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Fundamental_Interactions/9810249128/files/00000___5dd6fbb398f763a39bc9e51f0d0764c4.pdfProc Winter Institute

TERACTIONS ouise, Albe ; 18-24

Edito

B A Campbell F C Khanna M G Vincter

World Scientific

Fundamental_Interactions/9810249128/files/00001___101b82b50cd4379db841a46c3ae164db.pdfProceedings of the Sixteenth Lake Louise Winter Institute

FUNDAMENTAL INTERACTIONS

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Fundamental_Interactions/9810249128/files/00003___23541ffa404249510f9420416e1fdbf3.pdfProceedings of the Sixteenth Lake Louise Winter Institute

FUNDAMENTAL INTERACTIONS

Lake Louise, Alberta, Canada; 18-24 February 2001

Editors

A Astbury B A Campbell F C Khanna M G Vincter

V ^ World Scientific NewJersey London'Singapore' New Jersey London 'Singapore 'Hong Kong

Fundamental_Interactions/9810249128/files/00004___db9a92f835bea8cb7c745f36ddf4cb48.pdfPublished by

World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

FUNDAMENTAL INTERACTIONS Proceedings of the Sixteenth Lake Louise Winter Institute

Copyright 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-02-4912-8

Printed in Singapore by Fulsland Offset Printing

Fundamental_Interactions/9810249128/files/00005___7e2d7e80052216fbe24ecfe35bf22c54.pdfP R E F A C E

The sixteenth annual Lake Louise Winter Institute, entitled "Fundamen-tal Interactions", was held from February 18-24, 2001 at the Chateau Lake Louise located in the scenic Canadian Rocky Mountains. Pedagogical and re-view lectures were presented by invited experts. As well, a topical workshop was held in conjunction with the Institute, with contributed presentations by some of the participants. The sessions were scheduled in the mornings and in the evenings leaving the afternoons free to enjoy the many aspects of this beautiful part of western Canada.

The 2001 Lake Louise Winter Institute was devoted to precision mea-surements within the context of the Standard Model of Particle Physics and the possibilities for extensions to this model. The recent completion of the LEP program at CERN and results from other laboratories around the world have revealed to us the validity of this model to unprecedented precision. New results from neutrino experiments in Japan and North America have brought unexpected insight into the fundamental properties of these leptons. In addition, the state-of-the art in atomic trapping was clearly detailed to all participants.

We wish to express our most sincere gratitude to Lee Grimard for her efforts, organizational skills, and incredible patience (even in the most frus-trating circumstances!) in bringing this Winter Institute to fruition, from the very first email to the publication of these proceedings. She was well aided by David Shaw and Norm Buchanan in the logistics and transportation of the participants to the Institute. We are indebted to them.

We wish to thank the Physics Department at the University of Alberta for the infrastructure support essential to this conference. Finally, we wish to acknowledge the generous financial support of the University of Alberta (through the university conference fund and the Dean of Science), the Institute of Particle Physics, and TRIUMF.

organizing committee: A. Astbury B.A. Campbell

F.C. Khanna M.G. Vincter

v

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Fundamental_Interactions/9810249128/files/00007___524ed60694d644d3c76335ad7d6c495b.pdfCONTENTS

Preface v

I. Electroweak Physics at LEP2 1 R. J. Hemingway

II. The Neutrino A Review 42 R. G. Robertson

III. Beyond the Standard Model 60 G. G. Ross

Run II Perspectives at CDF: Top, Higgs and Searches 120 P. Azzi

Physics at TESLA 127 G. A. Blair

Radiation Concerns in High-Energy Physics and The Switched Capacitor Array Controller in ATLAS 134

N. J. Buchanan

Measurement of Direct CP Violation by NA48 Experiment at CERN 142 G. Collazuol

Searches for MSSM Neutral Higgs Bosons at LEP 149 S. Cucciarelli

The TESLA Linear Collider Design 157 W. Decking

Search for Charginos Nearly Mass-Degenerate with the Lightest Neutralino in e+e~ Collisions up to y/s = 209 GeV 164

N. De Filippis

Fermion Pair Production at LEP 171 P. Deglon

Searches at HERA 178 N. Delerue

VII

Fundamental_Interactions/9810249128/files/00008___d994f8f18a9f20cc5d8a5f66a9feebb6.pdfVIII

Detection of a Hypercharge Axion in ATLAS 185 E. Elfgren

TESLA-N: Future Polarized Electron-Nucleon Scattering at DESY 192 F. Ellinghaus

Particle Production and Multiplicity in Heavy Ion Collisions at PHENIX 199 L. Ewell

Recent QCD Results from D 0 at the Tevatron 207 E. Gallas

Two Photon Physics at LEP 214 D. Haas

Low x and Diffraction at HERA 221 R. J. Hall-Wilton

Higgs Searches with the DELPHI Detector 228 J. Hansen

Indirect CP Violation Results from BELLE 235 T. Hara

Noncummutative Field Theories and Spontaneous Symmetry Breaking 242 K. Kaminsky

The ALEPH Search for the Standard Model Higgs Boson 249 J. Kennedy

Searches for Gauge Mediated Supersymmetry Breaking Signatures at LEP2 256

K. Klein

Search for the Standard Model Higgs Boson at yfs =192-209 GeV with the OPAL Detector at LEP 263

T. Kuhl

Measurement of CP-Violating Asymmetries in B Decays to CP Eigenstates 270

D. Lange

Electromagnetic Interactions in Strong Magnetic Fields 277 D. Leahy

Fundamental_Interactions/9810249128/files/00009___de1962d5d31d172bab076991bc27dd02.pdfIX

CLEO Measurements of the CKM Elements \Vub\ and |Vc6| 284 T. Meyer

Recent Results from K2K 292 T. Nakaya

Measurements of B and B Lifetimes Using Fully Reconstructed B Decays at BABAR 301

J. H. Panetta

The D 0 Run II Detector and Physics Prospects 307 N. Parashar

Searches for R-Parity Violation Processes in DELPHI 314 V. Poireau

Doubly Resonant Z Pair Production with DELPHI 321 J. Rehn

Tests of QED with Multi-Photonic Final States 328 K. Sachs

Charmless Hadronic B Decays at BABAR 335 T. Schietinger

Computing the Wilson Loop in N = 4 Super-Yang-Mills Theory 342 G. Semenoff

Non-equilibrium Phase Transition Dynamics Beyond the Gaussian Approximation 349

S. Sengupta

ATLAS Physics Potential 356 J. Sjolin

Deep Inelastic Scattering at High Q2 363 A. Tapper

CLEO Results for b -> s 7 and B -> Kvv 370 J. G. Thayer

An Improved Measurement of the Anomalous Magnetic Moment of the Positive Muon 377

A. Trofimov

Fundamental_Interactions/9810249128/files/00010___62750f404545c7c6a2a6158d5d467cb5.pdfX

Physical Interpretation of String Theories and the Origin of Charge 385 F. Winterberg

List of Participants 391

Fundamental_Interactions/9810249128/files/00011___e5969efeb68dc009b882de694b251d15.pdfELECTROWEAK PHYSICS AT LEP2

RICHARD J. HEMINGWAY IPP and Ottawa- Carleton Institute for Physics, Department of Physics,

Carleton University, Ottawa, Ontario, Canada K1S 5B6 E-mail: ryh@physics. carleton. ca

On 2 November 2000 the LEP machine was finally closed after 12 years of glori-ous running. With the 4 operating detectors, ALEPH, DELPHI, L3, and OPAL, an enormous wealth of new data at the highest centre-of-mass energies has been recorded. These lectures will focus on aspects of electroweak physics within the energy span of LEP2, namely 130-209 GeV. All current data are in very good agreement with the electroweak Standard Model.

1 Introduction

Without a shadow of doubt e+e~ annihilation has been the most produc-tive environment for new physics during the last 20-30 years. The early experiments at Orsay, Novosibirsk, Frascati, and SLAC have clearly demon-strated the simplicity and cleanliness of e+e~ annihilation to fermion-pair final states. SPEAR and DORIS initiated charm spectroscopy in 1974-5, followed by DORIS and CESR with beauty spectroscopy in 1978. Experiments at PEP, PETRA, CESR, and TRISTAN have produced hundreds, if not thousands, of new results covering aspects of pure QED, weak interactions, strong interac-tions, 2-photon physics, spectroscopy of heavy quarks, particle lifetimes and decays, and precision tests of the Standard Model. In 1989 both SLC and LEP started operation on a higher energy scale to investigate the detailed proper-ties of the Z boson. LEP was able to raise the beam energy in 1996 to allow production of W+W~ boson pairs and, eventually, ZZ boson pairs. By the time LEP ceased operation, the e+e~ centre-of-mass energy had reached 209 GeV, a factor of 3 above the previous generation of e+e~ accelerators.

1.1 Setting the Scene, LEPl to LEP2

LEP was formally approved in 1981 and the 4 experiments (Aleph, Delphi, L3, and OPAL) selected in 1982. Construction of the accelerator began in 1983 and the very first e+e~ collisions were observed on 13 August 1989. The period 1989-1995, the LEPl era, provided each experiment with approximately 5 million Z events. With the addition of superconducting RF cavities the LEP energy was gradually increased above i y + W - threshold and heralded the LEP2 era (1996-2000) during which each experiment recorded approximately

1

Fundamental_Interactions/9810249128/files/00012___f9333fe0642d28dd01f8387ec5c62c97.pdf2

10,000 W^+W- pairs. The major physics goals of the LEP2 program were (a) to continue the precision tests of the validity of the Standard Model, (b) to make precise measurements of the W+W~ final state (cross-section, W branching ratios, triple-gauge couplings, and mw), (c) to continue the direct search for the Standard Model Higgs boson, and (d) to explore the increased phase-space for evidence of new physics, eg. SUSY. Only items (a) and (b) will be discussed in these lectures.

1.2 Major References I invite you to access the following sources for basic details, newer results, and (as ever) the very latest results.

CERN Yellow Reports: 1. Physics at LEP2 \ CERN 96-01, Volumes 1,2 edited by G. Altarelli, T. Sjostrand, F. Zwirner, and 2. Reports of the Working Groups on Precision Calculations for LEP2 Physics 2, CERN 2000-009, edited by S. Jadach, G. Passarino, R. Pittau. This latter reference is very important for details of the Monte Carlos and EW-libraries.

Newer Results: see CERN-EP-2001-021 A combination of preliminary EW measurements and constraints on the Standard Model, and the ref-erences therein.

Very Latest Results: see the website http://www.cern.ch/LEPEWWG/-for a continuously updated situation, reports, talks, figures, averages, and much more. Here you will find the LEP combinations which ultimately are accessed by the Particle Data Group. These combinations require sophisticated procedures and tests and involve many people from the 4 experiments. This is excellent work and we all owe them many thanks.

1.3 Basic Processes, Event Rates, and 2-f vs J^-f Diagrams Figure 1 shows the Standard Model expectation for the cross-sections of the major processes at LEP2 over the centre-of-mass energy range 100-250 GeV1 . Compared to the LEP1 era with \fs = mz giving a peak hadronic cross-section of approx 30 nb, all LEP2 cross-sections are several orders-of-magnitude smaller, with the more interesting ones in the range 1-20 pb. For example, at y/s = 196 GeV with a luminosity of 100pb_1, we would expect (with efficiency and purity both 100%) ~2,000 qq, ~ 300 n+fT or r + r " , ~ 2,000 W+W~, ~ 700 77 with cos07 < 0.9, and ~ 150 ZZ events. With the same luminosity at the Z we would record 3 million qq\

Fundamental_Interactions/9810249128/files/00013___dbc6a1a89ccc2c0f443f49ccd046ccc7.pdf3

3

a. a io3

to'

10

10 '

'" 100 120 140 160 ISO 200 220 2*0

/s (GeV)

Figure 1: Some Standard Model cross-sections as a function of centre-of-mass energy.

One big difference between LEP1 and LEP2 physics is that the major pro-cesses of interest at LEP2 involve 4-fermion diagrams. This can be appreciated by looking at Figure 2 which shows the different classes of 4-fermion diagrams involving neutral currents3. The dominant 2-fermion diagram of LEP1 will, as we shall see later, contribute a background to the 4-fermion channels.

1.4 Luminosity, Centre-of-Mass Energy, and Beam Energy As mentioned above, the LEP2 era started with the introduction of supercon-ducting RF cavities in 1995. Each winter shutdown more and more RF capa-bility was installed, culminating in 2000 when a record centre-of-mass energy of 209 GeV was achieved. Table 1 shows the integrated luminosity recorded by OPAL as a function of v ^ for the period 1995-2000. These numbers are within a few % of those recorded by the other 3 experiments. In total, LEP delivered almost l f b - 1 over the 12 years of operation, with 189pb_1 recorded at LEP1 and 721pb_1 at LEP2. The luminosity-weighted centre-of-mass en-ergy above W + VF - threshold is ~ 196 GeV. Each experiment had installed precision luminometers during the LEP1 era for the Z lineshape measurement and these provided typical luminosity uncertainities of < 0.3% at LEP2.

Fundamental_Interactions/9810249128/files/00014___bc444e0edd308d0294c5421a604f17d6.pdf4

Conversion Annihilation

Bremsstrahlung Multiperipheral

Figure 2: All possible classes of Neutral Current 4-fermion production diagrams.

Table 1: Summary of LEP2 integrated Luminosity during 1995-2000, as recorded by OPAL.

Year yfts) GeV

Luminosity pb 1

1995 130 136

3 3

1996 161 172

10 10

1997 130 136 183

3 3 57

1998 189 187

1999 192 196 200 202

30 78 79 38

2000 205 207 80 140

Figure 3 shows the luminosity recorded by OPAL as a function of A/S over the entire LEP era. In the lower part of the figure can be seen the data recorded during LEP's final year. Also to be remarked is the 2-3pb_1 of Z calibration data that was recorded each year during the LEP2 period. This data was essential to maintain a well-calibrated detector for the lower-statistics LEP2 final states.

Table 2 provides a summary of the exact statistics of the major channels analysed by OPAL. You will notice that the ZZ channel (where we quote candidates-background) is not overwhelming in statistics due, primarily, to its small cross-section.

To be able to determine mw with a precision of ~ 25 MeV we need to control the LEP beam energy to 1 part in 104.4 Unfortunately the LEP1 tech-nique of resonant depolarisation runs out of steam near Ej,eam=65 GeV when

Fundamental_Interactions/9810249128/files/00015___d9a5fa18fc75c491ae33e6cae162173c.pdf - 200

&150

3 IOO so

o

. LEP2 Z col. datu

IOO 120 140 160

%100 j *

80 \

-J 60 I 401 20 i

0, 'JOO JO/ 202 JO.! 20-/ 205 JO(i 207 208 209 210 is (GeV)

Figure 3: Total luminosity recorded by OPAL as a function of centre-of-mass energy.

the beam polarisation drops to zero.5 However, it is hoped that a combination of the following techniques might just provide the needed precision.

A combination of resonant depolarisation at E(,eaTO < 65 GeV followed by magnetic extrapolation via NMR probes to higher energies has given &Ebeam ~ 21 MeV in 1999.

A precision magnetic spectrometer in the LEP tunnel, with beam posi-tion monitors and accurately mapped Bfield, is hoped to provide AEbea,m '-15 MeV.

A machine physics relationship linking the synchrotron tune with applied RF voltage can provide an alternative measure of E&e0m This promises an uncertainty comparable to other methods.

Use the 'radiative return' (see next section) events to calibrate Ebeam with m z . This method, pioneered by Aleph6, may be subject to large systematics and currently suffers from small statistics. Nevertheless, a combination of the 4 experiments may provide a competitive Ef,eam de-termination.

2 2-Fermion Physics

Although the Standard Model has been shown to provide an excellent descrip-tion of 2-fermion physics at LEPl, it is important to continue these measure-

Fundamental_Interactions/9810249128/files/00016___a4c01be47f694d942852b8c52767b37f.pdf6

Table 2: Summary of actual event statistics, as recorded by OPAL. The 2-fermion final states require s/s^/y/s > 0.85, the Bhahba events require \cos9\ < 0.7 and 0acoi < 10 to enhance s-channel contribution, the 77 final state requires cos8* < 0.90 (except for 183,189 GeV that have cosB* < 0.97), and the ZZ final state is an estimate of the signal after background

subtraction.

Year 1995 1996 1996 1997 1998 1999 1999 1999 1999 2000 2000

Lumi pb 1

5.3 10.0 10.3 57.3 187.2 29.6 77.8 78.5 38.0 80.0 140.0

v/JGeV 133 161 172 183 189 192 196 200 202 205 207

TOTAL

QQ 380 370 339 1408 4072 662 1555 1519 705 1515 2410 14935

e+e

210 285 246 1260 3735 577 1448 1430 671 1423 2338 13623

IM+pT 56 45 37 174 527 81 208 200 81 217 353 1979

T+T 24 38 25 123 420 63 149 165 72 154 267 1500

77 66 102 92 620 1740 215 530 469 243 486 767 5330

ZZ

4 50 19 34 26 15 31 53 232

W+W~

28 120 877

3068 431 1277 1127 591 1355 2462 11336

ments at energies well above the Z-pole. The data at LEP2 allow new measure-ments at several discrete energy points over the range 130 < y/s < 209 GeV. The data from the 4 experiments have been combined: for the methodology and results see LEP2FF/00-03 7 and http://www.cern.ch/LEPEWWG/lep2.

2.1 Standard Model and Radiative Return

One major complication of e+e~ annihilation at LEP2 is the potential for Initial State Radiation (ISR) down to the Z-pole. If we wish to study full-energy annihilation events, then we must select those events with little or no such radiation. Figure 4 shows several distributions of Vs', the effective energy of the annihilation as estimated from the data. The Z-pole is clearly visible, particularly in the qq channel. Experiments typically choose ^/s'/^/s > 0.85 for full-energy events and y/s'/^/s > 0.10 for inclusive measurements.

2.2 Cross-sections and F-B Asymmetries for hadrons and leptons In general, cross-sections and angular distributions have been measured and averaged for qq, e+e~~, n+fj,~, and T+T~ final states. The e+e~ Bhabha scat-tering has a dominant contribution from t-channel photon exchange and ad-ditional cuts (eg acolinearity and cms scattering angle) are made to enhance the s-channel. A compilation of the cross-section data from OPAL is shown

Fundamental_Interactions/9810249128/files/00017___ada3f12f5ccf9d71db858da5beb60f2e.pdf7

OPAL 206 GeV preliminary

10 3

10 2

1 ., 1 - , r (a) hadrons

r

i . i

1 I ;

t

h i t

10"

103

10 2

10

1 1 ' 1

- (b) eV

r A,,,^^

i i i i . _

*

f , ,'i

200 Vs'/GeV

Figure 4: Distributions of reconstructed \fp for selected events. The arrows show the position of the cut used to select non-radiative events. Points are data and histograms are

Monte Carlo predictions with non-radiative events shaded.

in Figure 5 together with Standard Model expectations. One sees a very good agreement for all channels at all energies.

The combined LEP data on cross-sections for qq, n+fj,~, and are shown in Figure 6, together with the forward-backward asymmetries from final states where the outgoing charge is easily identified, fi+n~ and T+T~. The Standard Model expectations are superimposed. The theoretical uncertainties are estimated to be ~ 0.2% on qq and ~ 0.7% on +~.

2.3 Cross-sections and F-B Asymmetries for heavy flavours Heavy quark tagging allows cross-sections and asymmetries to be determined for both cc and bb final states. Figure 7 shows the ratio of the heavy flavour cross-sections to the total hadronic cross-section, R^ and Re, and the values of the forward-backward asymmetries, ApB and ApB, together with Standard Model expectations. The data is in excellent agreement with the Standard

Fundamental_Interactions/9810249128/files/00018___a2131bc7ee3299d2bad4a6e27094cc97.pdf8

OPAL preliminary

80 100 120 140 160 180 200 Vi/GeV

Figure 5: Compilation of measured 2-fermion cross-sections together with curves representing Standard Model predictions.

Model. In conclusion, although the combined hadronic cross-sections are on aver-

age 2.5sd above Standard Model predictions7, there is no significant evidence in the results for physics beyond the Standard Model.

3 Some Basic Checks

The excellent data on 2-fermion final states over such a large range of centre-of-mass energy has provided an opportunity to check the expected running of both the fine structure constant and the strong coupling constant, to check the size of the 7 - Z interference term, and to complete more neutrino counting tests.

3.1 Running of Fine Structure Constant In processes involving virtual photon exchange, vacuum polarisation effects lead to a Q2 dependence (running) of aem. The leptonic contributions can be calculated but the effect of quark loops (non- perturbative QCD) must be estimated. There are two recent results from LEP which support the running of aem. The L3 Collaboration has studied both small angle and large angle

Fundamental_Interactions/9810249128/files/00019___98840db2a42e6f3c9710e461a668bf55.pdf9

10'

$10

0.9 0.8

preliminary

e*e"->hadrons(Y) e*e"->u*n (y)

LEP

HtH

preiiminary

120 140 160 180 200 220 >/s(GeV)

120 140 160 180 200 220

^(GeV)

Figure 6: Combined LEP results on 2-fermion cross-sections and forward-backward asym-metries as a function of centre-of-mass energy. The lower plot sections show the ratio (or

difference) of data to the ZFITTER prediction (curves).

0.26

0.24

0.22

0.2

0.18

0.16

0.14

L E P preliminary

- Rt 7 , * * . ,

- Vs'/Vs >: . : . . 0.85

~-

, I, Wr

100 120 140 160 180 200 Vs (GeV)

032 0 1

0.28 0.26 0.24 0 72 0.2

0.18 0 16 0.14

LEP preliminary

- Re

- - " " " " ~ "

^"^"^ 1 x L. *

- V s 7 V s > ^ (S5

J. t I

180 200 Vs (GeV)

1

0.8

0.4

0.2

0

-0.2

_ L E P preliminary

- ^

**

i Vs'/Vs >t'i

L ]i

. 0.85

100 120 140 160 180 200 Vs (OeV)

1.2

1

0.8

0.6

0.4

0.2

0

" L E P preliminary

* Vs'/V s >;: : .> 83

180 200 Vs (GeV)

Figure 7: Combined LEP results on R^ and Rc, and ApB and A^B as a function of centre-of-mass energy. The curves represent the Standard Model prediction of ZFITTER.

Fundamental_Interactions/9810249128/files/00020___d5cc1c5ed0d0ec90a6fb21a78b1af13e.pdf10

136

134

'a

130

128

- 1 0 1 2 3 4 10log(-Q2/GeV2)

Figure 8: Measurements of the fine structure constant aem from small angle and large angle Bhabha scattering. The curve represents the Standard Model expectation.

Bhabha scattering8. In each case the data is divided into a small and large Q2 sample and the change in aem required to represent the data over the relevant Q2 span is determined. The results, shown in Figure 8, exhibit a 3.0sd and 2.9sd effect respectively, in agreement with the expected running of a e m .

The OPAL Collaboration has taken the non-radiative cross-sections and asymmetries for qq, n+fi~, and T+T~ over the range 130 T/S 207 GeV and used ZFITTER to determine the best value of aem, keeping all other variables fixed.9 They obtain a~^ = 126.12;2 at ^/i = 190.7 GeV which is 5.0sd below a~^(0). Figure 9 shows this result together with values from lower energy experiments.

3.2 Running of Strong Structure Constant

Using precision event shape distributions from the qq final state, the com-bined LEP data have been fitted to theory that uses second order calculations in as and NLLA. The event shapes are 1-T, M H , C, B T , B W , and y^3 and the derived values of as were presented at the LEP fest of October 2000: see http://lepqcd.web.cern.ch/LEPQCD/annihilations and are displayed in Fig-ure 10. Excellent agreement with the expected running of as is evident over a wide range of E c m .

Fundamental_Interactions/9810249128/files/00021___3b0e253e67827ec50975059ddeb795ed.pdf11

S155

V5 0 145

140

135

130

125

120

115

110

105

TOPAZ ^p/ee^l and qq average: * Fits to leptonic data from: * DORIS, vv^visiue- These latter results have been summarised by Mnich12 and provide N = 3.00 .08 from all 4 experi-

Fundamental_Interactions/9810249128/files/00022___b22fa3c61796ce9ab125fe6af3c4d7a2.pdf12

E0.15

0.14

0.13

0.12

0.11

0.1

LEP/Jade 35...205GeV NLLA+0(c# log(R)

< Jade T L3 DLO (preliminary) ADLO (preliminary)

til M

50 100 150 200 Ecm[GeV]

Figure 10: Running of the strong coupling constant as as derived from event shape data in e + e ~ annihilation.

ments at LEPl and N = 2.99 .10 from Delphi and L3 at LEP2. An example of the sensitivity of the e+e~ -> vv^ViSme cross-section to the number of light neutrino species is shown in figure 13 by the L3 Collaboration13. The ratio of measured/Standard Model cross-section averaged over the 4 experiments is 0.965 .028, perfectly compatible with 3 neutrino species.

4 Constraints on New Physics

LEP has measured cross-sections and angular distributions for e+e~ -> qq, e+e~ / ^ + / X ~ , T + T ~ , 7 7 , W + W _ , and ZZ and, within errors, everything agrees with the Standard Model expectations. We will now use this data to set limits on a variety of models incorporating new physics. In general, the Standard Model Lagrangian is modified by the addition of a new contribution representing the new physics and incorporating model specific parameters. This new contri-bution will be multiplied by an effective coupling constant and divided by an effective scale. Typically, both the coupling constant and scale are unknown and, in general, an assumption is made for one of them when obtaining limits on the other. Thus, care should be taken when interpreting the results below.

Fundamental_Interactions/9810249128/files/00023___f676ef706aaa6895faa7dd9878cdb343.pdf13

^

Figure 11: Hadronic cross-section

e+e ->hadrons(y)

ViTs > 0.85

r=0.00 -j=0.31 - r = 0 . 6 2 had had had.

1.1-

1-

0.9-

" T | i ' i

j t t

120 140 160 180 Vs(GeV)

200

as a function of centre-of-mass energy together with theory predictions for different values of j j ^ .

1.5-

1-

-DO.5-

0-

-0.5-

68% CL

\ \

SM ^

Zdata all data

\ > >:-^_

\

L3

\ ?\

\

\ . - :

91.17 91.18 91.19 91.2 mz [GeV]

Figure 12: Allowed contours in the mz jf^j plane showing the improvement with new LEP2 data. The vertical band shows the mz range from a fit assuming the Standard Model

value for 7 / Z interference.

Fundamental_Interactions/9810249128/files/00024___18946392130fc7cb2a7cdf91939ca9a5.pdf14

10 i

1 1

c

e10 i

10 =

100 150 200 Vs (GeV)

Figure 13: Cross-section measurements for e+e~ - vv*y compared to the Standard Model expectation for 2,3,4 neutrino species. The upper curve corresponds to the extrapolated full

cross-section e+e - > vv.

4-1 Limits on Z'

An introduction to Z' physics can be found in a paper by Altarelli, Mele, and Ruiz-Altaba 14 which should be consulted together with the mini-review in PDGT 200015. One motivation for Z' searches is that Grand Unified Theories, eg E(6), will contain extra U(l) gauge groups. Current analyses incorporate Z-Z' mixing into ZFITTER in which the couplings of the bare state Z0' are model dependent. Analyses with LEP1 data only, eg by the Delphi Collabora-tion 16 , already limited the mixing angle to a few mrad. The LEP2 analyses generally extend the exclusion region in the Z' mass-mixing angle plane as demonstrated by the OPAL Collaboration17 in Figure 14. The data from the 4 LEP experiments have been combined (see LEP2FF/00-03 from the LEP-EWWG ff subgroup), and with zero mixing, yields limits on possible Z' masses at 95% CL ranging from 400 GeV to 2260 GeV, depending on the specific model couplings.

4-2 4~f Contact Interactions Eichten, Lane, and Peskin have demonstrated a method to detect possible quark or lepton substructure via the introduction of a Lagrangian representing 4-fermion contact interactions 18. The coupling constant (g2/47r), which is

1 '

Nv = 2

L3;

e+e~ - vv(y)^

....e^e~ -> VVT(Y) '

Fundamental_Interactions/9810249128/files/00025___52ac00dc661634e562aa4d636736aa0a.pdf15

300 500 700 1000 2000 Z' mass [GeV]

Figure 14: Exclusion contours at 95% CL in the Z' mass-mixing angle plane for specific models. Only the inner area is allowed.

unknown, is generally set to unity by convention. Results on the scale on the contact interactions are given by A - and A+ , where the sign characterises the chiral structure of the interaction. The LEP2 data have been fitted by the LEPEWWG (see LEP2FF/00-03) using (a) purely leptonic final states fi,+H~ and T+T~ and (b) heavy flavour bb and cc final states. The results are displayed in Figures 15 and 16 respectively. In the leptonic case the limits range from 8.0-23.9 TeV, and in the hadronic case from 1.3-14.0 TeV.

4-3 Exchange of R-parity violating sneutrinos Since scalar neutrinos can decay to lepton-pairs via direct R-parity violating transitions, they can contribute to l+t~ final states via both s-channel and t-channel 2-fermion exchange diagrams. The analysis of LEP2 data thus allows limits to be derived on several products of couplings Xijk (where i j , k represent generation indices) as a function of u mass. A good example has been presented by the L3 Collaboration19 at yfs = 189 GeV and shown in Figure 17.

4-4 Exchange of Leptoquarks In the reaction e+e~ -> ff a contribution of t(or u)-channel leptoquark ex-change is possible. Analyses can provide limits on scalar or vector lepto-quark masses as a function of the relevant coupling constant. With a value of

Fundamental_Interactions/9810249128/files/00026___0fcf3a4fbd3bbff02dbf38a4c35624bf.pdf16

LEP Combined Preliminary

A" A+

LL 10.0 15.2 RR 9.1 15.6 VV 15.3 23.9 AA 15.6 18.8 RL 8.0 11.6 LR 8.0 11.6 V0 13.8 22.7 A0 11.0 16.2

11 0 20. A+ (TeV)

Figure 15: Limits on A for contact interactions from fj,+fi and T+T final states.

LEP Combined Preliminary LEP Combined Preliminary

A" A+

LL 9.1 11.1 RR 2.2 7.2 W 10.0 12.4 AA 11.2 14.0 RL 7.3 2.4 LR 3.2 5.7 V0 10.8 12.9 A0 6.4 4.1

bb 20. A'

1

E 1

c (TeV)

H

A+

ZJ

Zl

20

(TeV)

A" AT

LL 5.2 1.3

RR 4.5 1.5

W 7.3 6.6 AA 6.4 5.1 RL 2.9 2.6 LR 3.5 2.1 V0 6.7 1.4 A0 3.9 2.6

CC

ED 1 = ]

20. 0

A" (TeV) 20.

A+(TeV)

Figure 16: Limits on A for contact interactions from e+e -> bb and e+e > cc.

Fundamental_Interactions/9810249128/files/00027___3136374bebf368bc23b35c3b67ba7613.pdf17

vx(vM) mass [GeV]

150 200 250 vx mass [GeV]

300

v^ mass [GeV]

Figure 17: Upper limits at 95% CL on the coupling strengths A^j, of scalar leptons to leptons as a function of scalar neutrino mass.

Figure 18: Measurements of the cross-section e + e - -> 77 as a function of centre-of-mass energy together with the Standard Model QED expectation. The upper box shows the

data-Standard Model difference.

Fundamental_Interactions/9810249128/files/00028___5e236591195f798040fb9bbcf7598da4.pdf18

g2/47r = a the L3 Collaboration19 has been able to derive lower bounds for the leptoquark mass within the range 55-560 GeV.

4-5 QED cut-off parameters

The reaction e+e~ -> 77 is a pure QED process mediated by electron exchange in the t-channel. Figure 18 shows the cross-section data of the OPAL Collab-oration over the entire LEP energy range together with SM expectation.9 No discrepancy is observed. Deviations from pure QED are typically determined from a fit of the differential cross-section and expressed in terms of cut-off pa-rameters A. The sensitivity of this method improves as ^/s increases, see for example the results of the L3 Collaboartion20. A recent analysis by the OPAL Collaboration 9 using all data up to ^/s = 207 GeV gives limits on A in the 325-350 GeV range.

4-6 Exchange of Excited Electrons

The e+e~~ - 77 reaction can also be influenced by the exchange of an excited electron (e*) in the t-channel. The effect will depend on the e* mass and on the coupling ge*e7- A recent analysis by the OPAL Collaboration9, with the restriction gee7=gee7> has set a lower mass limit of 354 GeV at 95% CL.

4-7 Models with Low-scale Gravity

In string models involving extra dimensions, the possibility of spin=2 graviton exchange could influence the reactions e+e~ -> ff and also the final states 77, W + W ~ , and ZZ, see Mele and Sanchez21 and a recent talk by P. Krieger at SUSY2K 22. The differential cross-sections are modified by the addition of a pure graviton term and an interference term. Only the latter is relevant at LEP energies and contributes inversely proportional to the 4th power of Ms (the effective Planck mass at the string scale). The coupling constant is un-known (can only be calculated with a full knowledge of the underlying quantum gravitational theory) and is usually set to either A = -1 or + 1 . 95% CL lower limits on Ms from an analysis of 77, ZZ, i y + W ~ final states are 0.96 TeV and 0.92 TeV21 and from n+n~, T+T~, 77, ZZ final states are 0.88 TeV and 0.89 TeV2 3 . The latter results by the OPAL Collaboration are derived from the likelihood curves shown in Figure 19.

Fundamental_Interactions/9810249128/files/00029___95cfeaa2887b0686e32689cdfb0f8380.pdf19

OPAL preliminary * 6 7 <

5

4

3

2

1

" - 8 - 6 - 4 - 2 0 2 4 6 8 A/Ms< (TeV-4)

Figure 19: Log likelihood curves as a function of X/M* for different final states together with the combined result (solid curve).

4.8 Limits on FCNC single top production

With a top quark mass of 174.3 5.1 GeV, LEP2 cannot produce tt pairs. However, FCNC can produce a single top quark via a loop diagram leading to final states tc(u). Although Standard Model calculations of this process lead to impossibly small cross-sections24, an investigation of this channel may provide surprises. Two current searches for such final states with t -* bW decays have provided 95% CL upper limits of 0.48pb25 and 0.35pb26. The Aleph Collaboration has expressed its result in the form of exclusion limits in the couplings corresponding to t -> cZ and t -> cy 25. This exclusion region is displayed in Figure 20 together with a previous exclusion from CDF. The KZ limit is clearly improved and will continue to improve when all the LEP data are combined.

5 ZZ Physics

The reaction e+e~ > ZZ, with a threshold near y/s = 183 GeV, proceeds via the Standard Model diagrams NC02 involving the exchange of an electron in the t(u)-channel. The final state is of special interest because it constitutes an irreducible background to e+e~ HZ. Some of the final state character-istics that are used to identify Z-pair candidates are listed in Table 3 which

i i i 1 1 1 ] 11 i i i n . .

1 corabi,,ed / ;w / : LX/MJ= \

:^!IK

\ :. \ \

- , \ \

, , 11 , ' , ' : -^ '";-^I ,V\ 'J

/ / / /-/ ; /

Lj /^u :

fe^w.;

Fundamental_Interactions/9810249128/files/00030___c1de020c9ee68a26ace923226342c194.pdf20

^

Excluded by CDF

Figure 20: Exclusion curves at 95% CL in the Kz-K-y plane for different values of mt. The region excluded by CDF is shown by the dashed box.

is taken directly from a recent talk by G. Bella 27. Remember that the Z branching ratios are 70% to ff, 10% to +~, and 20% to vv. In general it is rather difficult to obtain 'clean' signals due to the large backgrounds, partic-ularly those due to 2-fermion QCD and VF+V7~-pairs. The channel qqi+t~ has the highest efficiency*purity. A beautiful qq(i+(t~ event at v^ = 205 GeV recorded by the OPAL Collaboration is shown in Figure 21.

Table 3: Final States used to identify ZZ-pairs. ME represents missing energy, and leptons refers to electrons/muons/taus.

Final State QQQq qqvv qgi+t-l+t-vv e+e~e+e-vvvii

Fraction 49% 28% 14% 4% 1% 4%

Signature 4jets 2jets + ME 2jets + 21eptons 21eptons + ME 4Ieptons invisible

Efficiency 30% 30%

50 - 80% 30%

40 - 60%

Purity 15 - 35%

60% 80 - 90% 45 - 55% 60 - 80%

Analyses typically use many sequential cuts and/or multivariate techniques and impose mass constraints where possible (eg. Z -> ff, i+~). The event rates are small, see Table 2, and the channels are combined in a maximum likelihood fit that assumes Standard Model Z branching ratios to determine the reaction cross-section at each energy. Figure 22 shows the combined-LEP

Fundamental_Interactions/9810249128/files/00031___13b5e8694e6e3ed256ed868b17260a39.pdf21

z * ->x

I " " I I r ' * "*"

Figure 21: A classic example of e+e~ Z Z > qq(i+fj,~ as recorded by the OPAL Collab-oration at v'* = 205GeV.

cross-section together with theory expectation from YFSZZ and ZZTO, which have a 2% uncertainty. The agreement is excellent. In fact, the ratio of mea-sured/theory cross-section, averaged over all y/s is 0.99 0.06 28.

All LEP Collaborations have analysed the ZZ cross-sections and angular distributions to search for anomalous neutral-current triple gauge couplings which are forbidden at tree-level within the Standard Model. No evidence has been found for non-zero couplings.

6 W+W- Physics

The main focus of the LEP2 program has been a detailed study of the e+e~ > W+W~ process to (a) confirm the presence of the non-abelian triple gauge couplings which are demanded by the Standard Model and to (b) make a precision measurement of mw

Fundamental_Interactions/9810249128/files/00032___1ee3c6300dcab3fab9db14952dd55147.pdf22

21/07/2000

15 LEP Preliminary * 2 . 0 % uncertainty

Y F S Z Z

o . Z Z T O

0.5 -

170 180 190 200 EOT[GeV]

Figure 22: Measurements of the ZZ-pair cross-section (points) compared to the Standard Model prediction (curves).

6.1 Cross-section Determination

W+W~-\>&\r production takes place via the Standard Model diagrams CC03 which are (a) a t-channel ve exchange, (b),(c) s-channel 7, Z exchange involv-ing the triple gauge couplings (TGCs) 7WW and ZWW respectively. Diagram (a) is dominant near threshold and gives the forward W~-peaking in the an-gular distribution. Some of the characteristics of the channels used to isolate W+W~-pair candidates are given in Table 4, which is taken directly from a recent talk by G. Bella29. Remember that the W decays hadronically (qqf) 67.5% and semi-leptonically [ivi) 32.5% of the time. The decay W -> tb is not kinematically allowed. In comparison to ZZ production (see Table 3) the W+W~ efficiencies and purities are significantly higher. There are still size-able QCD backgrounds, particularly in the fully-hadronic channel, and these must be estimated carefully from Monte Carlo.

The candidate event samples are isolated after applying sequential data cuts and/or multivariate techniques. A beautiful qqiqqi event at ^/s 208 GeV recorded by the OPAL Collaboration is shown in Figure 23.

The W + W ~ signal is estimated by subtracting the Standard Model back-ground and then applying a maximum likelihood fit to obtain the CC03 cross-section with/without a simultaneous extraction of the W branching ratios. If we assume Standard Model W branching ratios, the resulting all-LEP cross-

Fundamental_Interactions/9810249128/files/00033___9147eb27c731658b858d61d5f32e29f4.pdf23

Table 4: Final States used to identify VF+IV -pairs. ME represents missing energy, and leptons refers to electrons/muons/taus.

Class Fully-hadronic Semi-leptonic

Fully-leptonic

Final State qqlqql qqieu* qqlfiVf, qqirVT inui

Fraction 45.6%

43.9%

10.6%

Signature 4jets 2jets + isolated lepton + ME 2 acolinear jets + ME

Efficiency 85% 85% 90% 65%

45 - 80%

Purity 80% 95% 98% 85% 90%

Figure 23: A classic example of e+e > W+W -> qqlqql as recorded by the OPAL Collaboration at V^ = 208GeV.

section is displayed in Figure 24 (see LEPEWWG/XSEC/2000-0130). The fig-ure also shows the current theoretical predictions from RacoonWW/YFSWW3 and GENTLE that have inherent uncertainties of 0.4% and 0.7%, respectively. Clearly, the data are well-represented by the Standard Model predictions and provide a convincing case that all three CC diagrams are required, ie triple gauge couplings are needed. Figure 25 shows the latest LEP2 data in greater detail (see LEPEWWG/XSEC/2000-01).

Fundamental_Interactions/9810249128/files/00034___db23c090bf0a2c1dbec3ef008e492aa9.pdf24

LEP Preliminary

> ^ * - + r *"-"*

RacoonWW/YFSWW 1.14 Gentle 2.1 (+0.7%) no ZWW vertex only v exchange

160 170 180 190 200 210

Ecm fGeV]

Figure 24: Measurements of the W+W -pair cross-section (points) compared to the Stan-dard Model prediction (curves) with/without triple gauge couplings.

20

5" S 15 e

10

5

LEP 21/07/2000

Preliminary " -" RacoonWW/YFSWW 1.14

" " * Gentle 2.1 (0.7%) J , ^

/ "

/ 18

' 16

YFSWW 1.14 , RiicoonWW 1 | j

i x >pT

160 170 180 190 200 210

Ecm IGeV]

Figure 25: Measurements of the W+W -pair cross-section (points) compared to the Stan-dard Model prediction (curves).

Fundamental_Interactions/9810249128/files/00035___ca578e650e795504cbbddf8eb0f7ed82.pdf25

21/07/2000 Summer BO - Preliminary -1161-207) GeV

W Leptonic Branching Ratios

OPAL L E P W - e v

OPAL LEP W-nv

OPAL

LEP W-TV

LEP W-*lv [161-202] GeV 1161-202] GeV "

10 5 ? - 0 37 10 62 1 0 20

1 0 5 6 - 035

11P0+ 0 18

10 69 0 ) 9

11.07+ 0.25

10.74+ 0.10

"TO Vi 12 Br(W->lv) [%]

Figure 26: Measurements of the W leptonic branching ratios provided by the 4 LEP exper-iments together with the combined result. The solid vertical line represents the Standard

Model expectation.

6.2 Branching Ratios, Lepton Universality, and CKM Matrix

If the maximum likelihood fit does not assume Standard Model W branching ratios, then these can be determined from the fit to the channel data. Figure 26 shows the W-leptonic branching ratios as determined by each of the 4 LEP ex-periments and their combined values. For each leptonic channel the individual measurements are in good agreement and the 3 combined values are consistent within 3.3% of equality thus confirming the Standard Model expectation of uni-versal lepton couplings. Assuming lepton universality, the W to inug branching ratio is determined to be 10.740.10% per lepton decay channel, and the W to qql branching ratio is determined to be 67.78 0.32%, in good agreement with Standard Model expectation (10.83% and 67.51% respectively). The precision is now better than that from the pp collider experiments 31.

The determined branching ratios can now be used to set new values on specific terms of the CKM matrix (see LEPEWWG/XSEC/2000-0130). The

Fundamental_Interactions/9810249128/files/00036___5ce594b3dfa153b57efd9fe57ab653ba.pdf26

qql branching ratio is related to a sum of 6 terms in the CKM matrix, of which Vcs is the least well determined. Using PDGT 2000 for the sum of the other 5 terms, the LEP hadronic branching ratio (above), and aa{m%f) = 0.121 .002, a value of Vcs = 0.989 0.016 has been extracted. It should be noted that this value does not assume unitarity of the CKM matrix and that the error is dominated by the branching ratio uncertainty.

A more direct determination of VC3 follows from the measurement of R, the ratio of the charm to total hadronic branching ratio of the W. Since extra selections are needed to isolate the charm component, the resulting precision will be clearly inferior. The 4 experiments in combination have determined RY - 0.494 0.044 and this leads to an extraction of Vcs = 0.96 0.08, signif-icantly less precise than the value above. Nevertheless, the two determinations are in good agreement with each other, and with expectation.

LEP Preliminary

Figure 27: Measurements of the single-W cross-section (points) compared to Standard Model predictions (curves).

6.3 TGC Determination and W-polarisation

The W+W~-pair cross-section measurements (see above) have already shown the necessity to include the two s-channel diagrams involving triple gauge cou-plings. These W+W~/y and W+W~Z couplings are demanded by the gauge structure of the Standard Model. There are other reactions involving the

Fundamental_Interactions/9810249128/files/00037___57d71fd3d0f08055307b8635cf8c0e65.pdf27

Figure 28: Diagram representing the angle definitions in the TGC analysis - from a talk by A. Macchiolo, EPS-HEP99, Tampere, Finland.

W+W~y coupling, in particular the single-W diagram leading to the Wxl&Tl final state, and the single-7 diagram leading to the 1^71^ final state, both of which are accessible at LEP2. The form and strength of these vertex couplings are unambiguously predicted by the gauge structure of the Standard Model, see e.g. the paper of Bilenky et al. 32 and also the Yellow report CERN 96-01. Although the most general Lorentz-invariant Lagrangian describing TGCs has 14 terms, after insisting on gauge invariance and C+P conservation, only 3 terms remain which, in the Standard Model, 1, gf = 1, and A7 0, ie only 2 terms non-zero. The term 'anomalous' TGC refers to any TGC, includ-ing the 2 non-zero Standard Model TGCs, with values different from Standard Model expectation. The measured cross-sections for e+e~ -> W+W~, and WeV^, and the production/decay angular distributions for W+W~-pair pro-duction are sensitive to the form and strength of all possible TGCs. Figure 27 shows the LEP cross-section for the single-W final state, for those cases with W hadronic decays. The data is seen to be in good agreement with the Standard Model expectation, albeit with a 5% theoretical uncertainty.

Figure 28, taken from a talk by A. Macchiolo at EPS-HEP99, shows the definition of the 5 angles needed to specify the complete production and decay distributions in the W+W~ final state. We remark in passing that the entire angular phase-space is not always accessible due to ambiguities resulting from quark flavour identification, or missing neutrinos in the fully-leptonic channels,

Fundamental_Interactions/9810249128/files/00038___bb9f9bc0e0283c1d6e3834c2065c36b1.pdf28

and problems with imperfect jet pairing. Figure 29 gives some idea of the sensitivity of these angular distributions to anomalous values of gf, taken from the OPAL Collaboration33.

OPAL

-1-

....

Data SM A g ; -A g ; -

+0.5 -0.5

Figure 29: Sensitivity of angular distributions to anomalous values of g\ for data taken from semi-leptonic WW events at 189 GeV.

There are two methods in common use for an extraction of the TGCs. The first is model-dependent and determines the TGCs from maximum-likelihood fits to the cross-sections and angular distributions. The second is more gen-eral and evaluates the W + W ~ spin density matrix from which one can ex-tract the helicity structure and polarisation properties. Figure 30 shows the log-likelihood curves from method 1 using the combined LEP data (see LEP-EWWG /TGC/2000-0234) and Table 5 summarises the values and limits ob-tained for Agf = gf 1, A K 7 = K7 1, and A7. In each case, the fits vary 1 parameter at a time, the others being kept fixed at their Standard Model values (ie =0). The results show no evidence for anomalous values of the cou-plings. More complex analyses looking for the other 14-3=11 parameters also give no evidence for non-zero values (this is good because they would violate C, P, or CP conservation). When all the LEP data is analysed, the precision on Agf = gf 1, and A7 should be better than 0.02, and on A K 7 = K7 - 1 better than 0.05 35. Note that these direct determinations of the TGCs con-

Fundamental_Interactions/9810249128/files/00039___da70911f70f699fa43ef67d7958e49e2.pdf29

ALEPH + DELPHI > I * + OPAL - 3

| , 5 2

l.S

0.5

0 -0.4 -0.2 0 0.2 0.4 -0.2 -0.1 0 0.1 0.2

Al^ dg*

Akf -0.002 + Mg

Ag*= -0.0251 |fi{ xy =-o.o36i8;l!5?

"-0.2 -0.1 0 0.1 0.2

\ Preliminary

Figure 30: Log likelihood curves of the 4 LEP experiments and the combination (solid curve) for 3 triple gauge couplings.

trast with previous indirect estimations using EW radiative corrections at the Zpole 3 6 .

Table 5: Table of values and limits for triple gauge couplings. Parameter Agf = gf - 1

A7

Value -0.025+S -0.002;ggJ -0.036J;;o2?

95% CL limits [-0.074,+0.028] [-0.13,-1-0.13]

[-0.089,+0.020]

Standard Model expectation 0 0 0

The more general approach leading to helicity structure and polarisation has been formulated by Hagiwara, Peccei, and Zeppenfeld37. W's are expected in both transverse (helicity 1) and longitudinal (helicity 0) polarisation states. One can employ the full 9*9 spin density matrix for W+W~ or, more simply, just use the W-decay as a polarisation analyser to extract the fractional contri-butions of helicity -1 , 0, and +1 (denoted by f_,fo,f+ respectively). Hagiwara et alia37 have predicted the transverse and longitudinal components as a func-tion of the W production angle cos#w at y/s 190 GeV. A recent study by the L3 Collaboration38, whose results are displayed in Figure 31, shows that within

Fundamental_Interactions/9810249128/files/00040___a4270b0f547401e5525e890e731fecac.pdf30

38'40 of fo together with Standard Model expectations.

Table 6: Table of values of longitudinal polarisation fraction, fo-y/s (GeV) 183 183+189 183+189 183-202

Collaboration OPAL

L3 OPAL

L3

fo data 0.242 0.091 0.023 0.261 0.051 0.016 0.210 + 0.033 + 0.016 0.259 0.035

SM expectation 0.272 0.26 0.257 0.248

6.4 Mass Determination

The determination of mw is perhaps the most important, and certainly the most challenging, of the LEP2 precision measurements. See LEPEWWG/MASS/ 2000-0141 for more details. There are two standard methods [1] via the mea-surement of the cross-section (e+e~ -+ W + W ~ ) variation near W + W ~ thresh-old, and [2] via the direct mass reconstruction from the W decay products. In the latter case, as seen in Table 4, there are three event categories: (a) the fully-hadronic channel qqtqqt, (b) the semi-leptonic channel qq'iPe, and the

Fundamental_Interactions/9810249128/files/00041___3efe838654b7e1d22c6eabcea47742c1.pdf31

fully-leptonic channel t&tlvt. As discussed by R. Strohmer42, this last channel, which represents only 10.6% of all W + W - decays, has 2 undetected neutrinos and there are not enough constraints to perform a kinematic fit. Nevertheless, one can look at either the charged lepton energy spectrum or at a pseudo-mass estimator (which assumes the neutrinos are in the same plane as the leptons) to try and determine mw- However, the resulting error on mw ranges from 0.5 to 1.5 GeV and the channel is ignored for the time being.

The threshold method [1] (see CERN-PPE/97-154) was historically the first method used by the LEP Collaborations in 1996 when the beam en-ergy was raised above W + W - threshold. Approximately 30 W + W - events were observed by each experiment at y/s = 161 GeV and the resulting LEP-combined CC03 cross-section was determined to be 3.69 0.45pb. Knowing the variation of cross-section with W mass (see Figure 32), this translates into mw = 80.40to2i 0.03 GeV, where the systematic error of 0.03 GeV comes from the LEP energy calibration. As we will see later, the statistical weight of this threshold measurement will be overshadowed by the more precise direct mass determinations.

_ Vs~=161.33 0.05 GeV

6 J3 Q. ^ 5 o

$ 4 CO CO CO Q

2 3 o

"79 79.5 80 80.5 81 81.5 82 mw[GeV]

Figure 32: Extraction of mw from the LEP measurement of the W-pair cross-section near threshold. The curve represents the Standard Model.

The direct mass reconstruction [2] utilises both the fully-hadronic and semi-leptonic W^+W~ decay channels. The fully-hadronic channel, which con-stitutes 45.6% of all W + W ~ decays, was discussed recently by S. Schmidt-Karst at Osaka43. The events are forced into 4 jets, energy/momentum con-

v. C^y = 3.69 0.45 pb l \ mw = 8 0 . 4 0 ^ GeV \ N^ LEP Average

r :

I.I

i.in

.1

* ' :

Fundamental_Interactions/9810249128/files/00042___48660d9383026acb64f475c0f4d9b251.pdf32

straints are applied, and the two Ws are constrained to have the same mass. Of the 3 possible 2-jet pair combinations, current methods to choose the correct pairing succeed in about 90% of the cases. The resulting mass distribution is fitted with a variety of methods and systematics are evaluated. Currently there are two serious complications associated with potential final state interactions (FSI).

The first of these is associated with Bose-Einstein Correlations (BEC), see a recent talk by A. Valassi at Osaka44. BEC produce an enhancement of identical bosons in regions of close proximity of phase-space, giving more ir than 7T+_ at small values of Q. We already know that intra-W BEC exist, but if inter-W BEC were found to be present in the data then this could bias the determination of mw- The Aleph Collaboration 45 has recently shown strong evidence for intra-W BEC (see Figure 33 for semi-leptonic WW events) but their current data do not strongly favour inter-W BEC (see Figure 34) in fully-hadronic WW events. It will take the combined-LEP data to make a more definite statement.

The second FSI complication is associated with Colour-Reconnection (CR), see a recent talk by P. DeJong at Osaka 46. CR involves the exchange of coloured gluons during the non-perturbative hadronisation phase and could, in principle, give a bias to m w Several Monte Carlo models predict differ-ing CR behaviour and there is no firm conclusion yet from the 4 experiments. However, a new, promising, method involving a study of particle flow was pre-sented by the L3 Collaboration at Osaka47 and this is shown in Figure 35 together with the expectations of several CR models. It is hoped that, with the full statistics from all 4 experiments, several models of CR could be ruled out, thus limiting the size of the associated systematic error.

Direct mass reconstruction from the semi-leptonic channel has been dis-cussed recently by R. Strohmer at Osaka42. This channel represents 43.9% of all W+W~ decays and comprises the 3 separate leptonic decays eUe, fiv^, and TVT (see Table 4). There is clearly no problem here with inter-W FSI, nor is there any difficulty with jet-choice. The semi-leptonic channel has good effi-ciency and high purity. Energy and momentum, and mass equality constraints are applied as for the fully-hadronic channel previously. However, the TVT decay channel has additional missing neutrinos and the tau energy cannot be determined. One uses the mass from the hadronic decay in this case. Again, mass distributions are fitted with a variety of methods and systematic error contributions are evaluated.

Figure 36 shows some typical mass distributions from the 4 experiments. The shaded regions, which represents background contributions evaluated from MonteCarlo, are generally small and well-determined.

Fundamental_Interactions/9810249128/files/00043___e5fbaab614be997f45c3bfd28695ab60.pdf33

ALEPH Semileptonic W W events 172+183+189 GeV date

(i*(i+K-t>,irt)

* BK(JETSET)MC/*adardMC

+ i + + + V ^

0.25 03 0.75 1.25 1.5 1.75 2 Q(GeV)

Figure 33: Bose-Einstein correlation function for semi-leptonic W W events. The solid curve represents a fit to the data.

" ALEPH Hadronic WW events 172+183+189 GeV date

If MC

BEB (JETOET) MC / CMtotf MC BEI (JETSET) (knlila W o]]>) MC / MMdud MC

-4-==

X = 0.23 0.03 a = 4.26 0.43 GeV

t ^ t u t t4_7;4_4:t-

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Q(GeV)

Figure 34: Bose-Einstein correlation function for fully-hadronic W W events. The solid curve represents a fit to the data. The open circles represent the prediction of a model that

incorporates inter-W Bose-Einstein correlations.

Fundamental_Interactions/9810249128/files/00044___4dab2e63537308559af76dfb33576acc.pdf34

0 0.2 0.4 0.6 0.8 1 rescaled angle (fy^)

Figure 35: Ratio of particle flows between jets from the same W and between jets from different W's as a function of the rescaled angle. The histograms represent Monte Carlo

predictions.

5 70

a. eo

ALEPH Preliminary Vs = t88.6Gev cvqqqq

If

J \

Figure 36: Examples of reconstructed W mass distributions from the LEP experiments.

Fundamental_Interactions/9810249128/files/00045___3ecd71758240985082a2bbc8e3d3c9af.pdf35

6.5 Combination of Mass Values The LEPEEWG (see LEPEEWG/MASS/2000-01) has combined the results of the direct reconstruction from the fully-leptonic and semi-leptonic channels after carefully taking into account the correlations in the systematic errors. The results are summarised in Table 7. One immediately notices the large val-ues of systematic error associated with colour-reconnection and Bose-Einstein correlation in the fully-hadronic channel. We hope to reduce these by a sub-stantial factor before the final analysis is complete. With the current values, the qqiqqi statistical weight in the combination is but 27%. Another systematic that may reduce in the future is that labelled 'Hadronisation'. This is asso-ciated with the differing Monte Carlos currently employed and could benefit from improved 'tuning' of the models to data. One notices that the difference in m\y between the qqiqqi and the qqit&i channels is only 4-5 51 MeV, in-dicating that global FSI effects cannot be huge. This is somewhat reassuring. The current best measurement of m\y is the combination of all direct mass values together with the threshold mass value, and leads to a LEP result of m w = 80.427 0.046 GeV (see Table 8). It is hoped that a final LEP2 result will have a total error of ~ 30 MeV.

Table 7: Tabulation of systematic and statistical errors in the determination of the W-mass. Units are MeV.

Source of systematic error ISR/FSR Hadronisation Detector effects LEP beam energy Colour reconnection Bose-Einstein correlations Others Total systematic Statistical error Total error (MeV) Mass m w (GeV)

qq/i>l 8

26 11 17 0 0 5

35 38 51

80.427

QQ'QQl 10 23

7 17 50 25

5 64 34 73

80.432

combined 8

24 10 17 13

7 4

36 30 47

80.428

Table 8: Combination of LEP2 threshold and direct W-mass determinations. Source Threshold Method Direct Mass Measurement LEP2 combined

Mass value (GeV) 80.400 0.220 0.030 80.428 0.030 0.036 80.427 0.046

Fundamental_Interactions/9810249128/files/00046___0975e7a89a2ac73073eb61a7d701799d.pdf36

6.6 Comparison of Direct and Indirect Mass Estimates We can now compare the direct mw measurement from LEP2 with (a) the direct measurements from the pp colliders and (b) the indirect measurements from the Standard Model fits to precision data of LEPl/SLD and neutrino scattering data (see Figure 37). Within the current level of statistics, there is no difference between the separate measurements. It certainly looks as though the Standard Model has no surprises, at least within the energy range over which we are testing it. It is an experimental triumph that the direct and indirect mass measurements agree so well.

Figure 38 shows the direct and indirect error ellipses in the 2-dimensional plane of mw vs m t as a function of the Standard Model Higgs mass. One notices two things: (a) the error ellipses overlap substantially and (b) the overlap area indicates a strong preference for a low mass Higgs.

W-Boson Mass

pp-colliders

LEP2

Average

NuTeV/CCFR * -

LEP1/SLD/vN/mt

80 80.2

_

-*-

80.4 [Ge> /]

[GeV]

- 80.452 0.062

80.427 0.046

80.436 0.037 X2/DoF: 0.1 / 1

80.25 + 0.11

80.386 0.025

80.6

Figure 37: Comparison of W mass measurements. The direct measurements from LEP and pp colliders are averaged and compared to indirect determinations.

Finally, we show in Figure 39 the chisquare behaviour of the complete Standard Model fit as a function of the Standard Model Higgs mass in which all precision electroweak data has been used (LEP1 lineshape, SLD asymme-tries, neutrino scattering, tau polarisations, direct measurements of mw and m t , etc). For full details consult CERN-EP-2000-15348 for the combination procedures and CERN-EP-2001-02149 for the combination results themselves. In this figure the shaded region represents the area already excluded by di-

Fundamental_Interactions/9810249128/files/00047___f1099dec273b994c6723ab9908b35c6a.pdf37

80.6

80.5

>

80.4 5 E

80.3

80.2 130 150 170 190 210

m, [GeV]

Figure 38: Comparison of the indirect measurements of mw and "H (solid contour) and the direct measurements (dashed contour). Also shown is the Standard Model relationship as a

function of Higgs mass.

rect LEP Higgs searches (up to approximately 113 GeV at 95% CL50). The solid (dashed) curve provides a 95% CL upper limit for the Standard Model Higgs mass of 165 (206) GeV. This will provide a great incentive for dedicated searches at Tevatron2 and the LHC. Which laboratory will claim a discovery?

7 Conclusions

These two lectures have displayed the wealth and beauty of LEP2 electroweak physics. There is absolutely no evidence for any significant deviation from current Standard Model expectations. Long live the Standard Model of particle physics.

Acknowledgments

I would like to thank the organisers of the Lake Louise Winter Institute for the invitation to deliver these lectures and for their excellent hospitality in such a marvellous setting.

Fundamental_Interactions/9810249128/files/00048___d9d54072893db87c4ab74014c3dc28a6.pdf38

^

A a had ~ ';-0.O280410.00065I V - 0.02755+0.0004M

Excluded Preliminary

10 10 mH [GeV]

10

Figure 39: Chisquare versus Higgs mass. The theory uncertainty band represents missing higher order corrections. The excluded region is from direct Higgs searches. The dashed

curve is the result obtained with a new determination of the fine structure constant.

References

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Boson Pair Production at LEP, CERN-EP/99-118. 22. Searches for Extra Dimensions at LEP, P. Krieger,talk given at SUSY2K,

CERN, June 2000. See http://wwwth.cern.ch/susy2k/susy2ktalks/krieger.ps.gz

23. OPAL Collaboration, Search for Low Scale Quantum Gravity in Extra Spatial Dimensions in ZZ Production at LEP, OPAL Physics Note PN440. See http://opal.web.cern.ch/Opal/

24. C. Huang, X. Wu, and S. Zhu, Phys. Lett. B452, 143 (1999). 25. ALEPH Collaboration, Search for Single Top Production in e+e~~ Colli-

sions at y/s= 189-202 GeV, CERN-EP/2000-102. 26. OPAL Collaboration, Investigation of Single Top Quark Produc-

tion at yfs= 189 GeV, OPAL Physics Note PN444. See http://opal.web.cern.ch/Opal/

27. G. Bella, W and Z Couplings and Cross-sections, talk at IVth Rencontre du Vietnam, Hanoi (July 2000), Vietnam. See http://opal.web.cern.ch/Opal/confrep/

28. S. Mele, ZZ Cross-section Measurements, talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

29. G. Bella, W Properties and Decays at LEP2, talk at Tau Workshop 2000, Victoria, Canada. See http://tau2000.phys.uvic.ca/

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30. The LEP Collaborations ALEPH, DELPHI, L3, OPAL, and the LEP WW Working Group, LEPEWWG/XSEC/2000-01. See http://lepewwg.web.cern.ch/LEPEWWG/

31. A. Gurtu, Precision Tests of the Electroweak Gauge Theory, plenary talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

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35. C. Sbarra, LEP II Boson Cross-sections and Couplings, talk at Moriond Electroweak 2000. See http://opal.web.cern.ch/Opal/confrep/

36. P. Molnar and M. Grunewald, Phys. Lett. B461, 149 (1999). 37. K. Hagiwara et al, Nucl. Phys. B282, 253 (1987). 38. L3 Collaboration, M. Acciarri et al, Phys. Lett. B474, 194 (2000). 39. OPAL Collaboration, G. Abbiendi et al. EPJC 8, 191 (1999). 40. S. Jezequel, Charged Triple Gauge Coupling at LEP and W polarisation,

talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

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42. R. Strohmer, W Mass Measurements using Semileptonic and Fully Lep-tonic Events at LEPII, talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

43. S. Schmidt-Karst, W Mass Measurements using Fully Hadronic Events at LEP2, talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

44. A. Valassi, Bose-Einstein Correlations in W-pair events at LEP, talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

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hadrons, L3 Note 2560, submitted to ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

48. Combination procedure for the precise determination of Z boson param-

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eters from results of the LEP experiments, CERN-EP-2000-153. 49. A Combination of Preliminary Electroweak Measurements and Con-

straints on the Standard Model, CERN-EP-2001-021. 50. P. Igo-Kemenes, Search for New Particles and New Phenomena: Results

from e+e~~ Colliders, plenary talk at ICHEP 2000, Osaka, Japan. See http://ichep2000.hep.sci.osaka-u.ac.jp/

Fundamental_Interactions/9810249128/files/00052___a8182e4c11f6407217255cf944c38790.pdfTHE NEUTRINO - A REVIEW

R.G. HAMISH ROBERTSON

Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Box 354290, Seattle, WA 98195

E-mail: rghrQu.washington.edu

The evidence for neutrino mass from experiments on atmospheric and solar neutri-nos is now beyond significant doubt. It appears that active neutrinos are the major participants in these phenomena, although if the LSND experiment is confirmed, a light sterile neutrino would be unavoidable. Sufficient data now exist to allow reasonably quantitative statements about both the mixing and mass spectrum of the neutrinos. One sees a pattern very different from the quark sector.

1 Introduction

After seventy years of research, we still know remarkably little about the neu-trino, but the last few years have seen some dramatic progress. One could say, in light-hearted but genuine tribute to this progress, that we know considerably less about the neutrino than we did 30 years ago. Three neutrinos are known experimentally by direct detection: electron, mu, and tau. That statement could not have been made before this year, when the DONUT collaboration reported1 the first direct observation of the tau neutrino. While the existence of vT was never seriously in doubt since the observation of the decay modes of the T in the 1970s, we have learned not to be surprised at the oddness of neu-trinos, and so it is reassuring to have discovered the tau neutrino produced as expected at Fermilab in charm decays. The Standard Model cast of particles is now complete with the notable exception of the Higgs.

The fermions can be arranged in left-handed doublets and right-handed singlets of weak isospin:

42

Fundamental_Interactions/9810249128/files/00053___c46a50d7d1be55323a6449153f19713b.pdf43

d ' ) L { s ' ) J

( ) * ( c ) f l ( 0 R ( d' )n ( * ) R ( * ) *

( e ) R (l*)R ( T ) R

There are no VR. This peculiarity was built into the Standard Model in recognition of the experimental fact that neutrino masses are much, much smaller than the corresponding charged-lepton masses (see Table 1). At the time, the masses of the neutrinos were consistent with zero, and that could be explained in the Standard Model by depriving neutrinos of right-handed fields. Masses must be Lorentz scalars, and one cannot make a scalar out of a purely left-handed object. In other words, a particle that is always left-handed must also move always at the speed of light (and have no mass), or one could pass it in a speeding Studebaker and see it falling behind spinning as a right-handed particle.

One can find right-handed fields even in the minimal Standard Model among the antineutrinos. A mass term in the Lagrangian can be constructed with a neutrino and an antineutrino if lepton number is not conserved, but the Higgs sector must then include either a pair of doublets or a triplet in order to couple the weak isospin. That is not strictly the Standard Model, but it does little violence to it as an extension. The resulting mass term provides a way to understand the smallness of neutrino mass without making it zero. If neutrinos are in fact identical to their antiparticles (Majorana neutrinos) it is plausible that they begin with a Dirac mass not very different from that of the corresponding charged leptons, but there are mass terms coupling neutrino and antineutrino. The right-handed components of those terms may be as heavy as the scale at which parity is broken. Upon diagonalizing to find mass eigenstates, two states, one very light (compared to the Dirac mass) and one very heavy, emerge. This is the "seesaw" mechanism. Appealing though the seesaw is, the smallness of neutrino mass may be completely unrelated to this, neutrinos could be Dirac particles, and our understanding of mass generation (spectacularly) deficient.

Fundamental_Interactions/9810249128/files/00054___84d4059bd5be7f9837af9f2315eb145c.pdf44

Table 1: Masses of the charged and neutral leptons. Lepton

e

T

Mass vT interpretation (since matter effects are identical and can-celling for both species) and disfavors at the 99% CL the two-flavor sterile

Fundamental_Interactions/9810249128/files/00056___9b75c9d46ab74f260260b73b52a69551.pdf46

scenario v^ -> vs. However, significant admixtures of sterile neutrinos as a third component cannot be ruled out: up to 32% at 90% CL is permissible.

Neutral-current production of 7r is consistent with v^ -> uT, although the cross section is uncertain to 25%.

On a statistical basis, event topologies in Super-Kamiokande are consis-tent with r production at about 2o\

Results from the K2K long-baseline experiment using the v^ beam from KEK support i/M disappearance at about the 2a level.

The best-fit oscillation parameters are15,

Am2 = 2.4 x 1(T3 eV2 sin2 20 = 1.0

There is no evidence in the atmospheric data for the subdominant os-cillation Vp > ve channel at the same mass difference. Crucially important corroboration comes from the Chooz? and Palo Verde8 reactor antineutrino os-cillation searches, which have sensitivity to Ve disappearance in the same mass range.

In a combined analysis, Fig. 1, the Bari group9 find an upper limit on the corresponding admixture between the electron neutrino and active non-electron flavors,

tan2 = tan2 013 < 0.03 (90% CL) tan2 ip = tan2 023 = 1.0(x2.31) (90% CL)

Amf.3 ^ S . O x l O - ^ x l . Z ^ e V 2 (90% CL).

3 Neutrino Oscillations: Solar Neutrinos

Beginning with the Davis experiment in the late 1960's, every solar neutrino experiment has measured a flux lower than that predicted by solar models.

By 1997, data from 5 experiments (3 different types of experiment, Cl-Ar, Ga, and water Cherenkov) were providing information on different combina-tions of the various flux components that make up the solar spectrum. The current results are summarized in Table 2. Surprisingly, with only 3 inde-pendent types of measurement and 8 different neutrino sources in the sun, it is impossible to fit the data (well) without introducing neutrino oscillations

Fundamental_Interactions/9810249128/files/00057___26a25c7dfe39b43aa06ef2aa8e0fa5c2.pdf47

c o

> 0)

10'

10

1

- 1 10 t-

10~ ' n i 3v oscillations SK data (55 bin) + CH00Z(14bin)

90 % C.L 99 % C.L d.o.f. = 3

tan 2^ tan2 cp

Figure 1: Combined analysis of atmospheric neutrino data and Chooz data to extract an upper limit on the magnitude of Ue3 (Fogli et al.9.)

or some other non-standard-model physics. Requiring only that the neutrino spectrum of each individual component is as measured in the laboratory (or, in the case of the pp flux, calculated), that only electron neutrinos come from the sun, and that the energy output agrees with the solar luminosity, one finds that any combination of the 7Be and CNO flux is non-physical (i.e. negative) at more than 3 c The model-independent analyses18'19'20,21 made it clear for the first time that no astrophysical solution would resolve the solar neutrino problem, and the solution lay most likely with neutrino physics.

It could only be concluded that the shape of the 8B spectrum was not as expected, containing more strength at high energies and less at low, and/or the neutrino flavor content is not pure electron, which alters the relationship be-

Fundamental_Interactions/9810249128/files/00058___de9eb562b6dd7f3ab5f4d18e2b858772.pdf48

Table 2: Results of the 6 solar neutrino experiments (1 SNU = 10 - 3 6 events per atom per second).

Cl-Ar Kamiokande SuperKamiokande SAGE Gallex+GNO SNO

2.56 0.16 0.16 SNU (2.80 0.19 0.33) x 106 8B ue cm"2 s"1 (2.35 0.03 0.07) x 106 8B ve cm"2 s"1 75.4i5;S Hi SNU 74.15.4l^ SNU (1.750.16) x 106 8B ue cm"2 s"1

10 n 15 13

14 16

tween the water-Cherenkov results and the radiochemical experiments (because elastic scattering, unlike inverse beta decay, can occur via the neutral-current interaction with neutrinos of all active flavors). These features, not permit-ted in the Minimal Standard Model, are characteristic of neutrino-oscillation solutions18. In contrast to the standard-physics solution, such solutions can give an excellent account of all data.

A more direct demonstration of the presence of other active flavors in the solar flux besides the electron neutrino was to come from the Sudbury Neutrino Observatory. SNO22 is a 1000-tonne D20 Cherenkov detector sited at the 6800-foot level of INCO's Creighton Number 9 mine near Sudbury, Ontario. SNO can detect solar neutrinos in 3 different processes,

ve + d^p + p + e~ (CC) vx + d-^p + n + vx (NC) vx + e~ -> vx + e~ (ES)

By comparing the rates of CC reaction to the NC reaction, or CC to ES, one may deduce immediately if there are other flavors present, because the CC reaction detects only ve, the NC reaction is equally sensitive to all 3 active flavors, and the ES cross section for v^ and vT is 0.154 that for ve. Those comparisons, in the energy regime where only 8B neutrinos are present, are independent of solar physics. A determination of the hep neutrinos from the upper end of the spectrum is also needed to make the comparison rigorous; as expected, they play a minor role.

The construction of SNO began in 1990 and was complete in 1998. Water fill then commenced and after a period of calibration and adjustment, 'produc-tion' running began in November 1999. The first data from pure heavy water covering 241 live days between November 1999 and January 2001 were used16 to derive a precise measurement of the ve flux above an electron kinetic energy of 6.75 MeV:

Fundamental_Interactions/9810249128/files/00059___3631ede15528bf6e6b8e8ce4df11a92c.pdf49

*SNO = !-75 0.07^ 0.05 x 106 8B ve c m ^ s - 1

which may be compared with the flux measured23 by Super-Kamiokande in elastic scattering,

$! = 2.32 0.03i|j;{}? x 1Q6 8f i ve cm - 2 s - 1 The results can be displayed graphically in a variety of ways. Figure 2 is

a convenient form devised independently by Parke and by Hime25.

I ' I ' I

(106cm"V)

Figure 2: Extracting the flux of j / e and i /u r from a comparison of the data from SNO and Super-Kamiokande. The contours are joint confidence levels of 68%, 90%, and 99%.

The CC result is 3.3 a below the ES result, indicating the presence in the solar neutrino flux of active flavors other than electron. Indeed, the fluxes measured (in units of 106 8B ve cm -2 s_1) are,

=1.75 0.15 $, 3.69 1.13

*totai =5.44 0.99 $BPBOI = 5.05JIo;8i

Fundamental_Interactions/9810249128/files/00060___a28e74059f1794839047b1a4c2a3df8e.pdf50

Table 3: Two-flavor neutrino oscillation fits to the solar neutrino data, showing the 5 most probable solutions and the Goodness of Fit (Krastev and Smirnov17). The hep flux is constrained to the SSM value, 8 B is free. Shape information from SK1 6 but not SNO 1 6 is

used. Solution

Large-angle Vacuum Low Vacuum Small-angle

Ve -

Active Active Active Sterile Active

Am2 eV2

5.0 x 10-5 1.4 x 10~10 1.1 x 10~7 1.4 x 10~10 5.5 x 10"6

tan'2 9

0.36 0.363 (2.7) 0.69 0.35 (2.9) 0.0019

Amin

30.0 33.0 34.2 36.4 42.0

G.O.F.

0.85 0.74 0.69 0.59 0.34

and one sees that the flux of non-electron flavors is about twice that of the electron flavor. There is excellent agreement between the measured total flux and the theoretically predicted value24, which considerably predates the ex-perimental one. Thus the solar neutrino problem is resolved in favor of the astrophysical calculations and demands new neutrino physics. (These results were known within the SNO collaboration at the time of the Lake Louise Win-ter Institute in February 2001, but were not ready for publication until June 18 of that year. To keep the text reasonably current, the results are incorporated in the written version.)

Matter-enhanced neutrino oscillations between the electron neutrino and the other active flavors are consistent with the data. Mixing with a sterile neutrino alone is not compatible at the 3a level. There are 2-flavor solutions that describe the data well. Many analyses have been done; one example is that of Bandyopadhyay et al?6. The Large-Mixing-Angle (LMA) and the 'LOW solutions survive, with LMA being considerably more probable (Fig. 3).

Krastev and Smirnov17 find the best overall fit is for the LMA solution (see Table 3) but that other solutions are possible. Vacuum solutions tend to have significant shape distortions, which would be further disfavored if shape information from SNO were to be folded in to the analysis.

Day-night effects arise from matter regeneration in the varying path through the earth's core. No certain evidence for time variations beyond statistical fluc-tuations has shown up to date, and the most recent data from SK27 (1496 days) yield,

2 , r ~ = 0.020 0.020 0.013. N + D The absence of large day-night effects has already ruled out a large region of parameter space in the range 10 - 6 < Am 2 < 10~5 eV2 and 10 - 2 < sin2 26. As

Fundamental_Interactions/9810249128/files/00061___d05dcaa5816d36328fe4c5a88797e9e1.pdf51

IU

io-4

io-5

io-'

10"'

IO"*

IO"10

m-11

r

r

r

-

i i i mill T-rriini| I I 11 nnr CI+Oa+SK+SNO CC+SNO ES rates + SK D-N spectra + SNO CC spectra

90% C.L. 95% C.L.

99%C.L. 99.73% C.L.

rn . i i l ,1 mi l l

i i i t ^ i i ) i

tUk

%

1 .

1 -1

1

]

J ]

10 10

tan28

Figure 3: Two-neutrino mixing after SNO (from Bandyopadhyay et al.2

Suzuki27 shows (for further discussion, see also Bahcall et al?8), the small but general night enhancement matches better with the LMA solution than it does the SMA solution where effects are all negligible except when the sun is on the other side of the earth's core. The latter possibility seems disfavored at almost 3(7. The details of the LMA region are shown by Bahcall et al?8. The region of maximal day-night variation moves down in Am2 as the energy goes down, and provides a decisive marker for the LOW solution in Borexino29. However, if the LMA solution is the correct one, then the KamLAND experiment?0 will observe the disappearance of reactor Ve over a long baseline.

Fundamental_Interactions/9810249128/files/00062___ce80827d12d891fc7c6413ed2f49bcb1.pdf52

4 Neutrino Oscillations: Reactor and Accelerator

The Liquid Scintillator Neutrino Detector (LSND) Experiment31 at Los Alamos National Laboratory has found evidence for FM -* Ve with 0.2 < Am2 < 2.0 eV2 and 0.04 > sin2 26 > 0.0015. The statistical accuracy in the charge-conjugate channel i/p -> ve is not quite sufficient to provide a decisive confirma-tion, but the result is consistent. The KARMEN Experiment32 at Rutherford-Appleton Laboratory reports no signal in a region of parameter space over-lapping much of that explored by LSND. The small remaining region defines the parameters just given for LSND, plus a small island at Am2 = 4.5 eV2, sin2 26= 2.5 x 10~3. The Brookhaven E776 Experiment33 excludes (in the vn > ve channel) that small island.

As has been described, the Chooz7 and Palo Verde8 long-baseline reactor antineutrino experiments show no oscillation effects for Ve at Am 2 > 10~3 eV2.

Together with the results from atmospheric and solar neutrino measure-ments, these define the scenarios for neutrino mass and mixing that are most likely.

5 Mixing Matrix for Neutrinos

Without mass, a flavor state is just a matter of definition (representation), e.g.:

Ve = Ue\Vi + Ue2V2 + Ue3V3

This relationship would stay the same at all times and places. But if the masses of Vi are not zero, then

ve = UeXe-iE^vx + Ueie-^vz + Ue3e-iE^u3 ,

where Ef = p2 + mf and the state evolves with time or distance. The overall phase is unobservable

ve = e-iE

^{Uelvx + Ue2e-i^-E^tu2 + ...)

and m2 p2 , so Ej E{ = '~i and observable effects depend only on mass-squared differences.

In the presence of matter the forward scattering amplitude for neutrinos is not zero, which leads to a refractive index:

, 2?riV , , . ni = l + rfi(0)

Fundamental_Interactions/9810249128/files/00063___ea9e8e2b49f8410cae1d2ea6ed03f3f2.pdf53

which is different for / = e and I = fj, or r because W exchange can occur in addition to Z exchange for 1 = e.

, 2wN ( /-GFp \

The "matter oscillation length" L0 is defined by

V2GFNeL0 = 2TT

and the refractive index differs only microscopically from 1:

m ~ 1 - 1 x 1(T19

Small though this difference is, the additional phase leads to important effects for neutrinos. Moreover, matter effects contribute a phase shift in the flavor basis, while mass shifts the phase in the mass basis. The composite prop-agation phase is non-diagonal, which can give rise to strong avoided-crossing resonance effects and large flavor changes even when the vacuum mixing is small.

The observation in solar and atmospheric neutrinos of flavor change is thus compelling evidence for both mass and mixing. As it turns out, because the solar data favor large mixing, our knowledge of the mixing is quite detailed, while knowledge of the mass spectrum is still fragmentary.

It is illuminating to write the U matrix as the product of 3 Euler rotations:

Uel Ue2 Ue3 \ I VX Ufj.1 U^ C/M3 u2 Url UT2 UT3 J \U3

1 0 0 U = I 0 cos 623


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