The standard model and beyond

Physics Series in High Energy Physics, Cosmology, and Gravitation Langacker Series in High Energy Physics, Cosmology, and Gravitation Series Editors: Brian Foster and Edward W Kolb The Standard Model and Beyond Paul Langacker “The Standard Model and Beyond is a state-of-the-art description of what we know about the particles and forces that build up the world we see Most books that cover these topics are quantum field theory books that treat the quarks and leptons, and the electromagnetic, weak, and strong forces as examples This is the first treatment with the opposite priorities, focusing on the structure and applications of the standard model and bringing in the field theory as needed, in a pedagogically reliable and thorough treatment Langacker knows well that the standard model is the platform on which a deeper understanding of the laws of nature will be constructed, perhaps from clues soon to come from the Large Hadron Collider, and provides preparation so the reader can participate in that progress.” The Standard Model and Beyond —Gordon Kane, Victor Weisskopf Collegiate Professor of Physics and Director of the Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, USA The Standard Model and Beyond presents an advanced introduction to the physics and formalism of the standard model and other non-abelian gauge theories Thoroughly covering gauge field theories, symmetries, and topics beyond the standard model, this text equips readers with the tools to understand the structure and phenomenological consequences of the standard model, to construct extensions, and to perform calculations at tree level It establishes the necessary background for readers to carry out more advanced research in particle physics Features • Covers the fundamental interactions • Describes the construction, experimental tests, and phenomenological consequences of the standard model • Presents a self-contained treatment of the complicated technology needed for tree-level calculations • Explores applications in astrophysics and cosmology • Lists many useful reference books, review articles, research papers, and Web links • Offers supplementary materials on the author’s Web site C7906 an informa business w w w c r c p r e s s c o m 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK 1118 2014 ISBN: 978-1-4200-7906-7 90000 781420 079067 Paul Langacker The Standard Model and Beyond C7906_FM.indd 11/4/09 11:45:29 AM Series in High Energy Physics, Cosmology, and Gravitation Series Editors: Brian Foster, Oxford University, UK Edward W Kolb, Fermi National Accelerator Laboratory, USA This series of books covers all aspects of theoretical and experimental high energy physics, cosmology and gravitation and the interface between them In recent years the fields of particle physics and astrophysics have become increasingly interdependent and the aim of this series is to provide a library of books to meet the needs of students and researchers in these fields Other recent books in the series: Particle and Astroparticle Physics Utpal Sakar Joint Evolution of Black Holes and Galaxies M Colpi, V Gorini, F Haardt, and U Moschella (Eds.) Gravitation: From the Hubble Length to the Planck Length I Ciufolini, E Coccia, V Gorini, R Peron, and N Vittorio (Eds.) Neutrino Physics K Zuber The Galactic Black Hole: Lectures on General Relativity and Astrophysics H Falcke, and F Hehl (Eds.) The Mathematical Theory of Cosmic Strings: Cosmic Strings in the Wire Approximation M R Anderson Geometry and Physics of Branes U Bruzzo, V Gorini and, U Moschella (Eds.) Modern Cosmology S Bonometto, V Gorini and, U Moschella (Eds.) Gravitation and Gauge Symmetries M Blagojevic Gravitational Waves I Ciufolini, V Gorini, U Moschella, and P Fré (Eds.) Classical and Quantum Black Holes P Fré, V Gorini, G Magli, and U Moschella (Eds.) Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics F Weber C7906_FM.indd 11/4/09 11:45:29 AM Series in High Energy Physics, Cosmology, and Gravitation The Standard Model and Beyond Paul Langacker Institute for Advanced Study Princeton, New Jersey, USA Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A TA Y L O R & F R A N C I S B O O K C7906_FM.indd 11/4/09 11:45:29 AM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2010 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20110725 International Standard Book Number-13: 978-1-4200-7907-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xi Notation and Conventions 1.1 Problems Review of Perturbative Field Theory 2.1 Creation and Annihilation Operators 2.2 Lagrangian Field Theory 2.3 The Hermitian Scalar Field 2.3.1 The Lagrangian and Equations of Motion 2.3.2 The Free Hermitian Scalar Field 2.3.3 The Feynman Rules 2.3.4 Kinematics and the Mandelstam Variables 2.3.5 The Cross Section and Decay Rate Formulae 2.3.6 Loop Effects 2.4 The Complex Scalar Field 2.4.1 U (1) Phase Symmetry and the Noether Theorem 2.5 Electromagnetic and Vector Fields 2.5.1 Massive Neutral Vector Field 2.6 Electromagnetic Interaction of Charged Pions 2.7 The Dirac Field 2.7.1 The Free Dirac Field 2.7.2 Dirac Matrices and Spinors 2.8 QED for Electrons and Positrons 2.9 Spin Effects and Spinor Calculations 2.10 The Discrete Symmetries P , C, CP , T , and CP T 2.11 Two-Component Notation and Independent Fields 2.12 Quantum Electrodynamics (QED) 2.12.1 Higher-Order Effects 2.12.2 The Running Coupling 2.12.3 Tests of QED 2.12.4 The Role of the Strong Interactions 2.13 Mass and Kinetic Mixing 2.14 Problems 7 10 10 12 12 15 17 24 25 27 30 32 33 39 40 41 50 56 58 71 74 75 78 82 87 94 97 v vi The Standard Model and Beyond Lie Groups, Lie Algebras, and Symmetries 3.1 Basic Concepts 3.1.1 Groups and Representations 3.1.2 Examples of Lie Groups 3.1.3 More on Representations and Groups 3.2 Global Symmetries in Field Theory 3.2.1 Transformation of Fields and States 3.2.2 Invariance (Symmetry) and the Noether Theorem 3.2.3 Isospin and SU (3) Symmetries 3.2.4 Chiral Symmetries 3.2.5 Discrete Symmetries 3.3 Symmetry Breaking and Realization 3.3.1 A Single Hermitian Scalar 3.3.2 A Digression on Topological Defects 3.3.3 A Complex Scalar: Explicit and Spontaneous Symmetry Breaking 3.3.4 Spontaneously Broken Chiral Symmetry 3.3.5 Field Redefinition 3.3.6 The Nambu-Goldstone Theorem 3.3.7 Boundedness of the Potential 3.3.8 Example: Two Complex Scalars 3.4 Problems 103 103 103 105 106 112 112 114 119 130 132 133 133 136 137 140 141 143 145 146 149 157 158 160 164 169 177 179 Strong Interactions and QCD The QCD Lagrangian Evidence for QCD Simple QCD Processes The Running Coupling in Non-Abelian Theories 5.4.1 The RGE Equations for an Arbitrary Gauge Theory Deep Inelastic Scattering 5.5.1 Deep Inelastic Kinematics 5.5.2 The Cross Section and Structure Functions 5.5.3 The Simple Quark Parton Model (SPM) 5.5.4 Corrections to the Simple Parton Model Other Short Distance Processes The Strong Interactions at Long Distances The Symmetries of QCD 183 186 188 193 198 199 202 203 204 209 213 217 220 221 Gauge Theories 4.1 The Abelian Case 4.2 Non-Abelian Gauge Theories 4.3 The Higgs Mechanism 4.4 The Rξ Gauges 4.5 Anomalies 4.6 Problems The 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 vii Table of Contents 5.8.1 Continuous Flavor Symmetries 5.8.2 The (3∗ , 3) + (3, 3∗ ) Model 5.8.3 The Axial U (1) Problem 5.8.4 The Linear σ Model 5.8.5 The Nonlinear σ Model 5.9 Other Topics 5.10 Problems 221 223 229 232 235 236 237 The Weak Interactions 239 6.1 Origins of the Weak Interactions 239 6.2 The Fermi Theory of Charged Current Weak Interactions 245 6.2.1 µ Decay 250 6.2.2 νe e− → νe e− 256 6.2.3 π and K Decays 258 6.2.4 Nonrenormalization of Charge and the Ademollo-Gatto Theorem 266 6.2.5 β Decay 268 6.2.6 Hyperon Decays 273 6.2.7 Heavy Quark and Lepton Decays 274 6.3 Problems 278 The Standard Electroweak Theory 281 7.1 The Standard Model Lagrangian 281 7.2 Spontaneous Symmetry Breaking 287 7.2.1 The Higgs Mechanism 287 7.2.2 The Lagrangian in Unitary Gauge after SSB 289 7.2.3 Effective Theories 304 7.2.4 The Rξ Gauges 306 7.3 The Z, the W , and the Weak Neutral Current 308 7.3.1 Purely Weak Processes 309 7.3.2 Weak-Electromagnetic Interference 321 7.3.3 Implications of the WNC Experiments 328 7.3.4 Precision Tests of the Standard Model 330 7.3.5 The Z-Pole and Above 340 7.3.6 Implications of the Precision Program 350 7.4 Gauge Self-Interactions 358 7.5 The Higgs 362 7.5.1 Theoretical Constraints 362 7.5.2 Experimental Constraints and Prospects 368 7.6 The CKM Matrix and CP Violation 371 7.6.1 The CKM Matrix 372 7.6.2 CP Violation and the Unitarity Triangle 376 7.6.3 The Neutral Kaon System 378 7.6.4 Mixing and CP Violation in the B System 391 7.6.5 Time Reversal Violation and Electric Dipole Moments 397 viii The Standard Model and Beyond 7.7 7.8 7.6.6 Flavor Changing Neutral Currents (FCNC) Neutrino Mass and Mixing 7.7.1 Basic Concepts for Neutrino Mass 7.7.2 The Propagators for Majorana Fermions 7.7.3 Experiments and Observations 7.7.4 Neutrino Oscillations 7.7.5 The Spectrum 7.7.6 Models of Neutrino Mass 7.7.7 Implications of Neutrino Mass Problems 401 404 405 417 418 425 438 440 446 447 Beyond the Standard Model 453 8.1 Problems with the Standard Model 453 8.2 Supersymmetry 463 8.2.1 Implications of Supersymmetry 463 8.2.2 Formalism 469 8.2.3 Supersymmetric Interactions 482 8.2.4 Supersymmetry Breaking and Mediation 490 8.2.5 The Minimal Supersymmetric Standard Model (MSSM) 493 8.2.6 Further Aspects of Supersymmetry 505 8.3 Extended Gauge Groups 508 8.3.1 SU (2) × U (1) × U (1) Models 510 8.3.2 SU (2)L × SU (2)R × U (1) Models 519 8.4 Grand Unified Theories (GUTs) 525 8.4.1 The SU (5) Model 527 8.4.2 Beyond the Minimal SU (5) Model 534 8.5 Problems 537 A Canonical Commutation Rules 541 B Derivation of a Simple Feynman Diagram 545 C Unitarity, the Partial Wave Expansion and the Optical Theorem 547 D Two, Three, and n-Body Phase Space 549 E Calculation of the Anomalous Magnetic Moment of the Electron 555 F Breit-Wigner Resonances 559 G Implications of P , C, T , and G-parity for Nucleon Matrix Elements 563 ix Table of Contents H Collider Kinematics 567 I 573 Quantum Mechanical Analogs of Symmetry Breaking References I.1 Field Theory I.2 The Standard Model and Particle Physics I.3 The Strong Interactions, QCD, and Collider Physics I.4 The Electroweak Interactions I.5 CP Violation I.6 Neutrinos I.7 Supersymmetry, Strings, and Grand Unification I.8 Astrophysics and Cosmology I.9 Groups and Symmetries I.10 Articles 577 577 578 579 580 581 581 582 583 584 584 Web Sites 631 Index 635 References 621 Oakes, R J (1969) SU (2) × SU (2) breaking and the Cabibbo angle Phys Lett B29, 683–685 Okada, Y., M Yamaguchi, and T Yanagida (1991) Upper bound of the lightest Higgs boson mass in the minimal supersymmetric standard model Prog Theor Phys 85, 1–6 Okubo, S (1958) Decay of the Σ+ hyperon and its antiparticle Phys Rev 109, 984–985 O’Raifeartaigh, L (1975) Spontaneous symmetry breaking for chiral scalar superfields Nucl Phys B96, 331 Owens, J F., E Reya, and M Gluck (1978) Detailed quantum chromodynamic predictions for high p(T ) processes Phys Rev D18, 1501 Pagels, H (1975) Departures from chiral symmetry Phys Rept 16, 219 Paige, F E., S D Protopopescu, H Baer, and X Tata (2003) ISAJET 7.69: a Monte Carlo event generator for pp, p¯p, and e+ e− reactions ArXiv: hep-ph/0312045 Panagiotakopoulos, C and K Tamvakis (1999a) New minimal extension of MSSM Phys Lett B469, 145–148 Panagiotakopoulos, C and K Tamvakis (1999b) Stabilized NMSSM without domain walls Phys Lett B446, 224–227 Paschos, E A and L Wolfenstein (1973) Tests for neutral currents in neutrino reactions Phys Rev D7, 91–95 Pascoli, S., S T Petcov, and W Rodejohann (2002) On the CP violation associated with Majorana neutrinos and neutrinoless double-beta decay Phys Lett B549, 177–193 Pati, J C (2006) Grand unification as a bridge between string theory and phenomenology Int J Mod Phys D15, 1677–1698 Pati, J C and A Salam (1974) Lepton number as the fourth color Phys Rev D10, 275–289 Peccei, R D (1989) The strong CP problem Adv Ser Direct High Energy Phys 3, 503–551 Peccei, R D and H R Quinn (1977) CP conservation in the presence of instantons Phys Rev Lett 38, 1440–1443 Peebles, P J E and B Ratra (2003) The cosmological constant and dark energy Rev Mod Phys 75, 559–606 Pendleton, B and G G Ross (1981) Mass and mixing angle predictions from infrared fixed points Phys Lett B98, 291 622 The Standard Model and Beyond Perelstein, M (2007) Little Higgs models and their phenomenology Prog Part Nucl Phys 58, 247–291 Perl, M L et al (1975) Evidence for anomalous lepton production in e+ e− annihilation Phys Rev Lett 35, 1489–1492 Peskin, M E (2008) Supersymmetry in elementary particle physics ArXiv: 0801.1928 Peskin, M E and T Takeuchi (1990) A new constraint on a strongly interacting Higgs sector Phys Rev Lett 65, 964–967 Peskin, M E and T Takeuchi (1992) Estimation of oblique electroweak corrections Phys Rev D46, 381–409 Peskin, M E and J D Wells (2001) How can a heavy Higgs boson be consistent with the precision electroweak measurements? Phys Rev D64, 093003 Pich, A (1995) Chiral perturbation theory Rept Prog Phys 58, 563–610 Pich, A (1998a) Effective field theory ArXiv: hep-ph/9806303 Pich, A (1998b) Tau physics Adv Ser Direct High Energy Phys 15, 453–492 Pich, A (2004) / in the standard model: theoretical update ArXiv: hep-ph/0410215 Pich, A (2008) Tau physics: theory overview Nucl Phys Proc Suppl 181– 182, 300–305 Pierce, D M., J A Bagger, K T Matchev, and R.-J Zhang (1997) Precision corrections in the minimal supersymmetric standard model Nucl Phys B491, 3–67 Plehn, T (2008) LHC phenomenology for physics hunters ArXiv: 0810.2281 Pocanic, D et al (2004) Precise measurement of the π + → π e+ ν branching ratio Phys Rev Lett 93, 181803 Politzer, H D (1973) Reliable perturbative results for strong interactions? Phys Rev Lett 30, 1346–1349 Pontecorvo, B (1968) Neutrino experiments and the question of leptoniccharge conservation Sov Phys JETP 26, 984–988 Porod, W (2003) SPheno, a program for calculating supersymmetric spectra, SUSY particle decays and SUSY particle production at e+ e− colliders Comput Phys Commun 153, 275–315 Pospelov, M and A Ritz (2005) Electric dipole moments as probes of new physics Annals Phys 318, 119–169 References 623 Prescott, C Y et al (1979) Further measurements of parity nonconservation in inelastic electron scattering Phys Lett B84, 524 Preskill, J (1979) Cosmological production of superheavy magnetic monopoles Phys Rev Lett 43, 1365 Preskill, J (1984) Magnetic monopoles Ann Rev Nucl Part Sci 34, 461–530 Pulido, J (1992) The Solar neutrino problem and the neutrino magnetic moment Phys Rept 211, 167–199 Quenzer, A et al (1978) Pion form-factor from 480-MeV to 1100-MeV Phys Lett B76, 512–516 Quiros, M (1999) Finite temperature field theory and phase transitions ArXiv: hep-ph/9901312 Raby, S (2004) Desperately seeking supersymmetry (SUSY) Rept Prog Phys 67, 755–811 Raby, S (2009) SUSY GUT model building Eur Phys J C59, 223–247 Raffelt, G G (1999) Particle physics from stars Ann Rev Nucl Part Sci 49, 163–216 Raidal, M (2004) Relation between the neutrino and quark mixing angles and grand unification Phys Rev Lett 93, 161801 Rakshit, S (2004) Neutrino masses and R-parity violation Mod Phys Lett A19, 2239–2258 Ramond, P (1971) Dual theory for free fermions Phys Rev D3, 2415–2418 Ramond, P (1979) The family group in grand unified theories ArXiv: hepph/9809459 Ramsey-Musolf, M J and S A Page (2006) Hadronic parity violation: a new view through the looking glass Ann Rev Nucl Part Sci 56, 1–52 Randall, L and R Sundrum (1999) A large mass hierarchy from a small extra dimension Phys Rev Lett 83, 3370–3373 Rees, M J (2004) Numerical coincidences and ‘tuning’ in cosmology ArXiv: astro-ph/0401424 Reina, L (2005) Higgs boson physics ArXiv: hep-ph/0512377 Reines, F and C L Cowan (1953) Detection of the free neutrino Phys Rev 92, 830–831 Ringwald, A (2005) How to detect big bang relic neutrinos? ArXiv: hepph/0505024 624 The Standard Model and Beyond Ringwald, A and Y Y Y Wong (2004) Gravitational clustering of relic neutrinos and implications for their detection JCAP 0412, 005 Ritchie, J L and S G Wojcicki (1993) Rare K decays Rev Mod Phys 65, 1149–1198 Rizzo, T G (2006) Z phenomenology and the LHC ArXiv: hep-ph/0610104 Robinett, R W and J L Rosner (1982a) Mass scales in grand unified theories Phys Rev D26, 2396 Robinett, R W and J L Rosner (1982b) Prospects for a second neutral vector boson at low mass in SO(10) Phys Rev D25, 3036 Rosner, J L (1999) The arrival of charm AIP Conf Proc 459, 9–27 Rosner, J L (2004) Status of the CKM matrix ArXiv: hep-ph/0410281 Rosner, J L (2007) Hadron spectroscopy: theory and experiment Phys G34, S127–S148 J Rothstein, I Z (2003) TASI lectures on effective field theories ArXiv: hepph/0308266 Sakai, N and T Yanagida (1982) Proton decay in a class of supersymmetric grand unified models Nucl Phys B197, 533 Sakharov, A D (1967) Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe JETP Lett 5, 24–27 Salam, A (1968) Weak and electromagnetic interactions In Elementary Particle Theory, ed N Svartholm (Almquist and Wiksells, Stockholm 1969), 367-377 Salam, A and J A Strathdee (1974) Supergauge transformations Nucl Phys B76, 477–482 Sarantakos, S., A Sirlin, and W J Marciano (1983) Radiative corrections to neutrino-lepton scattering in the SU (2) × U (1) theory Nucl Phys B217, 84 Satz, H (2009) The states of matter in QCD ArXiv: 0903.2778 Schael, S et al (2006a) Precision electroweak measurements on the Z resonance Phys Rept 427, 257 Schael, S et al (2006b) Search for neutral MSSM Higgs bosons at LEP Eur Phys J C47, 547–587 Schaile, D and P M Zerwas (1992) Measuring the weak isospin of B quarks Phys Rev D45, 3262–3265 References 625 Schechter, J and J W F Valle (1980) Neutrino masses in SU (2) × U (1) theories Phys Rev D22, 2227 Schechter, J and J W F Valle (1982) Neutrinoless double-beta decay in SU (2) × U (1) theories Phys Rev D25, 2951 Schiff, L I (1963) Measurability of nuclear electric dipole moments Phys Rev 132 (5), 2194–2200 Schwetz, T., M Tortola, and J W F Valle (2008) Three-flavour neutrino oscillation update New J Phys 10, 113011 Schwinger, J S (1957) A theory of the fundamental interactions Annals Phys 2, 407–434 Schwinger, J S (1962) Gauge invariance and mass Phys Rev 125, 397–398 Seiberg, N (1993) Naturalness versus supersymmetric non-renormalization theorems Phys Lett B318, 469–475 Semenov, A (2009) LanHEP - a package for the automatic generation of Feynman rules in field theory Version 3.0 Comput Phys Commun 180, 431–454 Senjanovic, G and R N Mohapatra (1975) Exact left-right symmetry and spontaneous violation of parity Phys Rev D12, 1502 Severijns, N., M Beck, and O Naviliat-Cuncic (2006) Tests of the standard electroweak model in beta decay Rev Mod Phys 78, 991–1040 Shi, X., D N Schramm, R Rosner, and D S Dearborn (1993) On using a neutrino magnetic moment to attack the solar neutrino problem Comments Nucl Part Phys 21, 151–182 Shiozawa, M et al (1998) Search for proton decay via p → e+ π in a large water cherenkov detector Phys Rev Lett 81, 3319–3323 Simha, V and G Steigman (2008) Constraining the universal lepton asymmetry JCAP 0808, 011 Simkovic, F., A Faessler, V Rodin, P Vogel, and J Engel (2008) Anatomy of nuclear matrix elements for neutrinoless double-beta decay Phys Rev C77, 045503 Sirlin, A (1978) Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions Rev Mod Phys 50, 573 Sirlin, A (1980) Radiative corrections in the SU (2) × U (1) theory: a simple renormalization framework Phys Rev D22, 971–981 626 The Standard Model and Beyond Sirlin, A and W J Marciano (1981) Radiative corrections to νµ N → µX and their effect on the determination of ρ2 and sin2 θW Nucl Phys B189, 442 Sjostrand, T., S Mrenna, and P Skands (2008) A brief introduction to PYTHIA 8.1 Comput Phys Commun 178, 852–867 Skyrme, T H R (1962) A unified field theory of mesons and baryons Nucl Phys 31, 556–569 Slansky, R (1981) Group theory for unified model building Phys Rept 79, Sohnius, M F (1985) Introducing supersymmetry Phys Rept 128, 39–204 Sozzi, M S and I Mannelli (2003) Measurements of direct CP violation Riv Nuovo Cim 26N3, 1–110 Steigman, G (1979) Cosmology confronts particle physics Ann Rev Nucl Part Sci 29, 313–338 Steigman, G (2007) Primordial nucleosynthesis in the precision cosmology era Ann Rev Nucl Part Sci 57, 463–491 Sterman, G (2004) QCD and jets ArXiv: hep-ph/0412013 Stodolsky, L (1975) Speculations on detection of the neutrino sea Phys Rev Lett 34, 110 Strumia, A and F Vissani (2006) Neutrino masses and mixings ArXiv: hep-ph/0606054 Stueckelberg, E C G (1938) Interaction energy in electrodynamics and in the field theory of nuclear forces Helv Phys Acta 11, 225–244 Sudarshan, E C G and R E Marshak (1958) Chirality invariance and the universal Fermi interaction Phys Rev 109, 1860–1862 Suematsu, D and Y Yamagishi (1995) Radiative symmetry breaking in a supersymmetric model with an extra U (1) Int J Mod Phys A10, 4521– 4536 Sundrum, R (2005) To the fifth dimension and back (TASI 2004) ArXiv: hep-th/0508134 Susskind, L (1979) Dynamics of spontaneous symmetry breaking in the weinberg- salam theory Phys Rev D20, 2619–2625 Susskind, L (2003) The anthropic landscape of string theory ArXiv: hepth/0302219 Svrcek, P and E Witten (2006) Axions in string theory JHEP 06, 051 References 627 ’t Hooft, G (1971a) Renormalizable Lagrangians for massive Yang-Mills fields Nucl Phys B35, 167–188 ’t Hooft, G (1971b) Renormalization of massless Yang-Mills fields Nucl Phys B33, 173–199 ’t Hooft, G (1973) Dimensional regularization and the renormalization group Nucl Phys B61, 455–468 ’t Hooft, G (1974) A planar diagram theory for strong interactions Nucl Phys B72, 461 ’t Hooft, G (1976a) Computation of the quantum effects due to a fourdimensional pseudoparticle Phys Rev D14, 3432–3450 ’t Hooft, G (1976b) Symmetry breaking through Bell-Jackiw anomalies Phys Rev Lett 37, 8–11 ’t Hooft, G (1980) Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking NATO Adv Study Inst Ser B Phys 59, 135 ’t Hooft, G (1986) How instantons solve the U (1) problem Phys Rept 142, 357–387 ’t Hooft, G (1999) The physics of instantons in the pseudoscalar and vector meson mixing ArXiv: hep-th/9903189 ’t Hooft, G and M J G Veltman (1972) Combinatorics of gauge fields Nucl Phys B50, 318–353 TEVNPH (2009) Combined CDF and DZero upper limits on standard model Higgs-boson production with up to 4.2 fb−1 of data ArXiv: 0903.4001 Trodden, M (1999) Electroweak baryogenesis Rev Mod Phys 71, 1463– 1500 Uzan, J.-P (2003) The fundamental constants and their variation: observational status and theoretical motivations Rev Mod Phys 75, 403 van Ritbergen, T., A N Schellekens, and J A M Vermaseren (1999) Group theory factors for Feynman diagrams Int J Mod Phys A14, 41–96 van Ritbergen, T., J A M Vermaseren, and S A Larin (1997) The four-loop beta function in quantum chromodynamics Phys Lett B400, 379–384 Veltman, M J G (1977) Limit on mass differences in the Weinberg model Nucl Phys B123, 89 Vergados, J D (1986) The neutrino mass and family, lepton and baryon nonconservation in gauge theories Phys Rept 133, Vilenkin, A (1985) Cosmic strings and domain walls Phys Rept 121, 263 628 The Standard Model and Beyond Vogel, P (2008) Nuclear physics aspects of double beta decay ArXiv: 0807.2457 Vogel, P and J Engel (1989) Neutrino electromagnetic form-factors Phys Rev D39, 3378 Wang, L.-T and I Yavin (2008) A review of spin determination at the LHC Int J Mod Phys A23, 4647–4668 Weiglein, G et al (2006) Physics interplay of the LHC and the ILC Phys Rept 426, 47–358 Weiler, T J (1982) Resonant absorption of cosmic ray neutrinos by the relic neutrino background Phys Rev Lett 49, 234 Weinberg, S (1958) Charge symmetry of weak interactions Phys Rev 112, 1375–1379 Weinberg, S (1967a) A model of leptons Phys Rev Lett 19, 1264–1266 Weinberg, S (1967b) Dynamical approach to current algebra Phys Rev Lett 18, 188–191 Weinberg, S (1973a) Current algebra and gauge theories Phys Rev D8, 605–625 Weinberg, S (1973b) Current algebra and gauge theories nonabelian gluons Phys Rev D8, 4482–4498 Weinberg, S (1973c) General theory of broken local symmetries Phys Rev D7, 1068–1082 Weinberg, S (1973d) Perturbative calculations of symmetry breaking Phys Rev D7, 2887–2910 Weinberg, S (1975) The U (1) problem Phys Rev D11, 3583–3593 Weinberg, S (1976) Gauge theory of CP violation Phys Rev Lett 37, 657 Weinberg, S (1977) The problem of mass Trans New York Acad Sci 38, 185–201 Weinberg, S (1978) A new light boson? Phys Rev Lett 40, 223–226 Weinberg, S (1979) Implications of dynamical symmetry breaking: an addendum Phys Rev D19, 1277–1280 Weinberg, S (1980) Varieties of baryon and lepton nonconservation Phys Rev D22, 1694 Weinberg, S (1982) Supersymmetry at ordinary energies Masses and conservation laws Phys Rev D26, 287 629 References Weinberg, S (1989a) Larger Higgs exchange terms in the neutron electric dipole moment Phys Rev Lett 63, 2333 Weinberg, S (1989b) Phys 61, 1–23 The cosmological constant problem Rev Mod Weisberger, W I (1965) Renormalization of the weak axial vector coupling constant Phys Rev Lett 14, 1047–1051 Wess, J (2009) From symmetry to supersymmetry ArXiv: 0902.2201 Wess, J and B Zumino (1974a) A Lagrangian model invariant under supergauge transformations Phys Lett B49, 52 Wess, J and B Zumino (1974b) Supergauge transformations in fourdimensions Nucl Phys B70, 39–50 Weyl, H (1929) Electron and gravitation Z Phys 56, 330–352 Whalley, M R., D Bourilkov, and R C Group (2005) The Les Houches Accord PDFs (LHAPDF) and Lhaglue ArXiv: hep-ph/0508110 Wilczek, F (1978) Problem of strong P and T invariance in the presence of instantons Phys Rev Lett 40, 279–282 Williams, K E and G Weiglein (2008) Precise predictions for → hb hc decays in the complex MSSM Phys Lett B660, 217–227 Winstein, B and L Wolfenstein (1993) The Search for direct CP violation Rev Mod Phys 65, 1113–1148 Witten, E (1981) Dynamical breaking of supersymmetry Nucl Phys B188, 513 Witten, E (1982) Constraints on supersymmetry breaking Nucl Phys B202, 253 Witten, E (1996) Strong coupling expansion of calabi-yau compactification Nucl Phys B471, 135–158 Witten, E (2004) Perturbative gauge theory as a string theory in twistor space Commun Math Phys 252, 189–258 Wolfenstein, L (1964) Violation of CP Invariance and the possibility of very weak interactions Phys Rev Lett 13, 562–564 Wolfenstein, L (1978) Neutrino oscillations in matter Phys Rev D17, 2369–2374 Wolfenstein, L (1983) Parametrization of the Kobayashi-Maskawa matrix Phys Rev Lett 51, 1945 630 The Standard Model and Beyond Wu, C S., E Ambler, R W Hayward, D D Hoppes, and R P Hudson (1957) Experimental test of parity conservation in beta decay Phys Rev 105, 1413–1414 Wu, S L (1984) e+ e− physics at PETRA: the first 5-years Phys Rept 107, 59–324 Wu, T T and C.-N Yang (1964) Phenomenological analysis of violation of ¯ Phys Rev Lett 13, 380–385 CP invariance in decay of K and K Yamazaki, T (2009) On-shell ∆I = 3/2 kaon weak matrix elements with non-zero total momentum Phys Rev D79, 094506 Yanagida, T (1979) Horizontal gauge symmetry and masses of neutrinos In Proceedings of the Workshop on the Baryon Number of the Universe and Unified Theories, Tsukuba, Japan, 13-14 Feb 1979 Yang, C.-N and R L Mills (1954) Conservation of isotopic spin and isotopic gauge invariance Phys Rev 96, 191–195 Yndurain, F J (2007) Elements of group theory ArXiv: 0710.0468 Yoshimura, M (1978) Unified gauge theories and the baryon number of the universe Phys Rev Lett 41, 281–284 Young, R D., R D Carlini, A W Thomas, and J Roche (2007) Testing the standard model by precision measurement of the weak charges of quarks Phys Rev Lett 99, 122003 Copyright 2007 by the American Physical Society Yukawa, H (1935) On the interaction of elementary particles Proc Phys Math Soc Jap 17, 48–57 Zee, A (1973) Study of the renormalization group for small coupling constants Phys Rev D7, 3630–3636 Zee, A (1980) A theory of lepton number violation, neutrino Majorana mass, and oscillation Phys Lett B93, 389 Zeldovich, Y B (1952) Dok Akad Nauk CCCP 86, 505 Zeller, G P et al (2002) A precise determination of electroweak parameters in neutrino nucleon scattering Phys Rev Lett 88, 091802 Zhang, Y., H An, X Ji, and R N Mohapatra (2007) Right-handed quark mixings in minimal left-right symmetric model with general CP violation Phys Rev D76, 091301 Zhang, Z (2009) Electroweak and beyond the standard model results from HERA Nucl Phys Proc Suppl 191, 271–280 Web Sites • Particle physics PDG: The Review of Particle Physics, http://pdg.lbl.gov/ Particle properties and many useful review articles in particle physics, astrophysics, and cosmology SPIRES: http://www.slac.stanford.edu/spires/hep/ Extensive data base of high energy physics publications Archive: http://arXiv.org/ Archive of preprints in physics and related fields Online: Online Particle Physics, http://www.slac.stanford.edu/library/pdg/hepinfo.html List of particle physics links SMB: http://www.sns.ias.edu/~pgl/SMB/ Supplements and corrections to this book • Tevatron and LHC general purpose detectors CDF: CDF results, http://www-cdf.fnal.gov/physics/physics.html D0: D0 results, http://www-d0.fnal.gov/results/ ATLAS: http://atlas.ch/ CMS: http://cms.cern.ch/ • QCD and structure functions CTEQ: The Coordinated Theoretical-Experimental Project on QCD, http://www.phys.psu.edu/~cteq/ MRST: http://durpdg.dur.ac.uk/HEPDATA/PDF LHAPDF: Les Houches Accord PDFs (Whalley et al., 2005), http://hepforge.cedar.ac.uk/lhapdf/ • Electroweak Physics LEPEWWG: LEP Electroweak Working Group, http://lepewwg.web.cern.ch/LEPEWWG/ Major source for LEP and SLC results 631 632 The Standard Model and Beyond ZFITTER: http://www-zeuthen.desy.de/theory/research/zfitter/ Electroweak radiative corrections and fits (Arbuzov et al., 2006) GAPP: Global Analysis of Particle Properties (Erler, 1999), http://www.fisica.unam.mx/erler/GAPPP.html Gfitter: A Generic Fitter Project for HEP Model Testing (Flacher et al., 2009), http://project-gfitter.web.cern.ch/project-gfitter/ • Higgs physics LEPHIGGS: LEP Higgs Working Group, http://lephiggs.web.cern.ch/LEPHIGGS/www/Welcome.html TeV4LHC: Higgs production cross sections (SM and MSSM), http://maltoni.home.cern.ch/maltoni/TeV4LHC/ HDECAY: Higgs boson decays in the SM and MSSM (Djouadi et al., 1998), http://home.cern.ch/~mspira/proglist.html/ CPsuperH: MSSM Higgs with CP violation (Lee et al., 2004), http://www.hep.man.ac.uk/u/jslee/CPsuperH.html FeynHiggs: MSSM Higgs http://wwwth.mppmu.mpg.de/members/heinemey/feynhiggs/ HiggsBounds: LEP and Tevatron bounds for arbitrary model (Bechtle et al., 2008) http://www.ippp.dur.ac.uk/HiggsBounds • Supersymmetry: spectrum, renormalization group evolution SPA: Supersymmetry Parameter Analysis (Aguilar-Saavedra et al., 2006), http://spa.desy.de/spa/ Links to supersymmetry analysis programs SuSpect: http://www.lpta.univ-montp2.fr/users/kneur/Suspect/ (Djouadi et al., 2007) Spheno: http://ific.uv.es/~porod/SPheno.html (Porod, 2003) SoftSUSY: http://projects.hepforge.org/softsusy/ (Allanach, 2002) • Event generators (for a general description, see Mangano and Stelzer, 2005) and analysis programs Pythia: http://home.thep.lu.se/~torbjorn/ (Sjostrand et al., 2008) Herwig: http://hepwww.rl.ac.uk/theory/seymour/herwig/ (Corcella et al., 2001) Isajet: http://www.hep.fsu.edu/~isajet/ (Paige et al., 2003) Sherpa: http://projects.hepforge.org/sherpa/ (Gleisberg et al., 2009) Web Sites 633 ROOT: http://root.cern.ch/root/ Analysis package MARMOSET: Mass And Rate Matching In On-Shell Effective Theories (Arkani-Hamed et al., 2007) http://www.marmoset-mc.net/ PGS4: Pretty Good Simulation of particle collisions (generic collider detector) http://www.physics.ucdavis.edu/~conway/ research/software/pgs/pgs4-general.htm • Matrix elements MadGraph: http://madgraph.hep.uiuc.edu/ CalcHEP: http://theory.sinp.msu.ru/~pukhov/calchep.html LanHEP: Feynman rules from Lagrangian density (Semenov, 2009) http://theory.sinp.msu.ru/~semenov/lanhep.html CompHEP: http://comphep.sinp.msu.ru/ FeynArts: Generation and calculation of Feynman diagrams (Hahn, 2001), http://www.feynarts.de/ FeynRules: Calculation of Feynman rules (Christensen and Duhr, 2008), http://feynrules.phys.ucl.ac.be/ • K and B physics, CKM matrix FlaviaNet: Working group on K decays (Antonelli et al., 2008), http://www.lnf.infn.it/wg/vus/ CKMfitter: http://ckmfitter.in2p3.fr/ (Charles et al., 2005) UTfit: http://www.utfit.org/ (Ciuchini et al., 2001) HFAG: Heavy Flavor Averaging Group, http://www.slac.stanford.edu/xorg/hfag/ (Barberio et al., 2008) • Dark matter abundance MicrOMEGAs: http://lappweb.in2p3.fr/lapth/micromegas/ (Belanger et al., 2007) DarkSUSY: http://www.physto.se/~edsjo/darksusy/ (Gondolo et al., 2004) • Neutrinos Neutrino oscillation industry: Neutrino links http://www.hep.anl.gov/ndk/hypertext Physics Series in High Energy Physics, Cosmology, and Gravitation Langacker Series in High Energy Physics, Cosmology, and Gravitation Series Editors: Brian Foster and Edward W Kolb The Standard Model and Beyond Paul Langacker “The Standard Model and Beyond is a state-of-the-art description of what we know about the particles and forces that build up the world we see Most books that cover these topics are quantum field theory books that treat the quarks and leptons, and the electromagnetic, weak, and strong forces as examples This is the first treatment with the opposite priorities, focusing on the structure and applications of the standard model and bringing in the field theory as needed, in a pedagogically reliable and thorough treatment Langacker knows well that the standard model is the platform on which a deeper understanding of the laws of nature will be constructed, perhaps from clues soon to come from the Large Hadron Collider, and provides preparation so the reader can participate in that progress.” The Standard Model and Beyond —Gordon Kane, Victor Weisskopf Collegiate Professor of Physics and Director of the Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, USA The Standard Model and Beyond presents an advanced introduction to the physics and formalism of the standard model and other non-abelian gauge theories Thoroughly covering gauge field theories, symmetries, and topics beyond the standard model, this text equips readers with the tools to understand the structure and phenomenological consequences of the standard model, to construct extensions, and to perform calculations at tree level It establishes the necessary background for readers to carry out more advanced research in particle physics Features • Covers the fundamental interactions • Describes the construction, experimental tests, and phenomenological consequences of the standard model • Presents a self-contained treatment of the complicated technology needed for tree-level calculations • Explores applications in astrophysics and cosmology • Lists many useful reference books, review articles, research papers, and Web links • Offers supplementary materials on the author’s Web site C7906 an informa business w w w c r c p r e s s c o m 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK 1118 2014 ISBN: 978-1-4200-7906-7 90000 781420 079067 Paul Langacker ... introduction to the physics and formalism of the standard model and other non-abelian gauge theories, and thus to provide a thorough background for topics such as superxi xii The Standard Model and Beyond. .. matter and energy suggest new particle physics beyond the standard model Most current activity is directed towards discovering the new physics which must underlie the standard model Much of the theoretical... (2.66) 22 The Standard Model and Beyond is the Fourier transform of Φ, q = (0, q ), and we have used translation invariance for the matrix element Then, carrying out the x integral, where and pf