Particle Physics beyond the Standard Model (eBook)

Lecture Notes of the Les Houches Summer School 2005

Jean Dalibard, Dmitri Kazakov, Stephane Lavignac (Herausgeber)

eBook Download: PDF

2006 | 1. Auflage
712 Seiten
Elsevier Science (Verlag)
978-0-08-046314-8 (ISBN)

Infos

"The Standard Model of elementary particles and interactions is one of the best tested theories in physics. It has been found to be in remarkable agreement with experiment, and its validity at the quantum level has been successfully probed in the electroweak sector. In spite of its experimental successes, though, the Standard Model suffers from a number of limitations, and is likely to be an incomplete theory. It contains many arbitrary parameters, it does not include gravity, the fourth elementary interaction, it does not provide an explanation for the hierarchy between the scale of electroweak interactions and the Planck scale, characteristic of gravitational interactions, and finally, it fails to account for the dark matter and the baryon asymmetry of the universe. This led particle theorists to develop and study various extensions of the Standard Model, such as supersymmetric theories, Grand Unified Theories or theories with extra space-time dimensions - most of which have been proposed well before the experimental verification of the Standard Model. The coming generation of experimental facilities (such as high-energy colliders, B-physics experiments, neutrino superbeams, as well as astrophysical and cosmological observational facilities) will allow us to test the predictions of these theories and to deepen our understanding of the fundamental laws of nature.

This book is a collection of lectures given in August 2005 at the Les Houches Summer School on Particle Physics beyond the Standard Model. It provides a pedagogical introduction to the various aspects of particle physics beyond the Standard Model, covering each topic from the basics to the most recent developments: supersymmetric theories, Grand Unified Theories, theories with extra dimensions, flavour physics and CP violation, neutrino physics, astroparticle physics and cosmology.

?Provides a pedagogical introduction to particle physics beyond the Standard Model
?Covers the various aspects of particle physics beyond the Standard Model
?Addresses each topic from the basics to the most recent developments
?Addresses both the theoretical and phenomenological aspects of the subject
?Written in a pedagogical style by leading experts in the field"

Inhalt

Front cover 1
Copyright page 5
Previous sessions 7
Organizers 10
Lecturers 12
Participants 14
Preface 18
Table of contents 22
Course 1 Flavour physics and grand unification 34
Introduction 38
Theoretical reasons for new physics 39
"Observational" reasons for new physics 41
The SM as an effective low-energy theory 44
Flavor, CP and new physics 47
The flavor problem in SUSY 47
CP violation in SUSY 50
Grand unification and SUSY GUTS 51
SU(5) the prototype of GUT theory 53
The Georgi-Glashow minimal SU(5) model 56
Distinctive features of GUTs and problems in building a realistic model 57
Supersymmetric grand unification 62
The hierarchy problem and supersymmetry 62
SUSY GUT predictions and problems 67
"Realistic" supersymmetric SU(5) models 71
Other GUT Models 72
The seesaw mechanism 73
SO(10) 74
Flavour and CP violation in SUSY 75
Flavour changing neutral currents in the MSSM 85
Grand unification of FCNCs 91
Supersymmetric seesaw and lepton flavour violation 98
Seesaw in GUTs: SO(10) and LFV 100
References 106
Course 2 CP violation in meson decays 112
Introduction 116
Why believe the Kobayashi-Maskawa mechanism? 116
Why doubt the Kobayashi-Maskawa mechanism? 118
The baryon asymmetry of the universe 118
The strong CP problem 118
New physics 119
Will new CP violation be observed in experiments? 119
The Kobayashi-Maskawa mechanism 121
Yukawa interactions are the source of CP violation 121
CKM mixing is the (only!) source of CP violation in the quark sector 124
The three phases in the lepton mixing matrix 126
The flavor parameters 127
The unitarity triangles 129
The uniqueness of the Standard Model picture of CP violation 131
Meson decays 133
Charged and neutral meson decays 133
Neutral meson mixing 134
CP-violating observables 136
Classification of CP-violating effects 137
Theoretical interpretation: general considerations 139
K decays 141
Implications of epsilonK 143
D decays 144
B decays 146
b-> ccs transitions
Penguin dominated b-> s transitions
General considerations 151
Calculating the deviations from Sf=SpsiK 153
b-> uud transitions
b-> cus,uc s transitions
CP violation as a probe of new physics 161
Supersymmetric CP violation 166
CP-violating parameters 168
The supersymmetric CP problem 169
The supersymmetric epsilonK problem 170
More on supersymmetric flavor and CP violation 172
Discussion 173
Lessons from the B factories 174
References 175
Course 3 Supersymmetry breaking 180
Preamble 184
Structure and further reading 184
Basic features of supersymmetry breaking 185
Order parameters for supersymmetry breaking 185
The scalar potential and flat directions 186
The Goldstino 187
Tree-level breaking: F-type 188
Tree-level breaking: D-type 191
Going local 192
Beyond tree level: dynamical supersymmetry breaking 193
Indirect analysis-SU(5) with single antisymmetric 196
Direct analysis: the 3-2 model 196
Classical theory 197
Exact superpotential 198
Calculable minimum 201
Mediating the breaking 202
Mediating supersymmetry-breaking by Planck-suppressed operators 203
Anomaly mediated supersymmetry breaking 204
Gauge mediated supersymmetry breaking 207
How NOT to fix AMSB 209
Supersymmetry basics 211
References 212
Course 4 Extra dimensions: a primer 214
Introduction 218
Homogeneous and small extra dimensions: Kaluza-Klein 219
Localized matter 221
Simplest brane: domain wall 222
Scalars 222
Fermions 224
Gauge fields 226
Large extra dimensions: ADD 227
KK picture for gravitons 227
Potential conflict with cosmology and astrophysics 229
Warped extra dimension 234
Non-factorizable geometry 234
Slice of adS5 236
Matter on negative tension brane: RS1 239
Matter on positive tension brane 241
Infinite extra dimension: RS2 241
Localized graviton 241
Escape into extra dimension 244
Holographic interpretation 248
Brane worlds as a theoretical laboratory 250
References 258
Course 5 Phenomenology of extra dimensions 262
Introduction 266
Large extra dimensions 269
Short range tests of gravity 270
Astrophysical and cosmological constraints 271
Collider probes 276
TeV-1-sized extra dimensions 283
Warped extra dimensions 286
Summary 291
References 292
Course 6 Warped models and holography 296
Preamble 300
Introduction 300
Bulk fields in a slice of AdS5 301
A slice of AdS5 301
The bulk field Lagrangian 304
Scalar fields 304
Fermions 307
Summary 308
The Standard Model in the bulk 310
Yukawa couplings 310
Higher-dimension operators 312
Higgs as a pseudo Nambu-Goldstone boson 313
AdS/CFT and holography 314
Holography of scalar fields 316
nu- branch holography 319
nu+ branch holography 321
Dual 4D description of the Standard Model in the bulk 322
Yukawa couplings 323
Minimal composite Higgs model 325
Supersymmetric models in warped space 325
Supersymmetry in a slice of AdS 326
The warped MSSM: a model of dynamical supersymmetry breaking 327
The dual 4D interpretation 329
The partly supersymmetric Standard Model: a natural model of high-scale supersymmetry breaking 330
Higgs sector possibilities 332
Electroweak symmetry breaking 334
Dual 4D interpretation 334
Grand unification 335
Logarithmic running in 5D warped space 336
Partly supersymmetric grand unification 338
Conclusion 341
References 342
Course 7 New approaches to electroweak symmetry breaking 346
Preamble 350
Electroweak symmetry breaking and new physics 351
SM Higgs physics 351
Higgs mechanism 351
Counting the degrees of freedom 354
Custodial symmetry 354
Unitarity bound 356
Triviality bound 359
Stabilization of the Higgs potential by symmetries 364
EW precision tests 365
An example of EW corrections induced by a heavy particle 365
General structure of the EW corrections 367
An example of EW corrections induced by a higher dimensional operator 368
Little Higgs models 369
Gauge-Higgs unification models 369
Orbifold breaking. 5D SU(3) model 369
6D G2 model 372
Radiative corrections 374
Introducing matter and Yukawa interactions 377
Experimental signatures 377
Recent developments and open issues 377
5D Higgsless models 379
Gauge symmetry breaking by boundary conditions 380
Boundary conditions for a scalar field 380
Boundary conditions for a gauge field 383
Higgs mechanism localized on a boundary: scalar decoupling limit 385
Unitarity restoration by KK modes. Sum Rules of Higgsless theories 387
Toys models 391
En route vers a Higgsless model 392
Flat Higgsless model 393
Warped Higgsless model with custodial symmetry 396
A bit of AdS/CFT 396
Towards a realistic Higgsless model 397
Fermion masses 402
Chiral fermions from orbifold projection/boundary condition 403
Fermions in AdS background 406
Higgsless fermions masses 408
Electroweak precision tests 411
Collider signatures 417
Recent developments and conclusion 420
References 421
Course 8 Aspects of string phenomenology 428
Preamble 432
Introduction 432
String theories and D-branes: spectra and dualities 434
Orientifolds and the Type I string 437
Perturbative expansion, one-loop amplitudes 440
Various D-branes and O-planes: BPS and non-BPS configurations 447
Compactification to four-dimensions 448
Branes at angles: intersecting brane worlds 452
Mechanisms for supersymmetry breaking 456
The Scherk-Schwarz mechanism 456
Models based on non-BPS systems: brane supersymmetry breaking 458
Internal magnetic fields / intersecting branes 460
Anomalies and generalized four dimensional Green-Schwarz mechanism 460
Moduli stabilization 465
Flux moduli stabilization in orientifolds of the type IIB string 465
Supersymmetry breaking and moduli stabilization in Horava-Witten M-theory 468
Moduli stabilization and de Sitter vacua 471
Small and large extra dimensions 473
Compactification, mass scales and couplings 473
Large extra dimensions 476
Accelerated unification 478
Conclusions 482
References 483
Course 9 Particle astrophysics and cosmology 490
What is particle astrophysics or astroparticle? 494
The (not so) quiet universe 495
Gravity rules the evolution of the universe 495
A first try at solving Einstein's equations: the Schwarzschild solution 500
Gravitational instability I: galaxies 502
Gravitational instability II: compact objects, from dwarfs to black holes 504
Stars 505
Gravitational collapse: black holes 508
Gravitational waves 516
The violent universe 518
Stellar evolution 519
Active Galactic Nuclei and supermassive black holes 520
Accretion to a compact object 523
Supernovae 525
Gamma ray bursts 528
Gravitational waves 529
The universe at large 532
Energy budget 532
Measure of distances 534
Cosmic Microwave Background [CMB] 536
Baryon acoustic oscillations 539
Acceleration of the universe 541
Standard or standardizable candles? 541
The early universe 544
Inflation 546
Inflation scenarios 551
Dark energy 556
Astrophysical constants and scales 563
Burning fuel: nuclear reactions in stars 564
References 567
Course 10 Ultra-high energy cosmic rays 570
Introduction 574
Background information 575
The observed spectrum 575
Detection techniques 575
The arrival direction distribution 578
Propagation of UHECR 578
General remarks 578
Pion photoproduction 579
The GZK cutoff 580
Deflections in the magnetic fields 584
Summary: the UHECR puzzle 585
AGN models 589
Gamma-ray bursts as sources of UHECR 590
Young rapidly rotating neutron stars (magnetars) 590
Superheavy dark matter + AGNs 593
Topological defects 595
Violation of Lorentz invariance 596
Strong neutrino interactions 596
Quest for sources 597
Clustering of UHECR events 597
Predictions for future data 600
Conclusions and outlook 602
References 602
Course 11 Neutrino mass and mixing: toward the underlying physics 606
Preamble 610
Introduction 610
Notions and notations 612
Flavors, masses and mixing 612
Two aspects of mixing 612
Who mixes neutrinos? 614
Physical effects 614
To determination of oscillation parameters 614
Neutrino oscillation in vacuum 615
Evolution equation 617
Matter effect 618
Degrees of freedom 620
Oscillations in matter. Resonance enhancement of oscillations 620
MSW: adiabatic conversion 622
Adiabaticity violation 626
Determination of the oscillation parameters 627
Solar neutrinos 627
KamLAND 631
Atmospheric neutrinos 633
K2K 637
1-3 mixing: effects and bounds 638
Degeneracy of oscillation parameters and global fits 639
Neutrino mass and flavor spectrum 641
Spectrum 641
Absolute scale of neutrino mass 642
Neutrinoless double beta decay 643
Cosmology and neutrino mass 647
Physics of the long baseline experiments 649
Expecting the supernova neutrino burst 651
LSND result and new neutrinos 651
Toward the underlying physics 653
Mass and mixing 653
New symmetry of nature? 656
Bi-maximal mixing 656
Tri-bimaximal mixing 658
Neutrino mass and horizontal symmetry 659
Symmetry case 660
Leptons and quarks 663
Comparing results 663
Quark-lepton complementarity (QLC) 666
See-saw and GUT's 668
Seesaw: variations on the theme 668
GUT's and neutrino mass 670
Landscape of models and mechanisms 672
Small Dirac mass 672
Higgs triplet mechanism 674
Radiative mechanisms 674
Neutrino mass and SUSY 675
Extra dimensions and neutrino mass 679
Conclusion 681
References 682
Course 12 Baryogenesis via leptogenesis 688
Introduction 692
The DM abundancy 692
The baryon asymmetry 694
Baryogenesis 695
Baryogenesis in the SM? 695
Thermal leptogenesis: the basic physics 697
CP-asymmetry 697
Efficiency 698
Thermal leptogenesis: precise computation 700
Boltzmann equations 701
Boltzmann equations for leptogenesis 703
Testing leptogenesis? 707
Constraints from leptogenesis 708
Leptogenesis and supersymmetry 710
Leptogenesis in alternative neutrino-mass models 711
References 713

Textauszug

3 Flavour and CP violation in SUSY

The simplest Supersymmetric version of the Standard Model that we can build is the so-called Minimal Supersymmetric Standard Model (MSSM). Clearly, this model must include all the SM interactions and particle spectrum together with their Supersymmetric partners. This means that to every quark and lepton in the SM we add a scalar Supersymmetric partner, called “squark” or “slepton” respectively, with identical gauge quantum numbers and, in principle, identical mass, forming a “chiral supermultiplet”. In the same way, to the SM Higgs or more exactly to the Higgses in a 2 Higgs doublet version of the SM2 we add fermi-onic partners called “higgsinos” with the same quantum numbers and masses in another “chiral Supermultiplet”. Then every gauge boson is also joined by a gaugino (“gluino”, “wino”, “bino”…) with spin 1/2 in the adjoint representation in a “vector supermultiplet” (for a complete formulation of Supersymmetric theories in superfield notation see Ref. [60]).

The gauge interactions in our MSSM are completely fixed by the gauge quantum numbers of the different particles in the usual way. However, we still need the Yukawa interactions of the Standard Model that give masses to the fermions once we break the electroweak symmetry. These interactions are included in the MSSM Superpotential, which is a gauge invariant analytic function of the MSSM superfields (i.e. a function of fields φi but not of complex conjugate fields i*) with dimensions of mass cube. If we include all possible terms invariant under the gauge symmetry then it turns out that some of these terms violate either baryon or lepton number. As we have seen in the previous section, this endangers proton stability; hence one usually imposes a discrete symmetry called R-parity under which the ordinary particles are even while their SUSY partners are odd [61]3. The MSSM Superpotential (using standard notation) is then,

=YdijQiH1dRjc+YeijLiH1eRjc+YuijQiH2uRjc+μH1H2,

  (3.1)

and this gives rise to the interactions,

W=| ∂W∂Фi |2+ψiψj∂2W∂Фi∂Фj,

  (3.2)

with φi any scalar in the MSSM and ψi its corresponding fermionic partner.

Still, we know that Supersymmetry is not an exact symmetry in nature and it must be broken. If Supersymmetry is the solution to the hierarchy problem, the breaking of Supersymmetry must be soft, i.e. should not reintroduce the quadratic divergences which are forbidden in the SUSY invariant case, and the scale of SUSY breaking must be close to the electroweak scale. The most general set of possible Soft SUSY breaking terms (SBT) [42] under these conditions are,

1. Gaugino masses

soft(1)=12(M1B˜B˜+M2W˜W˜+M3g˜g˜)+h.c.,

2. Scalar masses

soft(2)=(MQ˜2)ijQ˜iQ˜j∗+(Mu˜2)iju˜Ricu˜Rjc∗+(Md˜2)ijd˜Ricd˜Rjc∗+(ML˜2)ijL˜iL˜j∗+(Me˜2)ije˜Rice˜Rjc∗+(mH12)H1H1∗+(mH22)H2H2∗,

3. Trilinear couplings and B–term

soft(3)=(YdA)ijQ˜iH1d˜Rj+(YeA)ijL˜iH1e˜Rjc+(YuA)ijQi˜H2u˜Rjc+BμH1H2,

where, Q˜2,Mu˜2,Md˜2,ML˜2 and e˜2 are hermitian 3 × 3 matrices in flavour space, while YdA),(YuA) and YuA) are complex 3 × 3 matrices and M 1, M 2, M 3 denote the Majorana gaugino masses for the U(1), SU(2), SU(3) gauge symmetries respectively.

This completes the definition of the MSSM. However, these conditions include a huge variety of models with very different phenomenology specially in the flavour and CP violation sectors.

It is instructive to identify all the observable parameters in a general MSSM [63]. Here we distinguish the flavour independent sector which includes the gauge and Higgs sectors and the flavour sector involving the three generations of chiral multiplets containing the SM fermions and their Supersymmetric partners.

In the flavour independent sector, we have three real gauge couplings, gi, and three complex gaugino masses, Mi. In the Higgs sector, also flavour independent, we have a complex μ parameter in the superpotential, a complex Bμ soft term and two real squared soft masses H12 and H22. However, not all the phases in these parameters are physical [64]. In the limit of μ = Bμ = 0, vanishing gaugino masses and zero trilinear couplings, YA, (we will discuss trilinear terms in the flavour dependent sector), our theory has two global U(1) symmetries:U(1)R and U(1)PQ. This implies that we can use these two global symmetries to remove two of the phases of these parameters. For instance, we can choose a real Bμ and a real gluino mass M 3. Then, in the flavour independent sector, we have 10 real parameters (gi, |Mi|, |μ|, Bμ, H12 and H22) and 3 phases (arg(μ), arg(M 1) and arg (M 2)).

Next, we have to analyse the flavour dependent sector. Here we do not take into account neutrino mass matrices. Then, in the superpotential we have the up quark, down quark and charged lepton Yukawa couplings, Yu, Yd and Ye, that are complex 3 × 3 matrices. In the soft breaking sector we have 5 hermitian mass squared matrices, Q˜2,MU˜2,MD˜2,ML˜2 and E˜2 and three complex trilinear matrices, uA,YdA and eA. This implies we have 6 × 9 moduli and 6 × 9 phases from the 6 complex matrices (Yu, Yd, Ye, uA,YdA and eA) and 5 × 6 moduli and 5 × 3 phases from the 5 hermitian matrices. Therefore, in the flavour sector we have 84 moduli and 69 phases. However, it is well-known that not all these parameters are observable. In the absence of these flavour matrices the theory has a global U(3) Q L⊗U(3)uR⊗U(3)dR⊗U(3)L L⊗U(3)eR flavour symmetry under exchange of the different particles of the three generations. The number of observable parameters is easily determined using the method in Ref. [65] as,

=Nfl−NG−NG′,

  (3.3)

where Nfl is the number of parameters in the flavour matrices. NG is the number of parameters of the group of invariance of the theory in the absence of the flavour matrices G = U(3)Q L⊗U(3)uR⊗U(3)dR⊗U(3)L L⊗U(3)eR. Finally NG′ is the number of parameters of the group G′, the subgroup of G still unbroken by the flavour matrices. In this case, G′ corresponds to two U(1) symmetries, baryon number conservation and lepton number conservation and therefore NG′ =  2. Furthermore Eq. (3.3) can be applied separately to phases and moduli. In this way, and taking into account that a U (N) matrix contains n(n − 1)/2 moduli and n(n + 1)/2 phases, it is straightforward to obtain that we have, Nph = 69 − 5 × 6 + 2 = 41 phases and Nmod = 84 − 5 × 3 = 69 moduli in the flavour sector. This amounts to a total of 123 parameters in the model4, out of which 44 are CP violating phases!! As we know, in the SM, there is only one observable CP violating phase, the CKM phase, and therefore we have here 43 new phases, 40 in the flavour sector and three in the flavour independent sector.

Clearly, to explore completely the flavour and CP violating phenomena in a generic MSSM is a formidable task as we have to determine a huge number of unknown parameters [66]. However, this parameter counting corresponds to a completely general MSSM at...

Produkt-Details

• Erscheint lt. Verlag: 4.7.2006
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 0-08-046314-2 / 0080463142
• ISBN-13: 978-0-08-046314-8 / 9780080463148