Braibant S., Giacomelli G., Spurio M. Particles and Fundamental Interactions: An Introduction to Particle Physics
Подождите немного. Документ загружается.
x Contents
7.11 The Vector Mesons ................................................. 165
7.12 Strangeness and Isospin Conservation ............................ 167
7.13 The Six Quarks...................................................... 168
7.14 Experimental Tests on the Static Quark Model.................... 170
7.14.1 Leptonic Decays of Neutral Vector Mesons ............ 170
7.14.2 Lepton Pair Production .................................. 171
7.14.3 Hadron-Hadron Cross-Sections at High Energies ...... 172
7.14.4 Baryon Magnetic Moments ............................. 173
7.14.5 Relations Between Masses .............................. 175
7.15 Searches for Free Quarks and Limits of the Model ............... 177
8 Weak Interactions and Neutrinos......................................... 179
8.1 Introduction ......................................................... 179
8.2 The Neutrino Hypothesis and the ˇ Decay ........................ 180
8.2.1 Nuclear ˇ Decay and the Missing Energy .............. 180
8.2.2 The Pauli Desperate Remedy............................ 181
8.2.3 How World War II Accelerated the
Neutrino Discovery ..................................... 183
8.3 Fermi Theory of Beta Decay ....................................... 184
8.3.1 Neutron Decay ........................................... 185
8.3.2 The Fermi Coupling Constant from
Neutron ˇ Decay ........................................ 186
8.3.3 The Coupling Constant ˛
W
from Fermi Theory........ 187
8.4 Universality of Weak Interactions (I) .............................. 187
8.4.1 Muon Lifetime ........................................... 187
8.4.2 The Sargent Rule......................................... 189
8.4.3 The Puppi Triangle ...................................... 189
8.5 The Discovery of the Neutrino .................................... 190
8.5.1 The Poltergeist Project................................... 190
8.6 Different Transition Types in ˇ Decay............................. 194
8.6.1 The Cross-Section of the ˇ-Inverse Process ........... 197
8.7 Lepton Families ..................................................... 198
8.8 Parity Violation in ˇ Decays ....................................... 201
8.9 The Two-Component Neutrino Theory ............................ 204
8.10 Charged Pion Decay ................................................ 205
8.11 Strange Particle Decays ............................................ 208
8.12 Universality of Weak Interactions (II). The Cabibbo
Angle ................................................................ 211
8.13 Weak Interaction Neutral Current ................................. 213
8.14 Weak Interactions and Quark Eigenstates ......................... 215
8.14.1 The WI Hamiltonian and the GIM
Mechanism .............................................. 215
8.14.2 Hints on the Fourth Quark from WI Neutral Currents . 217
8.14.3 The Six Quarks and the Cabibbo–
Kobayashi–Maskawa Matrix ........................... 218
Contents xi
8.15 Discovery of the W
˙
and Z
0
Vector Bosons ...................... 220
8.16 The V-A Theory of CC Weak Interaction.......................... 222
8.16.1 Bilinear Forms of Dirac Fermions ...................... 222
8.16.2 Current–Current Weak Interaction ..................... 225
9 Discoveries in Electron-Positron Collisions .............................. 229
9.1 Introduction ......................................................... 229
9.2 Electron-Positron Cross-Section and the
Determination of the Number of Colors .......................... 231
9.2.1 The Process e
C
e
! !
C
.................... 232
9.2.2 The Color Quantum Number ........................... 232
9.3 The Discovery of Charm and Beauty Quarks...................... 234
9.3.1 Mesons with c,
c Quarks ............................... 234
9.3.2 The J= Resonance Properties ........................ 235
9.3.3 Mesons with b,
b Quarks ............................... 236
9.4 Spectroscopy of Heavy Mesons and ˛
S
Estimate ................ 237
9.5 The Lepton ........................................................ 238
9.6 LEP Experiments and Examples of Events at LEP ............... 239
9.6.1 The LEP Detectors ...................................... 239
9.6.2 Events in 4 Detectors at LEP .......................... 243
9.7 e
C
e
Collisions at E
cm
91 GeV. The Z
0
Boson ............... 248
9.7.1 The Z
0
Resonance ...................................... 248
9.7.2 Z
0
Total and Partial Widths ............................. 249
9.7.3 Measurable Quantities,
invis
and the Number
of Light Neutrino Families .............................. 251
9.7.4 Forward–Backward Asymmetries A
FB
................ 253
9.7.5 Multihadronic Production Model ....................... 256
9.8 e
C
e
Collisions for
p
s > 100 GeV at LEP2 ..................... 257
9.8.1 e
C
e
! W
C
;W
;Z
0
Z
0
Cross-Sections ............ 258
9.8.2 The W Boson Mass and Width ......................... 261
9.8.3 Measurement of ˛
S
...................................... 262
9.8.4 The Higgs Boson Search at LEP ........................ 262
10 High Energy Interactions and the Dynamic Quark Model ............ 265
10.1 Introduction ......................................................... 265
10.2 Lepton–Nucleon Interactions at High Energies ................... 265
10.3 Elastic Electron-Proton Scattering ................................. 269
10.3.1 Kinematic Variables ..................................... 269
10.3.2 Proton Form Factors ..................................... 270
10.4 Inelastic ep Cross-Section .......................................... 275
10.4.1 Partons in the Nucleons: Their Nature and Spin ....... 278
10.4.2 Electric Charge of the Partons........................... 280
10.5 Cross-Section for CC
N Interactions ............................ 282
10.5.1 Comparison with Experimental Data ................... 287
10.5.2 The Neutrino-Nucleon Cross-Section................... 288
xii Contents
10.6 “Naive” and “Advanced” Quark Models........................... 290
10.6.1 Q
2
-Dependence of the Structure Functions ............ 290
10.6.2 Summary of DIS Results ............................... 294
10.7 High Energy Hadron-Hadron Collisions........................... 296
10.8 Total and Elastic Cross-Sections at High Energy ................. 298
10.8.1 Elastic Differential Cross-Sections ..................... 298
10.8.2 Total Cross-Sections ..................................... 301
10.9 High Energy Inelastic Hadron Collisions at Low-p
t
.............. 302
10.9.1 Outline on High Energy Nucleus-Nucleus Collisions.. 303
10.10 The LHC and the Search for the Higgs Boson .................... 305
10.10.1 Higgs Boson Production in pp Collisions .............. 306
10.10.2 Higgs Boson Decays..................................... 308
10.10.3 Search Strategies at LHC ................................ 309
11 The Standard Model of the Microcosm .................................. 313
11.1 Introduction ......................................................... 313
11.2 Weak Interaction Divergences and Unitarity Problem ............ 314
11.3 Gauge Theories ..................................................... 316
11.3.1 Choice of the Symmetry Group ......................... 317
11.3.2 Gauge Invariance ........................................ 318
11.4 Gauge Invariance in the Electroweak Interaction ................. 322
11.4.1 Lagrangian Density of the Electroweak Theory ........ 323
11.5 Spontaneous Symmetry Breaking. The Higgs
Mechanism ......................................................... 325
11.6 The Weak Neutral Current.......................................... 330
11.7 The Fermion Masses................................................ 333
11.8 Parameters of the Electroweak Interaction ........................ 334
11.8.1 Electric Charge Screening in QED...................... 336
11.8.2 Higher Order Feynman Diagrams,
Mathematical Infinities and
Renormalization in QED ................................ 337
11.9 The Strong Interaction .............................................. 338
11.9.1 Quantum Chromodynamics (QCD) .................... 338
11.9.2 Color Charge Screening in QCD ....................... 341
11.9.3 Color Factors ............................................. 342
11.9.4 The Strong Coupling Constant ˛
S
...................... 343
11.10 The Standard Model: A Summary ................................. 343
12 CP-Violation and Particle Oscillations ................................... 347
12.1 The Matter-Antimatter Asymmetry Problem ...................... 347
12.2 The K
0
K
0
System ............................................... 348
12.2.1 Time Development of a K
0
Beam.
K
0
1
Regeneration. Strangeness Oscillations ............ 350
12.3 CP-Violation in the K
0
K
0
System ............................. 353
12.3.1 The Formalism and the Parameters of CP-Violation ... 354
Contents xiii
12.4 What is the Reason for CP-Violation? ............................ 358
12.5 CP-Violation in the B
0
B
0
System.............................. 360
12.5.1 Future Experiments ...................................... 364
12.6 Neutrino Oscillations ............................................... 364
12.6.1 The Special Case of Oscillations Between
Two Flavors ............................................. 365
12.6.2 Three Flavor Oscillations................................ 367
12.6.3 The Approximation for a Neutrino
with Dominant Mass..................................... 368
12.6.4 Neutrino Oscillations in Matter ......................... 370
12.7 Neutrinos from the Sun and Oscillation Studies................... 371
12.8 Atmospheric
Oscillations and Experiments .................... 376
12.8.1 Long Baseline Experiments ............................. 379
12.9 Effects of Neutrino Oscillations .................................... 381
13 Microcosm and Macrocosm ............................................... 385
13.1 The Grand Unification .............................................. 386
13.1.1 Proton Decay ............................................. 389
13.1.2 Magnetic Monopoles .................................... 390
13.1.3 Cosmology. First Moment of the Universe ............. 391
13.2 Supersymmetry (SUSY) ........................................... 392
13.2.1 Minimal Standard Supersymmetric Model
(MSSM) ................................................. 393
13.2.2 Supergravity (SUGRA). Superstrings................... 397
13.3 Composite Models ................................................. 397
13.4 Particles, Astrophysics and Cosmology ........................... 400
13.5 Dark Matter ......................................................... 403
13.6 The Big Bang and the Primordial Universe........................ 407
14 Fundamental Aspects of Nucleon Interactions .......................... 415
14.1 Introduction ......................................................... 415
14.2 General Properties of Nuclei ....................................... 417
14.2.1 The Chart of Nuclides ................................... 419
14.2.2 Nuclear Binding Energy ................................. 420
14.2.3 Size of the Nuclei ........................................ 421
14.2.4 Electromagnetic Properties of the Nuclei............... 424
14.3 Nuclear Models ..................................................... 424
14.3.1 Fermi Gas Model ........................................ 425
14.3.2 Nuclear Drop Model ..................................... 426
14.3.3 Shell Model .............................................. 429
14.4 Properties of Nucleon-Nucleon Interaction........................ 431
14.5 Radioactive Decay and Dating ..................................... 433
14.5.1 Cascade Decays .......................................... 434
14.6 Decay.............................................................. 436
xiv Contents
14.7 ˛ Decay.............................................................. 437
14.7.1 Elementary Theory of ˛ Decay ......................... 439
14.7.2 Lifetime Calculation of the
238
92
U Nucleus .............. 440
14.8 ˇ Decay ............................................................. 441
14.8.1 Elementary Theory of Nuclear ˇ-Decay................ 443
14.9 Nuclear Reactions and Nuclear Fission............................ 444
14.9.1 Nuclear Fission .......................................... 445
14.9.2 Fission Nuclear Reactors ................................ 447
14.10 Nuclear Fusion in Astrophysical Environments ................... 448
14.10.1 Fusion in Stars ........................................... 449
14.10.2 Formation of Elements Heavier than Fe
in Massive Stars.......................................... 451
14.10.3 Earth and Solar System Dating.......................... 454
14.11 Nuclear Fusion in Laboratory ...................................... 455
Appendix A ....................................................................... 459
A.1 Periodic Table [P08] ................................................ 460
A.2 The Natural Units in Subnuclear Physics .......................... 461
A.3 Basic Concepts of Relativity and Classical Electromagnetism ... 462
A.3.1 The Formalism of Special Relativity.................... 462
A.3.2 The Formalism of Classical
Electromagnetism ....................................... 464
A.3.3 Gauge Invariance of the Electromagnetism............. 466
A.4 Dirac Equation and Formalism ..................................... 467
A.4.1 Derivation of the Dirac Equation........................ 467
A.4.2 General Properties of the Dirac Equation............... 469
A.4.3 Properties of the Dirac Equation Solutions ............. 472
A.4.4 Helicity Operator and States ............................ 475
A.5 Physical and Astrophysical Constants [P08] ...................... 478
References......................................................................... 481
Index ............................................................................... 487
Chapter 1
Historical Notes and Fundamental Concepts
1.1 Introduction
Elementary particle physics deals with the search and the study of the ultimate
constituents of matter as well as of their interactions. Within common usage, the
term elementary particle is considered to be a synonym of the ultimate constituent
of matter. It is with such a conviction that the first scientists in this particular field of
physics have attributed the name of elementary particle to objects that are not really
as such: as the atom (which etymologically means indivisible in Greek) is in fact
quite divisible, the largest part of elementary particles (the protons for instance) are
also not truly elementary.
With the increase of experimental knowledge, the actual definition of the
elementary particle underwent an evolution: in the 1940s, it only applied to a few
submicroscopic “objects” that were thought of as new indivisible “atoms;” about
thirty years ago, it was instead attributed to a few tens of objects, without worrying
that they were indeed elementary. Currently, the term elementary particle denotes
some particles such as the electron (e
), the muon (
)andthetau(
)and
the corresponding neutrinos (
e
;
;
), which are globally called leptons,andthe
quarks. Free quarks were never observed as they are confined inside hadrons.This
term includes a stable object (the proton), several particles with relatively long
lifetimes (as the neutron and the
0
hyperon) and many resonances having very
short lifetimes.
The quarks and leptons, currently considered to be the ultimate constituents of
matter, are fermions, that is, half-integer spin particles; they can be thought as matter
particles. Fermions obey the Fermi-Dirac statistics.
A description of the structure of matter cannot be complete without considering
the interactions (forces) that “join” the particles and more generally that regulate
the interactions amongst them. The strong, weak, electromagnetic and gravitational
interactions were identified. Each interaction has its own quantum field, namely,
the force particles that relay the interaction. These are particles with integer spin,
called bosons as they obey the Bose–Einstein statistics. The photons mediate
S. Braibant et al., Particles and Fundamental Interactions: An Introduction to Particle
Physics, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-94-007-2464-8
1,
© Springer Science+Business Media B.V. 2012
1
2 1 Historical Notes and Fundamental Concepts
Table 1.1 Fundamental fermions and bosons in the standard model of the
microcosm
Fermions Bosons
u
d
c
s
t
b
Quarks Fundamental
Interactions
Mediators
e
e
Leptons Strong
Electromagnetic
Weak
8 gluons
W
C
, W
, Z
0
First
family
Second
family
Third
family
Gravitational Graviton
Higgs Boson H
0
the electromagnetic interaction, the W
C
, W
and Z
0
vector bosons the weak
interaction, the eight gluons the strong interaction and the hypothetical graviton
the gravitational interaction. The bosons must be included in the lists of elementary
particles and ultimate constituents.
It should be noted that for every fermion exists an antifermion, that is, an
antiparticle having the same mass and spin of the corresponding particle, though
with opposite electric charge and magnetic dipole moment.
Currently, the stable particles are: the photon , the neutrinos and the antineu-
trinos, the electron e
, the positron e
C
, the proton p and the antiproton p; all the
others are unstable. The six leptons (electron, muon, tau and their neutrinos) and the
correspondingsix antileptons, the six quarks (d, u), (b, t) (s, c) and the corresponding
six antiquarks are considered to be the ultimate fermionic constituents of matter.
We will also see that quarks (and antiquarks) appear in three different colors
(and anticolors). To these ultimate fermionic constituents, the force carriers of
the fundamental interactions, the vector bosons, must be added (see Table 1.1).
To further complete the picture, one needs to introduce the scalar (spin 0) Higgs
boson. The Higgs boson has not yet been observed; it is thought to be the main
ingredient in the mechanism that attributes mass to the particles.
Only the electron, the proton and the neutron directly enter the composition of the
stable terrestrial matter. The photon is created when transitions occur amongst two
states. In the radioactive decays, particles and antiparticles (such as the positron)
are produced. Any particle can be created in collisions between two high energy
particles thanks to a process of transformation of energy in mass. The fact that there
are so many particles and that so few constitute the present stable matter cannot be
currently explained. It is also unclear as to why the ultimate fermionic constituents
appear in three families, each constituted of two leptons and two quarks, and each
being a replica of the same type, see Table 1.1. The first family includes
e
, e
, u,
d ; the second one includes
,
, c, s; the third one includes
,
, t, b. For each
fermion of every family, one has the corresponding antifermion (antiparticle).
In order to probe structures with ever smaller dimensions, one must study high
energies collisions between particles. It is therefore necessary to have powerful
accelerators. The physics laws that describe the collisions between two particles
1.2 The Discovery of Particles 3
become simpler at high energies in the sense that the laws acquire a larger degree of
mathematical symmetry. Besides, at high energies one has unification of forces:
the electromagnetic and weak unification (electroweak interaction) has already
been verified and models exist for the Great Unification (GUT) of the electroweak
interaction with the strong one; some models attempt to describe a super unification.
We may be close to a deeper level of comprehension of the “building blocks” of
the forces and of the laws of the microcosm. In addition, we have became aware
that laws governing the structure of the matter are connected to the structure of the
Universe and its evolution following the Big Bang.
Regarding the study of the interactions between constituents, the fundamental
notions of quantum mechanics and possibly of its mathematical formalism are
required. The terminology and some concepts may appear complicated initially,
and thus a second reading is recommended for a better understanding. Finally, one
should notice that the terminology used for classifying the observed particles was
historically introduced in a rather chaotic way.
1.2 The Discovery of Particles
At the beginning of the 1930s (when Hitler was entering into power in Germany and
after the great Wall Street stock market crash), only the proton, electron and photon
were known. Nevertheless, it was known that an ionizing radiation was constantly
bombarding the terrestrial surface. In 1912, Victor Hess (Nobel laureate in 1936)
showed by using aerostatic balloons that the level of ionizing radiation increased
with increasing altitude. Therefore, the measured radiation could not be of terrestrial
origin. This radiation was called cosmic radiation. In the following years, it became
more evident that the particles present in this radiation could be divided into two
categories: those coming from the extraterrestrial space (the primary cosmic rays)
and the secondary component produced by the interaction of primary cosmic rays
with the terrestrial atmosphere, that is, the secondary cosmic rays.
The flow of primary cosmic rays (CR) is about 1,000 cm
2
s
1
and is mainly
constituted of protons (85%), the nuclei of helium (10%) and heavier nuclei
(1%). Electrons only account for 2%. Starting in the 1930s, the experimental
techniques for the detection and measurement of some physics quantities (e.g.,
electric charge, mass, lifetime) of particles present in the secondary cosmic rays
started to become more refined. Particularly, Patrick Blackett (Nobel laureate in
1948) used a cloud chamber inside a magnetic field that bent the trajectory of
charged particles. For a long time, particle physics was identified with that of
the cosmic rays. This superposition remained well after the end of the Second
World War, when particle accelerators started to be developed. With the advent
of accelerators, the paths of particle physics and that of the cosmic rays (which
later became that of astroparticle physics) disentangled, though they have actually
reconnected in recent years (as we will see in Chaps. 12 and 13).
Using Blackett’s experimental techniques, in 1932, Anderson (Nobel laureate
in 1936) discovered a particle with the same mass of the electron, though with
4 1 Historical Notes and Fundamental Concepts
opposite electric charge. It was the antielectron, that is, the antiparticle predicted
by the quantum theory of the electron developed a few years before by Dirac
(Nobel laureate in 1933). Immediately afterwards, in 1934, James Chadwick (Nobel
laureate in 1935) experimentally identified a particle with a mass similar to that of
the proton, though without electric charge: the neutron.
In 1937, Anderson together with Neddermeyer again discovered a particle of
intermediate mass between that of the proton and that of the electron: they called
this new particle the meson. For some time, it was thought that this particle was the
mediator particle of the interactions between protons and neutrons for the formation
of nuclei. A theoretical model created by Hideki Yukawa (Nobel laureate in 1949)
predicted the existence of a particle with a mass very close to that of the just
discovered meson. Nevertheless, actually during World War II in Rome, Conversi,
Pancini and Piccioni showed in a famous experiment that the meson of Anderson
and Neddermeyer (nowadays called the muon) could not be the particle predicted
by Yukawa. Even if the theory of Yukawa (as we will see later) does not properly
describe the physics of nuclei, the predicted particle (the pion) was discovered
in 1947 by Lattes, Occhialini and Powell in secondary cosmic rays using nuclear
emulsions (i.e., sophisticated photographic films) at high altitudes.
Nonetheless, in 1947, in the interactions of cosmic rays in a cloud chamber with
magnetic field, particles with a particularly strange behavior were discovered. They
were thus named strange particles. As we will see, particles containing a quark of
mass higher than that of the quarks that compose protons and neutrons had just been
discovered (this was obviously understood only a few years later). Finally, Pauli at
the beginning of the 1930s had hypothesized the existence of an elusive particle
without mass and electric charge: the neutrino. However, one had to wait until 1954
to experimentally observe it (thanks to the advent of nuclear reactors).
With the advance of accelerators, the discovery of many new particles was
made possible; most of them are subject to the strong interaction and are named
hadrons. The fermionic particles that do not strongly interact were named leptons.
Etymologically, the term lepton means a particle of small mass. However, now that it
includes the
, heavier than the proton, the term lepton simply denotes the fermions
that do not strongly interact. This is yet another example of the typical contradiction
between the etymology of the word and the latest results obtained in this field of
research.
The development of particle physics following World War II has been amazing,
with continuous surprises, quite a collection of discoveries and a lot of system-
atic work. For instance, without pretension of completeness: the discovery of
the antiproton (1955), the classification of the hadrons in terms of quarks; the
discovery of the parity violation in the weak interaction. After the discovery of
the two types of neutrinos, electronic (1956) and muonic (1963), followed the
discovery of the hadronic resonances and the scheme of classification based on
SU(3) (1960s and 1970s). Furthermore, the list of developments continues with
the discovery of the hyperon ˝
with strangeness S D3 (1963), the evidence
for quarks and gluons (1960s), the increasing with energy of the total hadronic
cross-sections (1971–1974), the discovery of the neutral current weak interaction,
1.3 The Concept of the Atom and Indivisibility 5
the quark c (1974) and b (1976), the electroweak unification (1970s and 1980s),
the W
C
,W
and Z
0
vector bosons (1983), the quark t (1995), and the neutrino
oscillations (1998).
There was a continuous exchange between theories and experiments. Starting
from simple models to more elaborated ones, complete theories were finally
reached. In the experimental field, a rapid technological progress took place. The
first experiences were conducted by only a few physicists with small accelerators,
using less than five counters with simple “homemade” electronics. The actual
experiments are performed with circular accelerators with radius measuring several
kilometers (or linear accelerators several kilometers long), detectors with thousand
of counters, chambers of various types, elaborated electronics and high-speed
computers. Because of these huge dimensions, the principal experiments involve
hundreds and sometimes thousands of physicists. The ramifications of such research
are sometimes formidable: from the applications and uses of accelerators in the
medical field, to the birth at the CERN of the World-Wide Web (WWW), i.e., the
system of interlinked hypertext documents accessed via the Internet.
1.3 The Concept of the Atom and Indivisibility
As previously mentioned, towards the end of the nineteenth century, the word
“atom,” i.e., indivisible, was attributed to objects that were actually quite divisible.
The same error was repeated for many “elementary particles.” Now, one speaks
instead of the “ultimate constituent,” knowing that perhaps they will not be as such.
In fact, some physicists already speak about subconstituents!
One must wonder why so many errors have been made in attributing the title
of indivisibility to objects that did not deserve it. One may also ask if the concept
of an indivisible object is a relative concept: a concept that depends on particular
environmental conditions, for example, on the temperature.
Let us illustrate this evolutionary concept with an ideal experiment. We
consider a gas of particles placed in a container, for example, nitrogen
(N
2
) gas in a room. To the environment pressure of one atmosphere and
to the temperature of 20
ı
C, equal to 293 K, the nitrogen molecules can be
considered as indivisible objects, the Democritus atoms. In fact, the gas can
be thought of as constituted of many little balls, the molecules, of small
dimensions (some 10
8
cm) with respect to the volume of the room, so that they
can be considered almost point-like. These molecules move in a disordered
way, each of them independently from the others. The mean velocity of the
molecules hvi is related to the temperature according to