Table Of ContentInternational School for Advanced Studies
Lecture Series No. 2
GRAND UNIFICATION WITH
AND WITHOUT SUPERSYMMETRY
AND COSMOLOGICAL IMPLICATIONS
World Scientific
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Library of Congress Cataloging In Publication Date
‘Main entry under tle:
Grind unifieation with and without supertymmeury and ccamalogical
Imptiatlons.
(Mrteenational school for slvanced studies lecture serie 0.2
gummer 1982)
1, Grand urified theorje (Nuclear physics). 2. Supertyemmetty.
3. Commology. I. Kounnas, C. If Serv: Interoutional school for advanced
Qc796.67G73 1985397 4-27085
ISBN 9971.966-39-5
{ISBN 5971-966-40-9 (pba)
Copyright © 1984 by World Scientific Publishing Co Pre Lid,
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PREFACE
Unification of all elementary particle forces seems to be the central theme of
contemporary particle physics. During these last fifteen years, we have witnessed
enormous progress towsrds u realization of the unification dream. The proof of
the resormalizabitity and unitarity of spontaneously- broken gauge thsories, together
‘wath the astonthing phenomenclogical socestes of the realization of such theories
which is the Standard Model, have provided a tremendous momentum for wnified
gauge theories, Since eleciromagnetic and weak Intezactions have found a common
framework — the Standitd Model of the elecicoweak interactions — thest last
‘en years have seen an enormous amount of work in the subsequent logical steps of
the “unifcation project”: grand unitication, ie. electroweakand strong interactions
-merging together, and superunificstion, encompessing even gravitattonal interactions
swithin supergeavity schemes.
Remarkably enough, all these breakthroughs in particle physics have triggered
very interesting developments in cosmology, which allow for a better comprehension
of the evolution of the Universe almost since its “bieth”. On the other hand, the
comnotogy “feedbeck” on particle physics imposed severe and crucial constraints
‘on possible unified seherres.
Although several good reviews on some topics of the enormous amount of
material conceming the “unification projects” already exist, a comprehensive
snd updated work stacting from the Standard Model and golng through the overall
pleture of giand- and auperunification and thelr cosmological implications was
lacking. This book hopet to fil this gap: we ty to present in a rather detailed
and methodic way the current status of unification of elementary parlicle interactions
end their cosmological consequences. The book is naturally divided into four
arta, .
1m the fire part, which is concetved in a very pedagogical way, we start by
briefly discussing the present status of the Standard Modal of the electrowesk
‘interactions, ax welt s1 the reason behind the efforts to extend this model. Then,
the theoretical framework of grand unification i introduced and its theoretical
and phenomenctogical consequences are discussed In some depth, Some problems
(including the gauge hierarchy problem) indicating extensions of grand unified
theosles (GUTS) ate alao analyzed.
The second part provides the calculations! framework for grand unification
with o€ without supersymmetry) and a detaled analysis of experimentally messur-
able consequences of GUTS (Gn8y Tp, my/m,) ia set oul. Further reasons are
given for extensions of GUTs and tome discutsion of giuge hiecarchy- free (no-scéle)
model is presented.
In the thitd part, the physlcs of supersymmetry and supergravity is discussed In
conalderable detail, Motivation, physieal content and structure, model building and
experimental consequences of these theorelea are presented,
vw
Finally, the fourth part contains an In-depth exposé of the present status of the
Big Beng Coamology (BBC) and tts correlations to pertkls physics. Tt includes the
standard arguments which established BBC, its problemsand thely possible resolution
in a GUT ond Inflation framework, ox well as the Importance and central role of
supersymmetry and wapergravity Ln all this Cosmmo-partlcle programme,
We heve tried to maintain a coherent continuity throughout the book, but, at
the same timo, eech partis self-contained enough to be read separately.
‘We stress that, although this book encompasses some of the most recent and
advanced remultx of the “unification project”, it Is also suitnble for readers with
some knowledge of spootancously- broken gauge theories, but no previous specific
experlonce af grend unification.
‘Thin work grew out of a series of lectures that we gave at the SISSA of Trieste
during spring 1982, and It natucelly contains all further developments until summer
1984. We should like to take the oppoctunlty here to expres ove heartfelt thanks
to Profesor R, lengo for organizing such an interesting course at SISSA end encour-
aging us in the difficult task of collecting the widespread material on unified theories
for the present book.
Geneva, November 1984 C. KOUNNAS.
A, MASTERO
D. V. NANOPOULOS
K.A. OLIVE
CONTENTS
Preface v
PARTI: INTRODUCTION TO GRAND UNIFIED THEORIES
A. Masieca 1
PARTI: CALCULATIONAL SCHEMES IN GUTs
C. Kounnas 14s
PART III: THE PHYSICS OF SUPERSYMNETRY
AND SUPERGRAVITY
D. V. Nanopoulos 283
PARTIV: COSMOLOGY AND GUTs
K. A. Olive 347
INTRODUCTION TO GRAND
UNIFIED THEORIES
Antonio MASIERO*
CBRN, Geneve
SWITZERLAND
‘Permanent addreor: INFN, Sectone di Prov, Pada, TTALY
CONTENTS.
THE STANDARD MODEL: A CRITICAL APPRAISAL
1.1 The “Low Energy” Linvit of Renormalizable Gaoge Theories
1.2. The Standard Model: tts Purity
L3 The Standard Model: Its Impurity
14 Vices and Virtues of the Standard Model
INTRODUCTION TO GRAND UNIFIFD THEORIES
2.1. When “Strong” and "Weak" Merge Together
2.2. The “Big Desort” Picture of the World
2.3 A Persistent Cloud: The Hierarchy Problem
PHENOMENOLOGICAL CONSEQUENCES OF GUTs
3.1 What isNew in GUTa
3.2 General Features of the B and L Violating Processes
‘A FIRST GLIMPSE AT THE SU(S) MODEL
4.1 Why SUS)?
4.2 The Higgh Sector and the Hierarchy Nightmare
LOW ENERGY PHENOMENOLOGICAL CONSFQUENCES OF SU(5)
5.1 Tha Successful sin?Oy, Prediction of SUS)
$.2 Fermilon Massex In SU(S)
3.3 Mixing Angles and Phases
$.4 Proton Lifetime: A Death Blow to the SU(5) Model?
5.5 B-Land Neutrino Masses in SUS)
5.8 SU(S): A Final Score
NEW PHYSICS NOT FAR FROM THE FERMI SCALE?
6.1 Left-Right Symmetry: 4 Fundamental Symmetry?
6:2 Massive Majorana Neutrinos .
63 Neutron -Antineutron Oscillations
64 Lepton Number as @ Fourth Colour
7. THE SO(10) MODEL
7.1 Few Generalities on the Oithogonsl Groups
7.2 The SO{L0) Gauge Enterectlons
7.3. Patterns of Symmetry Breaking in the S0(10) Model
7.4 The Permlon Mass Spectrum
7.5 The Quesilon of the Newteino Mass
8. PHENOMENOLOGY OF THE INTERMEDIATE MASS SCALES
8.1 Renormatization Group Equations in the Presence of IMS.
8.2 Myand Mx in IMS models
8.3 Higgs Contcibutions to the f-Punetions
£4 Phenomenological Consequences of IMS
9, AGENERAL OUTLOOK ON GUTs
9.1 General Constralnts on GUTS
9.2 Major Unsolved Questions in GUTS
Bibliography
References
8
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1, THE STANDARD MODEL: A CRITICAL APPRAISAL
The recent discovery of the W and Z bosons represents so for
the most triunphant milestone of the successful history of the Standard
Hoe? of the electroweak Interactions. Verious alternatives to this
Model in the description of the low energy phenonena result strongly
weakened and by now the general consensus 1s that any theory of the
fundaments1 interactions should strictly reproduce the Standard Model
At Teast betow the Ferm scale. ft behooves us, then, to stert our
excursion to the Tend of Grand Unified Theories by exploring briefiy,
first, the solid ground of the Standard Model, That shall accompl {sh
2 twofold function: first, we shall sumartze the salfent features of
the lew energy phenonenology and #4x our notation, secondly we shalt
make clear the constraints and the purposes of any theory which wants
‘to go beyond the Stendard Hodel.
4s for the description of the strong interactions, we shall adopt
the gauge theory of Quantum Chronodynamics (QCD). In making this
assumption, we certainly start moving into a much less solid ground:
no crucial evidence of the validity of QCD fs s0 far known, but
certainly a wide material of at least circumstantial evidence in its
favour comforts cur choice.
This section 1s structured as follows, Section 1.1 introduces
‘the tmportant notion af the correspondence between 8 renormalszable
gauge theory and {ts “low energy" lintt given by effective non-renorma-
Vizable interactions. We shalT insist on this notion given its relevance
1n the construction of Grand Unified Theartes. This process will be
Applied here to introduce the SU(2) xU(1) guuge theory of the electro
weak interactions, In Secs. 1.2 and 1.3, we sumurize the main features
of the Standard Model. In particular, the intriguing problem of the
fermantc mass spactrun 1s antlyzed tn Sec. 1.4, The rise end fall of
the Standard Model sre criticelly discussed in Sec. 1.$ which prepares
tthe ground for the unknown land lying "beyond" the Standard Model.
