Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1 Higgs physics at LEP1 5

1.1 M. Boutemeur: Search for the Higgs boson and bounds from elec-

troweak precision test at LEP1 . . . . . . . . . . . . . . . . . . . . . 6 1.2 P. Gambino: Two-loop heavy-top effects on precision observables and

the Higgs mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 B. Lampe: A nonstandard loop contribution to R_{b} . . . . . . . . . . 25 1.4 E. H. Simmons: Testing extended technicolor with R_{b} and single top-

quark production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2 Higgs resonance: gauge invariance and CP violation 40

2.1 A. Sirlin: Analysis of the Z^{0} resonant amplitude in general R_{ξ} gauges

and related problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2 R. G. Stuart: Gauge invariance in boson production . . . . . . . . . 49 2.3 A. Pilaftsis: Resonant CP violation in Higgs production, mixing, and

decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3 Higgs physics at LEP2 68 3.1 H.-G. Moser: New results from LEP2 . . . . . . . . . . . . . . . . . 69 3.2 P. Janot: Searches for Higgs bosons at LEP2 and status of ALEPH

four-jet events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4 Higgs physics at LHC 93 4.1 K. Jakobs: The search for the Higgs at LHC—Experimental aspects 94 4.2 Z. Kunszt: Theoretical aspects of Higgs hunting at LHC . . . . . . . 104 4.3 M. Dittmar and H. Dreiner: h^{0} → W^{+}W^{−} → ℓ^{+}ℓ^{′−}ν_{ℓ}ν̄_{ℓ′} as the domi-

nant SM Higgs search mode at the LHC for M_{h^{0}} = 155–180 GeV . . 114 4.4 M. Spira: Higgs-boson production at the LHC . . . . . . . . . . . . 123

5 Higgs physics at NLC and FMC 133 5.1 R. Settles: Aspects of Higgs physics at the ILC . . . . . . . . . . . . 134 5.2 J. F. Gunion: Higgs physics at a muon collider . . . . . . . . . . . . 143 6 Supersymmetric Higgs bosons 154

6.1 A. Djouadi: SUSY Higgs-boson decays . . . . . . . . . . . . . . . . 155 6.2 W. Hollik: Radiative corrections in the MSSM Higgs sector . . . . . 165

7 Higgs physics beyond one loop 176

7.1 M. Steinhauser: Corrections of O(α_{s}^{2}) to the decay of an intermediate-

mass Higgs boson into two photons . . . . . . . . . . . . . . . . . . . 177 7.2 K. Riesselmann: SM Higgs decay and scattering processes at two loops 186

8 Strongly interacting Higgs sector 195

8.1 T. Han: Strong W W scattering physics: A comparative study for the

LHC, NLC, and a muon collider . . . . . . . . . . . . . . . . . . . . 196 8.2 H.-J. He: Testing the strong W system at the LHC and linear colliders 206 8.3 W. Kilian: Strongly interacting W bosons below the new-physics

threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

9 Compositeness and grand unification 226 9.1 M. Lindner: Phenomenologically viable dynamical symmetry breaking 227 9.2 P. Langacker: Unification or compositeness? . . . . . . . . . . . . . 237 9.3 R. Hempfling: SUSY without R parity—Symmetry breaking and LSP

phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 9.4 Z. Berezhiani: 2/3 splitting in SUSY GUT—Higgs as Goldstone boson 266

10 Electroweak phase transition 277

10.1 M. Quirós: Electroweak phase transition and baryogenesis in the

MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 10.2 M. E. Shaposhnikov: The Higgs puzzle—What can we learn from

electroweak phase transition? . . . . . . . . . . . . . . . . . . . . . . 286

11 Higgs mechanism to all orders, in noncommutative geometry, and on the lattice 294 11.1 E. Kraus: Callan-Symanzik and renormalization-group equations in

theories with spontaneously broken symmetry . . . . . . . . . . . . . 295 11.2 F. Scheck: The Higgs mechanism as a geometric phenomenon in non-

commutative geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 303 11.3 I. Montvay: The Higgs mechanism on the lattice . . . . . . . . . . . 313

12 Future directions 322 12.1 H. E. Haber: Future directions in Higgs phenomenology . . . . . . . 323 List of participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Foreword

The international workshop entitled The Higgs Puzzle—What Can we Learn from LEP2, LHC, NLC, and FMC? took place on 8–12 December 1996 at Ringberg Castle, which overlooks Lake Tegernsee in the foothills of the Bavarian Alps, one of the most picturesque locations to be found in the whole of Germany. The castle was built during the first half of this century by Duke Luitpold in Bavaria (Herzog Luitpold in Bayern), a member of the Wittelsbach family, who ruled Bavaria over 800 years, and his friend Friedrich Attenhuber, an all-round artist, architect, and interior decorator. The castle is entirely their creation, from the massive Renaissance-inspired exterior right down to the fittings and furniture, which, in every detail, were designed by Attenhuber himself and executed by native craftsmen. Attenhuber also painted every single picture hanging in the castle. He found his models in the farmhouses around Lake Tegernsee. The castle embodies all trends of art and styles which dominated the first half of this century, combined with local Alpine originality and the individual creative power of its constructors. According the the Duke’s last will, the castle passed into the hands of the Max Planck Society after his death, in 1973. The castle was then transformed into a conference venue where scientists can exchange their latest ideas and discuss problems with their colleagues from all over the world in beautiful surroundings and in a relaxed mountain atmosphere, high above the daily business activities.

This event has continued a series of Ringberg workshops on electroweak physics in high-energy reactions, which include: Hadronic Matrix Elements and Weak Decays on 17–22 April 1988; Radiative Corrections for e^{+}e^{−} Collisions on 3–7 April 1989; High Precision versus High Energies in e^{+}e^{−} Collisions on 15–19 April 1991; Perspectives of the Electroweak Interactions in e^{+}e^{−} Collisions on 4–8 April 1993; Advances in Non-Perturbative and Perturbative Techniques on 13–19 November 1994; Perspectives for Electroweak Interactions in e^{+}e^{−} Collisions on 5–8 February 1995. On the occasion of the 1996 Ringberg workshop, forty-two experts of elementary-particle physics, both theoreticians and experimentalists, from twenty-seven universities and research institutions in ten countries congregated to present their latest results on the various aspects of Higgs phenomenology.

The motivation for this workshop may be summarized as follows. Despite the great success of the standard model of electroweak and strong interactions to describe the phenomena observed in high-energy-physics experiments, the mechanism by which the elementary particles are endowed with their masses is yet to be unraveled. Does nature choose the Higgs mechanism of spontaneous symmetry breaking as predicted by the standard model, or do we need some alternative explanation? The purpose of the workshop was to capture new trends and ideas in this exciting area of fundamental physics, and to explore the potential of recent (CERN LEP1), present (CERN LEP2, DESY HERA, Fermilab Tevatron, SLAC SLC), and future (CERN LHC, Next Linear Collider, First Muon Collider) colliding-beam experiments to shed light on the Higgs puzzle.

There was a total of 35 presentations of 45 minutes each. This proceedings volume is to give a comprehensive account of the novel ideas and results discussed by the speakers. The topics include: experimental and theoretical status reports from LEP1, LEP2, LHC, NLC, and FMC; electroweak precision tests; multi-loop calculus; Callan-Symanzik and renormalization-group equations; lattice field theory; gauge independence and invariance; resonant CP violation; strongly interacting Higgs sector; effective Lagrangians; supersymmetry; extended technicolor; dynamical symmetry breaking; compositeness; grand unification; electroweak phase transition; baryogenesis; and noncommutative geometry. We also hope that the high-energy-physics community at large will find this document useful in their ongoing efforts of solving the Higgs puzzle.

At this point, I should like to thank my friends and colleagues who have contributed their shares to these proceedings. I am indebted to the workshop secretary, Mrs. Renate Saffert, for her assistance before, during, and after the workshop. Last but not least, I am grateful to Wolfgang Hollik and Stefan Pokorski for contributions from their EU budgets towards the cost of catering and lodging, and to the Werner Heisenberg Institute for their generous financial support.

Finally, I wish to express my serious concern against the plan of the Max Planck Society to eliminate 61 positions in the Werner Heisenberg Institute, Germany’s second largest high-energy-physics laboratory after DESY, during the next few years. I hope that the responsible persons will reconsider this detrimental measure against the heritage of Max Planck and Werner Heisenberg, and the progress in elementary particle physics, the most fundamental area of research there is in natural sciences.

Munich, March 1997 Bernd A. Kniehl

Chapter 1 Higgs physics at LEP1

1.1 M. Boutemeur: Search for the Higgs boson and bounds from electroweak precision test at LEP1 1.2 P. Gambino: Two-loop heavy-top effects on

precision observables and the Higgs mass 1.3 B. Lampe: A nonstandard loop contribution

to R_{b} 1.4 E. H. Simmons: Testing extended technicolor

with R_{b} and single top-quark production

Chapter 2 Higgs resonance: gauge invariance and CP violation

2.1 A. Sirlin: Analysis of the Z^{0} resonant amplitude in general R_{ξ} gauges and related problems 2.2 R. G. Stuart: Gauge invariance in boson pro-

duction 2.3 A. Pilaftsis: Resonant CP violation in Higgs

production, mixing, and decay 3.1 H.-G. Moser: New results from LEP2 3.2 P. Janot: Searches for Higgs bosons at LEP2

and status of ALEPH four-jet events

Chapter 4 Higgs physics at LHC

4.1 K. Jakobs: The search for the Higgs at LHC— Experimental aspects 4.2 Z. Kunszt: Theoretical aspects of Higgs hunt-

ing at LHC 4.3 M. Dittmar and H. Dreiner: h^{0} → W^{+}W^{−} →

ℓ^{+}ℓ^{′−}ν_{ℓ}ν̄_{ℓ′} as the dominant SM Higgs search mode at the LHC for M_{h^{0}} = 155–180 GeV 4.4 M. Spira: Higgs-boson production at the LHC

Chapter 5 Higgs physics at NLC and FMC

5.1 R. Settles: Aspects of Higgs physics at the ILC 5.2 J. F. Gunion: Higgs physics at a muon collider

Chapter 6 Supersymmetric Higgs bosons

6.1 A. Djouadi: SUSY Higgs-boson decays 6.2 W. Hollik: Radiative corrections in the MSSM

Higgs sector

Chapter 7 Higgs physics beyond one loop

7.1 M. Steinhauser: Corrections of O(α_{s}^{2}) to the decay of an intermediate-mass Higgs boson into two photons 7.2 K. Riesselmann: SM Higgs decay and scat-

tering processes at two loops

Chapter 8 Strongly interacting Higgs sector

8.1 T. Han: Strong W W scattering physics: A comparative study for the LHC, NLC, and a muon collider 8.2 H.-J. He: Testing the strong W system at the

LHC and linear colliders 8.3 W. Kilian: Strongly interacting W bosons be-

low the new-physics threshold

Chapter 9 Compositeness and grand unification

9.1 M. Lindner: Phenomenologically viable dynamical symmetry breaking 9.2 P. Langacker: Unification or compositeness?

9.3 R. Hempfling: SUSY without R parity—Symmetry breaking and LSP phenomenology 9.4 Z. Berezhiani: 2/3 splitting in SUSY GUT—

Higgs as Goldstone boson

Chapter 10 Electroweak phase transition

10.1 M. Quirós: Electroweak phase transition and baryogenesis in the MSSM 10.2 M. E. Shaposhnikov: The Higgs puzzle—

What can we learn from electroweak phase transition?

Chapter 11

Higgs mechanism to all orders, in noncommutative geometry, and on the lattice

11.1 E. Kraus: Callan-Symanzik and renormalizationgroup equations in theories with spontaneously broken symmetry 11.2 F. Scheck: The Higgs mechanism as a ge-

ometric phenomenon in noncommutative geometry 11.3 I. Montvay: The Higgs mechanism on the

lattice

Chapter 12 Future directions

12.1 H. E. Haber: Future directions in Higgs phenomenology List of participants

Z. Berezhiani  Ferrara  BEREZHIANI@AXPFE1.FE.INFN.IT
M. Boutemeur  LMU Munich  MADJID.BOUTEMEUR@CERN.CH

K. G. Chetyrkin  Moscow/MPI Munich CHET@MPPMU.MPG.DE
S. Davidson MPI Munich SACHA@MPPMU.MPG.DE
G. Degrassi  Padua/MPI Munich DEGRASSI@PADOVA.INFN.IT

A. Djouadi  Montpellier  DJOUADI@LPM.UNIV-MONTP2.FR
H. Dreiner  RAL  DREINER@V2.RL.AC.UK
P. Gambino  MPI Munich  GAMBINO@MPPMU.MPG.DE
J. F. Gunion  Davis  JFGUCD@UCDHEP.UCDAVIS.EDU
H. E. Haber  Santa Cruz  HABER@SCIPP.UCSC.EDU
T. Han  Davis  THAN@UCDHEP.UCDAVIS.EDU
H.-J. He  DESY  HJHE@MAIL.DESY.DE
R. Hempfling  Davis  HEMPF@BETHE.UCDAVIS.EDU
W. Hollik  Karlsruhe  HOLLIK@ITPAXP3.PHYSIK.UNI-KARLSRUHE.DE
K. Jakobs  Mainz  JAKOBS@DHEMZE.PHYSIK.UNI-MAINZ.DE
P. Janot  CERN  PATRICK.JANOT@CERN.CH
C. Jin  LMU Munich  JIN@PHOTON.HEP.PHYSIK.UNI-MUENCHEN.DE

J. Kalinowski  Warsaw/DESY  KALINO@X4U2.DESY.DE

W. Kilian  Heidelberg  KILIAN@THPHYS.UNI-HEIDELBERG.DE
B. A. Kniehl  MPI Munich  KNIEHL@VMS.MPPMU.MPG.DE
J. Körner  Mainz  KOERNER@VIPMZT.PHYSIK.UNI-MAINZ.DE
E. Kraus  Bonn  KRAUS@AVZW02.PHYSIK.UNI-BONN.DE
J. H. Kühn  Karlsruhe  JOHANN.KUEHN@PHYSIK.UNI-KARLSRUHE.DE
Z. Kunszt  ETH Zurich  KUNSZT@ITP.PHYS.ETHZ.CH
B. Lampe  LMU Munich  BOL@MPPMU.MPG.DE
P. G. Langacker  Philadelphia  PGL@LANGACKER.HEP.UPENN.EDU
M. Lindner  TU Munich  MANFRED.LINDNER@PHYSIK.TU-MUENCHEN.DE
I. Montvay  DESY  ISTVAN.MONTVAY@DESY.DE

H.-G. Moser  MPI Munich  MOSER@MPPMU.MPG.DE

E. A. Paschos  Dortmund  PASCHOS@HET.PHYSIK.UNI-DORTMUND.DE
A. Pilaftsis  MPI Munich  PILAFTSI@MPPMU.MPG.DE

S. Pokorski  Warsaw/MPI Munich POKORSKI@FUW.EDU.PL

M. Quiros  Madrid  QUIROS@ROCA.CSIC.ES

K. Riesselmann  Zeuthen  KURTR@IFH.DE
R. Saffert  MPI Munich  REL@MPPMU.MPG.DE

F. Scheck  Mainz  SCHECK@DIPMZA.PHYSIK.UNI-MAINZ.DE

R. D. Settles  MPI Munich  STS@CERNVM.CERN.CH

M. E. Shaposhnikov CERN  MSHAPOSH@NXTH04.CERN.CH

E. H. Simmons  Boston University  SIMMONS@BU.EDU
A. Sirlin  New York University SIRLIN@ACF2.NYU.EDU

M. Spira  CERN  MSPIRA@CERN.CH

M. Steinhauser  MPI Munich  MSTEINH@MPPMU.MPG.DE
R. G. Stuart  Ann Arbor  STUARTR@UMICH.EDU