CONTENTS 5
8.10 broken symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
8.11 Gauge symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
9 Symmetries of the theory of strong interactions 67
9.1 The first symmetry: isospin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
9.2 Strange particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
9.3 The quark model of strong interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9.4 SU(4), . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
9.5 Colour symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
9.6 The feynman diagrams of QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
9.7 Jets and QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
10 Relativistic kinematics
75
10.1 Lorentz transformations of energy and momentum . . . . . . . . . . . . . . . . . . . . . . . . . 75
10.2 Invariant mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
10.3 Transformations between CM and lab frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
10.4 Elastic-inelastic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
10.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 CONTENTS
Chapter 1
Introduction
In this course I shall discuss nuclear and particle physics on a somewhat phenomenological level. The mathe-
matical sophistication shall be rather limited, with an emphasis on the physics and on symmetry aspects.
Course text:
W.E. Burcham and M. Jobes,
Nuclear and Particle Physics
, Addison Wesley Longman Ltd, Harlow, 1995.
Supplementary references
1. B.R. Martin and G. Shaw,
Particle Physics, John Wiley and sons, Chicester, 1996. A solid book on
particle physics, slighly more advanced than this course.
2. G.D. Coughlan and J.E. Dodd, The ideas of particle physics, Cambridge University Press, 1991. A more
hand waving but more exciting introduction to particle physics. Reasonably up to date.
3. N.G. Cooper and G.B. West (eds.), Particle Physics: A Los Alamos Primer, Cambridge University Press,
1988. A bit less up to date, but very exciting and challenging book.
4. R. C. Fernow,
Introduction to experimental Particle Physics
, Cambridge University Press. 1986. A good
source for experimental techniques and technology. A bit too advanced for the course.
5. F. Halzen and A.D. Martin,
Quarks and Leptons: An introductory Course in particle physics
, John Wiley
and Sons, New York, 1984. A graduate level text book.
6. F.E. Close, An introduction to Quarks and Partons, Academic Press, London, 1979. Another highly
recommendable graduate text.
7. The course home page:
http://walet.phy.umist.ac.uk/P615/ a lot of information related to the
course, links and other documents.
8. The particle adventure: http://www.phy.umist.ac.uk/Teaching/cpep/adventure.html. A nice low level
introduction to particle physics.
7
8 CHAPTER 1. INTRODUCTION
9
10 CHAPTER 2. A HISTORY OF PARTICLE PHYSICS
Chapter 2
A history of particle physics
2.1 Nobel prices in particle physics
1903 BECQUEREL, ANTOINE HENRI, France,
´
Ecole Polytechnique, Paris, b. 1852, d. 1908:
”in recognition of the extraordinary services he
has rendered by his discovery of spontaneous
radioactivity”;
CURIE, PIERRE, France, cole municipale de
physique et de chimie industrielles, (Municipal
School of Industrial Physics and Chemistry),
Paris, b. 1859, d. 1906; and his wife CURIE,
MARIE, n´ee SKLODOWSKA, France, b. 1867
(in Warsaw, Poland), d. 1934:
”in recognition of the extraordinary services
they have rendered by their joint researches on
the radiation phenomena discovered by Profes-
sor Henri Becquerel”
1922 BOHR, NIELS, Denmark, Copenhagen Univer-
sity, b. 1885, d. 1962:
”for his services in the investigation of the
structure of atoms and of the radiation ema-
nating from them”
1927 COMPTON, ARTHUR HOLLY, U.S.A., Uni-
versity of Chicago b. 1892, d. 1962:
”for his discovery of the effect named after
him”;
and WILSON, CHARLES THOMSON REES,
Great Britain, Cambridge University, b. 1869
(in Glencorse, Scotland), d. 1959:
”for his method of making the paths of electri-
cally charged particles visible by condensation
of vapour”
1932 HEISENBERG, WERNER, Germany, Leipzig
University, b. 1901, d. 1976:
”for the creation of quantum mechanics, the
application of which has, inter alia, led to the
discovery of the allotropic forms of hydrogen”
SCHR
¨
ODINGER, ERWIN, Austria, Berlin
University, Germany, b. 1887, d. 1961; and
DIRAC, PAUL ADRIEN MAURICE, Great
Britain, Cambridge University, b. 1902, d.
1984:
”for the discovery of new productive forms of
atomic theory”
1935 CHADWICK, Sir JAMES, Great Britain, Liv-
erpool University, b. 1891, d. 1974:
”for the discovery of the neutron”
1936 HESS, VICTOR FRANZ, Austria, Innsbruck
University, b. 1883, d. 1964:
”for his discovery of cosmic radiation”; and
ANDERSON, CARL DAVID, U.S.A., Califor-
nia Institute of Technology, Pasadena, CA, b.
1905, d. 1991:
”for his discovery of the positron”
1938 FERMI, ENRICO, Italy, Rome University, b.
1901, d. 1954:
”for his demonstrations of the existence of new
radioactive elements produced by neutron irra-
diation, and for his related discovery of nuclear
reactions brought about by slow neutrons”
1939 LAWRENCE, ERNEST ORLANDO, U.S.A.,
University of California, Berkeley, CA, b. 1901,
d. 1958:
”for the invention and development of the cy-
clotron and for results obtained with it, espe-
cially with regard to artificial radioactive ele-
ments”
1943 STERN, OTTO, U.S.A., Carnegie Institute of
Technology, Pittsburg, PA, b. 1888 (in Sorau,
then Germany), d. 1969:
”for his contribution to the development of the
molecular ray method and his discovery of the
magnetic moment of the proton”
2.1. NOBEL PRICES IN PARTICLE PHYSICS 11
1944 RABI, ISIDOR ISAAC, U.S.A., Columbia Uni-
versity, New York, NY, b. 1898, (in Rymanow,
then Austria-Hungary) d. 1988:
”for his resonance method for recording the
magnetic properties of atomic nuclei”
1945 PAULI, WOLFGANG, Austria, Princeton Uni-
versity, NJ, U.S.A., b. 1900, d. 1958:
”for the discovery of the Exclusion Principle,
also called the Pauli Principle”
1948 BLACKETT, Lord PATRICK MAYNARD
STUART, Great Britain, Victoria University,
Manchester, b. 1897, d. 1974:
”for his development of the Wilson cloud cham-
ber method, and his discoveries therewith in
the fields of nuclear physics and cosmic radia-
tion”
1949 YUKAWA, HIDEKI, Japan, Kyoto Impe-
rial University and Columbia University, New
York, NY, U.S.A., b. 1907, d. 1981:
”for his prediction of the existence of mesons on
the basis of theoretical work on nuclear forces”
1950 POWELL, CECIL FRANK, Great Britain,
Bristol University, b. 1903, d. 1969:
”for his development of the photographic
method of studying nuclear processes and his
discoveries regarding mesons made with this
method”
1951 COCKCROFT, Sir JOHN DOUGLAS, Great
Britain, Atomic Energy Research Establish-
ment, Harwell, Didcot, Berks., b. 1897,
d. 1967; and WALTON, ERNEST THOMAS
SINTON, Ireland, Dublin University, b. 1903,
d. 1995:
”for their pioneer work on the transmutation of
atomic nuclei by artificially accelerated atomic
particles”
1955 LAMB, WILLIS EUGENE, U.S.A., Stanford
University, Stanford, CA, b. 1913:
”for his discoveries concerning the fine struc-
ture of the hydrogen spectrum”; and
KUSCH, POLYKARP, U.S.A., Columbia Uni-
versity, New York, NY, b. 1911 (in Blanken-
burg, then Germany), d. 1993:
”for his precision determination of the mag-
netic moment of the electron”
1957 YANG, CHEN NING, China, Institute for Ad-
vanced Study, Princeton, NJ, U.S.A., b. 1922;
and LEE, TSUNG-DAO, China, Columbia
University, New York, NY, U.S.A., b. 1926:
”for their penetrating investigation of the so-
called parity laws which has led to important
discoveries regarding the elementary particles”
1959 SEGR
´
E, EMILIO GINO, U.S.A., University of
California, Berkeley, CA, b. 1905 (in Tivoli,
Italy), d. 1989; and CHAMBERLAIN, OWEN,
U.S.A., University of California, Berkeley, CA,
b. 1920:
”for their discovery of the antiproton”
1960 GLASER, DONALD A., U.S.A., University of
California, Berkeley, CA, b. 1926:
”for the invention of the bubble chamber”
1961 HOFSTADTER, ROBERT, U.S.A., Stanford
University, Stanford, CA, b. 1915, d. 1990:
”for his pioneering studies of electron scattering
in atomic nuclei and for his thereby achieved
discoveries concerning the stucture of the nu-
cleons”; and
M
¨
OSSBAUER, RUDOLF LUDWIG, Ger-
many, Technische Hochschule, Munich, and
California Institute of Technology, Pasadena,
CA, U.S.A., b. 1929:
”for his researches concerning the resonance ab-
sorption of gamma radiation and his discovery
in this connection of the effect which bears his
name”
1963 WIGNER, EUGENE P., U.S.A., Princeton
University, Princeton, NJ, b. 1902 (in Bu-
dapest, Hungary), d. 1995:
”for his contributions to the theory of the
atomic nucleus and the elementary particles,
particularly through the discovery and appli-
cation of fundamental symmetry principles”;
GOEPPERT-MAYER, MARIA, U.S.A., Uni-
versity of California, La Jolla, CA, b. 1906
(in Kattowitz, then Germany), d. 1972; and
JENSEN, J. HANS D., Germany, University of
Heidelberg, b. 1907, d. 1973:
”for their discoveries concerning nuclear shell
structure”
12 CHAPTER 2. A HISTORY OF PARTICLE PHYSICS
1965 TOMONAGA, SIN-ITIRO, Japan, Tokyo,
University of Education, Tokyo, b. 1906, d.
1979;
SCHWINGER, JULIAN, U.S.A., Harvard Uni-
versity, Cambridge, MA, b. 1918, d. 1994; and
FEYNMAN, RICHARD P., U.S.A., Califor-
nia Institute of Technology, Pasadena, CA, b.
1918, d. 1988:
”for their fundamental work in quantum
electrodynamics, with deep-ploughing conse-
quences for the physics of elementary particles”
1967 BETHE, HANS ALBRECHT, U.S.A., Cornell
University, Ithaca, NY, b. 1906 (in Strasbourg,
then Germany):
”for his contributions to the theory of nuclear
reactions, especially his discoveries concerning
the energy production in stars”
1968 ALVAREZ, LUIS W., U.S.A., University of
California, Berkeley, CA, b. 1911, d. 1988:
”for his decisive contributions to elementary
particle physics, in particular the discovery of a
large number of resonance states, made possi-
ble through his development of the technique of
using hydrogen bubble chamber and data anal-
ysis”
1969 GELL-MANN, MURRAY, U.S.A., California
Institute of Technology, Pasadena, CA, b.
1929:
”for his contributions and discoveries concern-
ing the classification of elementary particles
and their interactions”
1975 BOHR, AAGE, Denmark, Niels Bohr Institute,
Copenhagen, b. 1922;
MOTTELSON, BEN, Denmark, Nordita,
Copenhagen, b. 1926 (in Chicago, U.S.A.); and
RAINWATER, JAMES, U.S.A., Columbia
University, New York, NY, b. 1917, d. 1986:
”for the discovery of the connection between
collective motion and particle motion in atomic
nuclei and the development of the theory of the
structure of the atomic nucleus based on this
connection”
1976 RICHTER, BURTON, U.S.A., Stanford Linear
Accelerator Center, Stanford, CA, b. 1931;
TING, SAMUEL C. C., U.S.A., Massachusetts
Institute of Technology (MIT), Cambridge,
MA, (European Center for Nuclear Research,
Geneva, Switzerland), b. 1936:
”for their pioneering work in the discovery of a
heavy elementary particle of a new kind”
1979 GLASHOW, SHELDON L., U.S.A., Lyman
Laboratory, Harvard University, Cambridge,
MA, b. 1932;
SALAM, ABDUS, Pakistan, International
Centre for Theoretical Physics, Trieste, and
Imperial College of Science and Technology,
London, Great Britain, b. 1926, d. 1996; and
WEINBERG, STEVEN, U.S.A., Harvard Uni-
versity, Cambridge, MA, b. 1933:
”for their contributions to the theory of the uni-
fied weak and electromagnetic interaction be-
tween elementary particles, including inter alia
the prediction of the weak neutral current”
1980 CRONIN, JAMES, W., U.S.A., University of
Chicago, Chicago, IL, b. 1931; and
FITCH, VAL L., U.S.A., Princeton University,
Princeton, NJ, b. 1923:
”for the discovery of violations of fundamental
symmetry principles in the decay of neutral K-
mesons”
1983 CHANDRASEKHAR, SUBRAMANYAN,
U.S.A., University of Chicago, Chicago, IL, b.
1910 (in Lahore, India), d. 1995:
”for his theoretical studies of the physical pro-
cesses of importance to the structure and evo-
lution of the stars”
FOWLER, WILLIAM A., U.S.A., California
Institute of Technology, Pasadena, CA, b.
1911, d. 1995:
”for his theoretical and experimental studies
of the nuclear reactions of importance in the
formation of the chemical elements in the uni-
verse”
2.1. NOBEL PRICES IN PARTICLE PHYSICS 13
1984 RUBBIA, CARLO, Italy, CERN, Geneva,
Switzerland, b. 1934; and
VAN DER MEER, SIMON, the Netherlands,
CERN, Geneva, Switzerland, b. 1925:
”for their decisive contributions to the large
project, which led to the discovery of the field
particles W and Z, communicators of weak in-
teraction”
1988 LEDERMAN, LEON M., U.S.A., Fermi Na-
tional Accelerator Laboratory, Batavia, IL, b.
1922;
SCHWARTZ, MELVIN, U.S.A., Digital Path-
ways, Inc., Mountain View, CA, b. 1932; and
STEINBERGER, JACK, U.S.A., CERN,
Geneva, Switzerland, b. 1921 (in Bad Kissin-
gen, FRG):
”for the neutrino beam method and the demon-
stration of the doublet structure of the leptons
through the discovery of the muon neutrino”
1990 FRIEDMAN, JEROME I., U.S.A., Mas-
sachusetts Institute of Technology, Cambridge,
MA, b. 1930;
KENDALL, HENRY W., U.S.A., Mas-
sachusetts Institute of Technology, Cambridge,
MA, b. 1926; and
TAYLOR, RICHARD E., Canada, Stanford
University, Stanford, CA, U.S.A., b. 1929:
”for their pioneering investigations concerning
deep inelastic scattering of electrons on protons
and bound neutrons, which have been of es-
sential importance for the development of the
quark model in particle physics”
1992 CHARPAK, GEORGES, France,
´
Ecole
Sup`erieure de Physique et Chimie, Paris and
CERN, Geneva, Switzerland, b. 1924 ( in
Poland):
”for his invention and development of particle
detectors, in particular the multiwire propor-
tional chamber”
1995 ”for pioneering experimental contributions to
lepton physics”
PERL, MARTIN L., U.S.A., Stanford Univer-
sity, Stanford, CA, U.S.A., b. 1927,
”for the discovery of the tau lepton”
REINES, FREDERICK, U.S.A., University of
California at Irvine, Irvine, CA, U.S.A., b.
1918, d. 1998:
”for the detection of the neutrino”
14 CHAPTER 2. A HISTORY OF PARTICLE PHYSICS
2.2 A time line
Particle Physics Time line
Year Experiment Theory
1927 β decay discovered
1928 Paul Dirac: Wave equation for electron
1930 Wolfgang Pauli suggests existence of neu-
trino
1931 Positron discovered
1931 Paul Dirac realizes that positrons are part
of his equation
1931 Chadwick discovers neutron
1933/4 Fermi introduces theory for β decay
1933/4 Hideki Yukawa discusses nuclear binding in
terms of pions
1937 µ
discovered in cosmic rays
1938 Baryon number conservation
1946 µ is not Yukawa’s particle
1947 π
+
discovered in cosmic rays
1946-50 Tomonaga, Schwinger and Feynman de-
velop QED
1948 First artificial
π
’s
1949 K
+
discovered
1950 π
0
→ γγ
1951 ”V-particles” Λ
0
and
K
0
1952 ∆: excited state of nucleon
1954 Yang and Mills: Gauge theories
1956 Lee and Yang: Weak force might break
parity!
1956 CS Wu and Ambler: Yes it does.
1961 Eightfold way as organizing principle
1962 ν
µ
and
ν
e
1964 Quarks (Gell-man and Zweig) u, d, s
1964 Fourth quark suggested (c
)
1965 Colour charge all particles are colour neu-
tral!
1967 Glashow-Salam-Weinberg unification of
electromagnetic and weak interactions.
Predict Higgs boson.
1968-69 DIS at SLAC constituents of proton seen!
1973 QCD as the theory of coloured interac-
tions. Gluons.
1973 Asymptotic freedom
1974 J/ψ
(c¯c
) meson
1976 D0 meson (¯uc
) confirms theory.
1976 τ lepton!
1977 b (bottom quark). Where is top?
1978 Parity violating neutral weak interaction
seen
1979 Gluon signature at PETRA
1983 W
±
and
Z
0
seen at CERN
1989 SLAC suggests only three generations of
(light!) neutrinos
1995 t (top) at 175 GeV mass
1997 New physics at HERA (200 GeV)
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