standardmodel Higgs boson are
M
H
.
114 GeV/
c
2
via direct
searches
208
and
M
H
,
193 GeV/
c
2
from fits to precise elec
troweak data.
209
Discovering the nature of the Higgs boson is a key to
further progress in understanding what may lie beyond the
standard model. There may exist one Higgs boson or more
than one. There may exist other particles in the spectrum
related to it. The Higgs boson may be elementary or com
posite. If composite, it points to a new level of substructure
of the elementary particles.
I. Precision electroweak measurements
Precision electroweak measurements can yield informa
tion on many newphysics possibilities in addition to the
Higgs boson. The seminal paper of Veltman
210
showed how
the ratio of
W
and
Z
masses could shed light on the top
quark’s mass. A systematic study of electroweak radiative
corrections within the standard model was performed by
Marciano and Sirlin
211
and used to analyze a wide variety of
electroweak data, initially in Ref. 212 and most recently in
Ref. 209. Widelyused parametrizations of deviations from
StandardModel predictions
213–215
have been used to con
strain new particles in higherorder loop diagrams associated
with
W
,
Z
, and photon selfenergies. Some reviews include
Refs. 216–219.
206.
‘‘Report of the Tevatron Higgs Working Group,’’ M. Carena
et al.
,
Fermilab report FERMILABCONF00279T, hepph/0010338
~
un
published
!
.
~
A
!
207.
‘‘The Higgs Working Group: Summary Report,’’ D. Cavalli
et al.
, in
Proceedings of Workshop on Physics at TeV Colliders, Les Houches,
France, 21 May–1 June 2001, edited by P. Aurenche
et al.
~
Paris,
IN2P3, 2001
!
, pp. 1–120.
~
A
!
208.
LEP Higgs Working Group, results quoted in web page of LEP Elec
troweak Working Group,
/
LEPEWWG/
.
~
I
!
209.
LEP Electroweak
Working
Group,
http://
lepewwg.web.cern.ch/LEPEWWG/
.
~
I
!
210.
‘‘Limit on Mass Differences in the Weinberg Model,’’ M. Veltman,
Nucl. Phys.
B123
, 89
~
1977
!
.
~
A
!
211.
‘‘Radiative Corrections to Neutrino Induced Neutral Current Phenom
ena in the SU
~
2
!
L
3
U
~
1
!
Theory,’’ W. J. Marciano and A. Sirlin, Phys.
Rev. D
22
, 2695
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!
;
31
, 213
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!
.
~
A
!
212.
‘‘A Comprehensive Analysis of Data Pertaining to the Weak Neutral
Current and the Intermediate Vector Boson Masses,’’ U. Amaldi
et al.
, Phys. Rev. D
36
, 1385
~
1987
!
.
~
I
!
213.
‘‘A New Constraint on a Strongly Interacting Higgs Sector,’’ M. E.
Peskin and T. Takeuchi, Phys. Rev. Lett.
65
, 964–967
~
1990
!
.
~
A
!
214.
‘‘Estimation of Oblique Electroweak Corrections,’’ M. E. Peskin and
T. Takeuchi, Phys. Rev. D
46
, 381–409
~
1992
!
.
~
A
!
215.
‘‘Vacuum Polarization Effects of New Physics on Electroweak Pro
cesses,’’ G. Altarelli and R. Barbieri, Phys. Lett. B
253
, 161–167
~
1991
!
.
~
A
!
216.
‘‘Electroweak Theory. Framework of OnShell Renormalization and
Study of HigherOrder Effects,’’ K. I. Aoki
et al.
, Prog. Theor. Phys.
Suppl.
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, 1–225
~
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!
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~
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!
217.
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M
Z
,
M
W
, and the Heavy Top,’’
W. Hollik, Adv. Ser. Direct. High Energy Phys.
10
, 1–57
~
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!
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~
A
!
218. The Standard Model in the Making: Precision Study of the Elec
troweak Interactions
, D. Yu. Bardin and G. Passarino
~
Clarendon
Press, Oxford, 1999
!
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~
A
!
219.
‘‘Radiative Corrections in Gauge Theories,’’ H. Anlauf, lectures at
Adriatic School on Particle Physics and Physics Informatics, Septem
ber 11–21,
2001,

darmstadt.de/
;
anlauf/halectures.html
.
~
A
!
X. PROPOSED EXTENSIONS
A. Supersymmetry
Unification of the electroweak and strong interactions at a
high mass scale leads to the
hierarchy problem
, in which this
scale contributes through loop diagrams to the Higgs boson
mass and requires it to be finetuned at each order of pertur
bation theory. A similar problem is present whenever there is
a large gap between the electroweak scale and
any
higher
mass scale contributing to the Higgs boson mass.
Supersym
metry
solves this problem by introducing for each particle of
spin
J
a
superpartner
of spin
J
6
1/2 whose contribution to
such loop diagrams cancels the original one in the limit of
degenerate masses. Recent reviews of supersymmetry and its
likely experimental signatures include Refs. 40, 62–67,
while earlier discussions are given by Refs. 68, 69, and 70.
For an article at the popular level see Ref. 119.
B. Dynamical electroweak symmetry breaking
If the Higgs boson is not fundamental but arises as the
result of a new superstrong force which, in analogy with
color, causes the
dynamical
generation of one or more scalar
particles, the hierarchy problem can be avoided. This
scheme, sometimes called ‘‘technicolor,’’ was proposed in
the 1970s.
220–222
For recent reviews, see. e.g., Refs. 223–
225.
220.
‘‘Implications of Dynamical Symmetry Breaking,’’ S. Weinberg,
Phys. Rev. D
13
, 974–996
~
1976
!
.
~
A
!
221.
‘‘Implications of Dynamical Symmetry Breaking: An Addendum,’’ S.
Weinberg, Phys. Rev. D
19
, 1277–1280
~
1979
!
.
~
A
!
222.
‘‘Dynamics of Spontaneous Symmetry Breaking in the Weinberg–
Salam Theory,’’ L. Susskind, Phys. Rev. D
20
, 2619–2625
~
1979
!
.
~
A
!
223.
‘‘Lectures on Technicolor and Compositeness,’’ R. S. Chivukula, in
Ref. 47, pp. 731–772.
~
A
!
224.
‘‘Two Lectures on Technicolor,’’ K. Lane, Fermilab report
FERMILABPUB02 040T, preprint hepph/0202255
~
unpub
lished
!
.
~
A
!
225.
‘‘Strong dynamics and electroweak symmetry breaking,’’ C. T. Hill
and E. H. Simmons, Fermilab report FERMILABPUB02045T,
preprint hepph/0203079, submitted to Phys. Rep.
~
A
!
C. Fermion mass and mixing patterns
The transitions between the (
u
,
c
,
t
) and (
d
,
s
,
b
) quarks
owing to virtual
W
emission or absorption are described by
the Cabibbo–Kobayashi–Maskawa
~
CKM
!
matrix men
tioned in Sec. IXA.
~
For one parametrization of this matrix
see Ref. 226.
!
The CKM matrix arises because the matrices
that diagonalize the mass matrices of (
u
,
c
,
t
) and of (
d
,
s
,
b
)
are not the same. A theory of quark masses would thus entail
a specific form of the CKM matrix. For the corresponding
matrix for leptons, see Refs. 227–229. While a theory of
quark and lepton masses still eludes us, attempts have been
made to guess some of its general features.
230–235
226.
‘‘Parametrization of the KobayashiMaskawa Matrix,’’ L. Wolfen
stein, Phys. Rev. Lett.
51
, 1945–1947
~
1983
!
.
~
I
!
227.
‘‘Remarks on the Unified Model of Elementary Particles,’’ Z. Maki,
M. Nakagawa, and S. Sakata, Prog. Theor. Phys.
28
, 870–880
~
1962
!
.
~
A
!
228.
‘‘Muon and Electron Number Nonconservation in a
V
–
A
Gauge
Model,’’ B. W. Lee, S. Pakvasa, R. Shrock, and H. Sugawara, Phys.
Rev. Lett.
38
, 937–939
~
1977
!
.
~
A
!
312
312
Am. J. Phys., Vol. 71, No. 4, April 2003
Jonathan L. Rosner