubble constant at that time This is roughly equal to the age of the universe at that time

Cosmological observations of phenomena such as the cosmic microwave background and the cosmic abundance of elements, together with the predictions of the Standard Model of particle physics, place constraints on the conditions of the early universe The success of the Standard Model at explaining these observations provides a confirmation of its validity outside

of laboratory conditions In addition, phenomena extrapolated from cosmological observations, such as dark matter and CP-violation, suggest a need for physics that goes beyond the Standard Model

Protons, electrons, neutrons, neutrinos and even quarks are often featured in news of scientific discoveries All of these are tiny sub-atomic particles too small to be seen even in microscopes While molecules and atoms are the basic elements of familiar substances that we can see and feel,

we have to "look" within atoms in order to learn about the "elementary" subatomic particles and to understand the nature of our Universe The science

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of this study is called Particle Physics, Elementary Particle Physics or sometimes High Energy Physics (HEP)

Atoms were postulated long ago by the Greek philosopher Democritus, and until the beginning of the 20th century, atoms were thought to be the fundamental indivisible building blocks of all forms of matter Protons, neutrons and electrons came to be regarded as the fundamental particles of nature when we learned in the 1900's through the experiments of Rutherford and others that atoms consist of mostly empty space with electrons surrounding a dense central nucleus made up of protons and neutrons

The science of particle physics surged forward with the invention of particle accelerators that could accelerate protons or electrons to high energies and smash them into nuclei — to the surprise of scientists, a whole host of new particles were produced in these collisions

By the early 1960s, as accelerators reached higher energies, a hundred

or more types of particles were found Could all of these then be the new fundamental particles? Confusion reigned until it became clear late in the last century, through a long series of experiments and theoretical studies, that there existed a very simple scheme of two basic sets of particles: the quarks and leptons (among the leptons are electrons and neutrinos), and a set of fundamental forces that allow these to interact with each other By the way, these "forces" themselves can be regarded as being transmitted through the exchange of particles called gauge bosons An example of these is the photon, the quantum of light and the transmitter of the electromagnetic force we experience every day (We should state here that all these sets of particles also include their anti-particles, or in plain language what might roughly be called their complementary opposites These make up matter and anti-matter.)

Today, the Standard Model is the theory that describes the role of these fundamental particles and interactions between them And the role of Particle Physics is to test this model in all conceivable ways, seeking to discover

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whether something more lies beyond it Below we will describe this Standard Model and its salient features

All of the known matter in the Universe today is made up of quarks and leptons, held together by fundamental forces which are represented by the exchange of particles known as gauge bosons

strange-quark mass = 0.16

(t) top-quark mass = 186 (b)

bottom-quark mass = 5.2

Charge = +2/3

Charge = -1/3

(ντ) tau-neutrino mass ~ 0 (τ ) tau mass = 1.9

Charge

= 0

Charge = -1

Forces and Interactions

Now we must tackle the fundamental forces or interactions among the quarks and leptons: Gravity, the Weak Force, Electromagnetism, and the Strong Force Of these, our everyday world is controlled by gravity and electromagnetism The strong force binds quarks together and holds nucleons (protons & neutrons) in nuclei The weak force is responsible for the radioactive decay of unstable nuclei and for interactions of neutrinos and other leptons with matter

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Force

Relative Strength

Gauge Boson

Mass (rel to proton)

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Chapter 2: Dark Matter

TABLE II: The total number of scatters within a human body per year for the given WIMP masses and WIMP-proton scattering cross-sections The CoGeNT, CRESST, and DAMA benchmarks are those that best fit the data for the respective experiments (CRESST has two maximum likelihood points); these points are all strongly disfavored by the null results

of CDMS and XENON in the standard framework used in this analysis The XENON benchmarks are compatible with the null results of CDMS and XENON We assume a human mass of 70 kg and identical couplings to the proton and neutron.[10]

Most of the matter in the universe is dark Without dark matter, galaxies and stars would not have formed and life would not exist It holds the universe together What is it?

2.1 A brief understanding about Dark Matter

2.1.1 What is dark matter?

Today, dark matter is one of the biggest problems in cosmology The dark matter problem has been with us since 1930s, and was first postulated in

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the 1930s by Dutch astronomer Jan Oort and Swiss astrophysicist Fritz Zwicky[7] Calculations show that it is five times more abundant in the universe than standard matter, but since it doesn’t emit, absorb, or reflect light, it is very tricky to spot In fact, its existence can only inferred from the gravitational force it exerts on its surroundings By the early 1980’s, better cosmological technology enabled scientists to collect experimental evidence about the rotation of spiral galaxies[6] However, the orbital velocities measured did not obey Kepler’s law in the relative between orbital velocity and mass of planet There is not enough visible mass in the galaxy to account for the velocities So that, there must existence another form of matter and we call it is Dark Matter They find out that dark matter constitutes over ninety percent of the matter in the universe including 74% dark energy and 22% dark matter [2] However it has never been directly detected In fact, it does not respond to the strong or electromagnetic force because it does not emit or absorb light Dark matter interacts with the ordinary matter only weakly and gravitationally

2.1.2 The evidence for dark matter

* Evidence for dark matter in spiral galaxies

In spiral galaxies like the Milky Way, we derive the gravitational mass from observing the motions of stars and gas clouds in the disk as they orbit the center The rotation curve of a galaxy shows how the velocity of stars around the center varies as the distance from the center increases Most spiral galaxies show flat rotation curves out as far as we can trace them, even where

no more stars are visible Therefore we conclude that the gravitational mass is more than 10 times more massive than the luminous mass

*Evidence for dark matter in clusters of galaxies

In clusters of galaxies, we derive the gravitational mass by measuring the orbital motions of the member galaxies Since the galaxies in a cluster are roughly at the same distance from us, we can interpret any spread in their red-shifts as orbital motion around the center of the cluster; it might amount to more than 1000 km/sec! By measuring the red-shifts of lots of galaxies in the

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cluster, we can calculate the gravitational mass required to keep the galaxies

in orbit (rather than escaping) This gravitational mass then can be compared

to the luminous mass contributed by the galaxies plus that contributed by the X-ray gas

2.1.3 Type of dark matter

The main three types of dark matter[8] are:

- Hot dark matter (HDM) – neutrinos with rest masses of the order of few eV

- Cold dark matter (CDM) – supersymmetric particles with masses ~ 100 GeV

or axions with ma ~ 10-5 eV

- Ultra – cold (vacuum – like) matter – the cosmology constant

2.1.4 Particles candidate for dark matter

- Weakly Interacting Massive Particle: It is thought be a kind of

particle made in the big bang Their general name is “Weakly Interacting Massive Particle” or WIMP This key features of this particle class are exactly

as described: interactions around or near typical weak-force interactions (the fine-structure constant α near the weak – scale particle masses near the weak scale (m ~ 100GeV in particle physic units, similar to the mass of a silver atom)

- Axions: Axions claim to fame is that they emerge out of a solution to

the strong – CP problem in particle physics The new field’s fluctuations about the new vacuum of the broken theory are axions, the pseudo-Nambu-Goldstone bosons of the broken theory Axions are some ways less natural than WIPMs because it is tricky to get their commoving number densitu to match the observed dark-matter density There are a number of axions production mechanisms (all of which must be present to some extent), but the preferred way to produce dark-matter axions is through non-thermal coherent oscillations of the axions field near the QCD phase transition In that case, axions are light and are born with not momentum

- Gravitinos: The supersymetric partner of the graviton, may be dark

matter Depending on exactly how supersymmetry is broken, the gravitino

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could be anywhere in the mass range of eV to TeV, although masses < KeV are disfavored because they wash out too much small-sacle structure Because these massive gravitinos are born out of decays at relatively high momentum, they can smear out primordial density perturbations on small scales Gravitinos are not nearly as beloved as WIMPs as dark-matter candidates because of the difficultly of getting the abundance just right and because they are much harder to detect using conventional methods There are other dark-matter candidates that are plausible and solve some other problems in physics, although they to not provide quite the same bargain-hunting thrill of the previously discussed candidates

- Sterile neutrinos: Sterile neutrinos are neutrinos that do not interact

electroweakly Since mass eigenstates are not the same as the electroweak eigenstates(νe, νµ, ντ), sterile neutrinos may fix with electroweak or active, neutrinos Sterile neutrinos have been proposed in a number of contexts; they can be a mass – generating mechanism for the active neutrinos, they can simply be the right-handed counterparts to the active species, or explain certain neutrino-experiment anomalies As dark matter, sterile neutrinos may

be created in the early universe in a variety ways Depending on their creation mechanism, they can be constrained ny their effects on smaller-scale structure

in the Universe Because sterile neutrinos mix with active neutrinos, they have a small decay probability to an active neutrino and a photon The simplest model of sterile neutrino dark matter (Dodelson-Windrow neutrinos) are excluded by a combination of small-scale structure observations and non-detections of X-rays from galaxies

2.1.5 Detecting for dark matter

Methods of detecting dark matter

Direct and indirect detection methods are used to detect dark matter, which cannot be directly observed since it does not emit radiation The former include simultaneous light and heat detection (such as the technique used by the scintillating bolometers), simultaneous heat and ionisation detection, and simultaneous light and ionisation detection, such as research into distinctive

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signals (the most famous being the search for an annual modulation in the dark matter signal caused by the orbiting of the Earth

There are also indirect detection methods, where, instead of directly

seeking the dark matter particles, researchers try to identify other particles, (neutrinos, photons, etc.), produced when the Universe's dark matter particles are destroyed

2.2 Neutrinos

2.2.1 Neutrinos – What are they?

Certainly one of the most exciting areas or research at present is

neutrino physics Neutrinos are fantastically numerous in the universe and so

to understand the universe we must understand neutrinos

“Neutrinos, they are very small

They have no charge and have no mass

And do not interact at all.”

_Cosmic ball, John Updike, 1963_

In fact, neutrinos are subatomic particles produce by the decay of radioactive elements and are elementary particles that lack a charge It was first postulated by Wolfgang Pauli in 1930 to save conversation of energy[5]

in beta decay Because of their "ghostly" properties, the first experimental detection of neutrinos had to wait until about 25 years after they were first discussed In 1956 Clyde Cowan, Frederick Reines, F B Harrison, H W Kruse, and A D McGuire published the article "Detection of the Free Neutrino: a Confirmation" in Science, a result that was rewarded with the

1995 Nobel Prize

In 1962 Leon M Lederman, Melvin Schwartz and Jack Steinberger showed that more than one type of neutrino exists by first detecting interactions of the muon-neutrino When a third type of lepton, the tau, was discovered in 1975 at the Stanford Linear Accelerator, it too was expected to have an associated neutrino First evidence for this third neutrino type came from the observation of missing energy and momentum in tau decays

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analogous to the beta decay that had led to the discovery of the neutrino in the first place The first detection of actual tau neutrino interactions was announced in summer of 2000 by the DONUT collaboration at Fermilab, making it the latest particle of the Standard Model to have been directly observed

2.2.2 Where are they coming from?

From what we know today, a majority of the neutrinos floating around were born around 15 billion years ago, soon after the birth of the universe Since this time, the universe has continuously expanded and cooled, and neutrinos have just kept on going Theoretically, there are now so many neutrinos that they constitute a cosmic background radiation whose temperature is 1.9 degree Kelvin (-271.2 degree Celsius) Other neutrinos are constantly being produced from nuclear power stations, particle accelerators, nuclear bombs, general atmosphere phenomena, and during the births, collisions, and deaths of stars, particularly the explosions of supernova

2.2.3 Interactions and properties

Several properties of neutrinos have been measured:

The classic experiment of Wu et al.[9] in 1957 determined that the weak interaction maximally violates parity conservation Applying this result

to massless neutrinos leads to the condition that neutrinos must be fully polarized with a helicity of +1 or –1 In 1958, an experiment by Goldhaber et al.[9] measured the helicity of the neutrino and determined that only left-handed neutrinos (spin anti-parallel to neutrino direction) participate in the weak interaction;

Experimental results indicate that neutrinos observe lepton number conservation, that is they are always associated with their like-flavour charged lepton;

Studies of the Z boson line width at LEP and SLC have determined that there are only three neutrino species with standard couplings to the Z and masses less than 45 GeV/c2 [9] Neutrinos with non-standard (much weaker)

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couplings, so-called sterile’ neutrinos, could exist in addition to the three standard species

2.2.4 Neutrino mass

Dirac or Majorana Neutrino?

A neutral fermion may exist either as a Dirac particle (fermion

antifermion) or as a Majorana particle (fermion  antifermion) For a Dirac fermion (neutral or charged), the mass term is

If the neutrinos are of the Majorana type, even in the absence of right- handed components, we can build a mass term by using the antiparticle which

is identical to its conjugate, only with opposite chirality Indeed, contrary to charged fermions, the neutrino and the antineutrino, being charge less , can be self-conjugated vM  vM c They are called the Majorana neutrino vM

To each fermionic field  there corresponds the field of its antiparticle, denoted by  C, obtained with the help of the charge conjugation operator C =i  2 0 We have C  C C  1  i   2 0 T  i  2 * The field of

a fermion F is  and the field of its antifermion F is C

While for a charged fermion m  is the only possible mass term, for a neutral fermion there are other possibilities In addition to the standard term

 , the terms    C C, C and Care equally valid The first  C Cis equivalent to  , but the last two,  C and C, may be written respectively as  C L L   C R R and  L L C   R R C Indeed

The existence of Majorana neutrinos implies that their interactions violate the leptonic number L Since vMis (   C) / 2 , the weak charged current connecting the electron to the Majorana neutrino contains both L  e 1terms The most spectacular manifestation of vM would be the neutrinoless double  -decay of nuclei N Z1( )  N (2 Z  2) e   e

(Fig.3a), denoted by  0v The initial state has zero leptonic quantum number (Le=0), while the final state with two electrons has Le = 2 In   0v, the Majorana neutrino vMemitted by n  p  e  vM can be absorbed by the second neutron n to become p   e This is because vM does not have a well-defined lepton number; when emitted by n, it has Le = -1 and when reabsorbed by n, it has Le = +1

On the other hand, with the Dirac neutrino for which the leptonic

N Z  Z   e  e  v  v (Fig 3b), referred to as  2v, can only occur with two antineutrinos ve emitted together with two electrons Unlike the VM, the Dirac V e emitted in n  p  e  v cannot be absorb.ed by n to become p   e

mass is too small (through the vMpropagator effect), then   0vmay still escape observation

Fig.1 (a) Double neutrino less   0vdecay by Majorana neutrino; (b) double   2vdecay by Dirac neutrino

2.2.5 Direct searches for neutrino mass

A direct measurement of neutrino mass can be performed by studying decay processes that involve neutrinos If neutrinos possess mass, the decay kinematics will be different from the massless case and could lead to

m that are negative and there are some apparent systematic effects associated with the data In particular, the Troitsk group observes a bump-like structure near the end-point which changes position over time These uncertainties mean that it is difficult to produce a definitive limit on the electron neutrino mass using this technique, although the two groups feel that if the electron neutrino had a mass of 25 eV/c2 then they should be able to observe a clear signal above the systematic effects

An entirely independent method of obtaining a limit on the electron neutrino mass was obtained by analysing the time structure of electron neutrinos detected in the Kamiokande and IMB water Cerenkov detectors from the recent supernova SN1987A If the electron neutrino has a finite mass, the propagation time from the supernova core to the Earth will be correlated with the neutrino energy since high energy neutrinos will be observed sooner than those of low energy (the mean neutrino energy is approximately 15 MeV) By analysing the time structure of the 11 neutrino interactions that were observed in Kamiokande [9] and the 8 interactions recorded by IMB [9] over a period of ten seconds, Bahcall and Glashow have obtained a conservative upper limit on the electron neutrino mass of 11 eV/c2 [9]

Limits on the mass of the vare obtained by studying the following tau decays:

5 v, 3 v

        These decays are chosen to minimise the amount of phase space available to the tau neutrino A limit on the neutrino mass is obtained by reconstructing the invariant mass of the hadronic system The experiment that currently sets the most stringent limit on the mass of the tau neutrino is the ALEPH experiment at LEP which sets an upper limit of 23.1 MeV/c2 at 90% C.L [9]

Neutrino masses also have consequences for big-bang cosmology Over the past 60 years, a number of measurements have led to the conclusion that a large fraction (between 90 and 99%) of the mass in the universe is in the form

of non-luminous, or dark, matter Bounds placed by nucleosynthesis limit the baryonic content of dark matter to 10% However, neutrinos were prodigiously produced in the aftermath of the big-bang and if they possess a small non-zero mass, they could constitute a significant fraction of the dark matter in the universe In order to prevent an overclosed universe (i.e Ω≥1) then the sum of all neutrino masses must satisfy the following relationship [9]:

2 , ,