Supersymmetry. Theory, Experiment, and Cosmology

Supersymmetry

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British Library Cataloguing in Publication Data

Data available

Library of Congress Cataloging in Publication Data

Bin´etruy, P.

Supersymmetry : theory, experiment, and cosmology / P. Bin´etruy. p. cm.

Includes index.

ISBN-13: 978-0-19-850954-7 (alk. paper) ISBN-10: 0-19-850954-5 (alk. paper)

1.Supersymmetry. I. Title.

QC174.17.S9B56 2006 539.7 25—dc22 2006017203

Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain

on acid-free paper by Biddles Ltd. www.biddles.co.uk

ISBN 0–19–850954–5 978–0–19–850954–7 (Hbk)

1 3 5 7 9 10 8 6 4 2

Contents

6.9Infrared fixed points, quasi-infrared fixed points and focus

7Phenomenology of supersymmetric models:

7.3Avoiding instabilities in the flat directions of the scalar

8.4Example of supersymmetric SU (Nc) with Nf flavors. The rˆole

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Introduction

The turn of the century witnesses a somewhat unprecedented situation in the study of fundamental interactions. On one hand, we have a theory, the Standard Model, which has been tested successfully to a few per mil: present data shows no deviation from this theory. On the other hand, we have a symmetry, supersymmetry, which seems to be the necessary ingredient to discuss the questions left aside by the Standard Model: diversity of masse scales, vacuum energy, etc. Supersymmetry is obviously not realized in the spectrum of fundamental particles. If it is realized at some deeper level, it must therefore be spontaneously broken. But even though it might be hidden in this way, there must be a level of precision to which experiments should be able to test deviations from the Standard Model. Clearly, this has not happened yet. But the ideas developed within the supersymmetric framework have lead to a general picture which seems supported by recent experimental data: gauge coupling unification, small neutrino masses, relatively light Higgs, a Universe with a density close to the critical density, etc.

It is the purpose of this book to give the tools necessary to discuss these issues. Because fundamental interactions provide, at some deeper level, a general picture of our own world, these issues may be solved at di erent levels: consistency of the theory, experimental discoveries, observation of the Universe. It would be preposterous to say at this point which will be the most decisive approach. It is therefore important to develop as much as possible a common language and to be able to follow the progress of each path: this will ease the way to a very enriching and most probably fruitful exchange between the di erent communities involved in the search for supersymmetry. This is why this book is conceived for readers with di erent backgrounds and varied interests: it may provide an introduction to the concepts and methods of supersymmetry for theorists; it can also be used as an introduction to the phenomenology of supersymmetric models for high energy experimentalists involved in supersymmetry searches; finally it targets the community of cosmologists involved in unravelling the properties of the early Universe. Of course supersymmetry, as we understand it now, may not be found in the end but one may be confident that the theory that will emerge eventually will feed upon the concepts, the methods and the results developed in a supersymmetric context.

Regarding experimental results, the present times represent a turning point. The precision tests at the LEP collider have successfully confronted the Standard Model and have started constraining the bulk of the parameter space of supersymmetric models. If supersymmetry is realized as we think now, the discovery of supersymmetric

xIntroduction

particles should wait for the turning on of the LHC collider. This does not mean that there is nothing to expect besides: searches at the Tevatron collider and precise measurements in B factories have been confronted with supersymmetry. Moreover, astrophysics and cosmology will most probably provide another perspective to study supersymmetric models: searches for dark matter will reach their maturity and cosmology which has become a quantitative science will provide a unique window on the very high mass scale regime of the theory.

On a parallel track, fundamental theories are being developed. It is probable that string theories provide, as they did from the beginning, the logical framework for supersymmetry. They are still under construction but it is important to be aware of the general picture they present us with. For example, recent ideas about extra spacetime dimensions have enriched the phenomenology of high energy colliders. Therefore, one chapter of this book (Chapter 10) presents in a non-technical way the general string and brane picture.

Roadmap

The text is organized in such a way that it can be read using di erent tracks depending on the interests of the reader. It can provide: (i) a theoretical introduction to supersymmetry; (ii) a presentation of supersymmetric models for high energy experimentalists; and (iii) an introduction to supersymmetry emphasizing its rˆole in the early Universe. The sections that should be read in each case are summarized in the following table.

In the course of the general text, some comments intended solely for readers who are following the “Theoretical introduction” track are put between square brackets: [...].

One should note that some very elementary knowledge of quantum field theory is assumed. Appendix A provides a sketch of the basic notions which are needed, which might prove useful to some readers to refresh their memory. It also describes some more