xi
22.2 The SU(2) × U(1) electroweak gauge theory . . . . . . . . . 377
22.2.1 Quantum number assignments; Higgs, W and Z masses 377
22.2.2 The leptonic currents (massless neutrinos): relation to
current–current model . . . . . . . . . . . . . . . . . . 382
22.2.3 The quark currents . . . . . . . . . . . . . . . . . . . . 386
22.3 Simple (tree-level) predictions . . . . . . . . . . . . . . . . . 387
22.4 The disco ery of the W
±
d Z
0 at the CERN p¯ ollider . 39
v
an
p c
3
22.4.1 Production cross sections for W and Z in p¯ olliders
393
p c
22.4.2 Charge asymmetry in W
± decay . . . . . . . . . . . . 394
±
0
22.4.3 Discovery of the W and Z at the pp ¯ collider, and their
properties . . . . . . . . . . . . . . . . . . . . . . . . . 395
22.5 Fermion masses . . . . . . . . . . . . . . . . . . . . . . . . . 401
22.5.1 One generation . . . . . . . . . . . . . . . . . . . . . . 401
22.5.2 Three-generation mixing . . . . . . . . . . . . . . . . . 407
22.6 Higher-order corrections . . . . . . . . . . . . . . . . . . . . . 410
22.7 The top quark . . . . . . . . . . . . . . . . . . . . . . . . . . 419
22.8 The Higgs sector . . . . . . . . . . . . . . . . . . . . . . . . . 420
22.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 421
22.8.2 Theoretical considerations concerning m H . . . . . . . 423
22.8.3 Higgs boson searches and the 2012 discovery . . . . . 425
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
M Group Theory
435
M.1 Definition and simple examples . . . . . . . . . . . . . . . . . 435
M.2 Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
M.3 Generators of Lie groups . . . . . . . . . . . . . . . . . . . . 437
M.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
M.4.1 SO(3) and three-dimensional rotations . . . . . . . . . 438
M.4.2 SU(2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
M.4.3 SO(4): The special orthogonal group in four dimensions 440
M.4.4 The Lorentz group . . . . . . . . . . . . . . . . . . . . 441
M.4.5 SU(3) . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
M.5 Matrix representations of generators, and of Lie groups . . . 443
M.6 The Lorentz group . . . . . . . . . . . . . . . . . . . . . . . . 447
M.7 The relation between SU(2) and SO(3) . . . . . . . . . . . . 450
N Geometrical Aspects of Gauge Fields
453
N.1 Covariant derivatives and coordinate transformations . . . . 453
N.2 Geometrical curvature and the gauge field strength tensor . . 460
O Dimensional Regularization
463
P Grassmann Variables
467
22.2 The SU(2) × U(1) electroweak gauge theory . . . . . . . . . 377
22.2.1 Quantum number assignments; Higgs, W and Z masses 377
22.2.2 The leptonic currents (massless neutrinos): relation to
current–current model . . . . . . . . . . . . . . . . . . 382
22.2.3 The quark currents . . . . . . . . . . . . . . . . . . . . 386
22.3 Simple (tree-level) predictions . . . . . . . . . . . . . . . . . 387
22.4 The disco ery of the W
±
d Z
0 at the CERN p¯ ollider . 39
v
an
p c
3
22.4.1 Production cross sections for W and Z in p¯ olliders
393
p c
22.4.2 Charge asymmetry in W
± decay . . . . . . . . . . . . 394
±
0
22.4.3 Discovery of the W and Z at the pp ¯ collider, and their
properties . . . . . . . . . . . . . . . . . . . . . . . . . 395
22.5 Fermion masses . . . . . . . . . . . . . . . . . . . . . . . . . 401
22.5.1 One generation . . . . . . . . . . . . . . . . . . . . . . 401
22.5.2 Three-generation mixing . . . . . . . . . . . . . . . . . 407
22.6 Higher-order corrections . . . . . . . . . . . . . . . . . . . . . 410
22.7 The top quark . . . . . . . . . . . . . . . . . . . . . . . . . . 419
22.8 The Higgs sector . . . . . . . . . . . . . . . . . . . . . . . . . 420
22.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 421
22.8.2 Theoretical considerations concerning m H . . . . . . . 423
22.8.3 Higgs boson searches and the 2012 discovery . . . . . 425
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
M Group Theory
435
M.1 Definition and simple examples . . . . . . . . . . . . . . . . . 435
M.2 Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
M.3 Generators of Lie groups . . . . . . . . . . . . . . . . . . . . 437
M.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
M.4.1 SO(3) and three-dimensional rotations . . . . . . . . . 438
M.4.2 SU(2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
M.4.3 SO(4): The special orthogonal group in four dimensions 440
M.4.4 The Lorentz group . . . . . . . . . . . . . . . . . . . . 441
M.4.5 SU(3) . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
M.5 Matrix representations of generators, and of Lie groups . . . 443
M.6 The Lorentz group . . . . . . . . . . . . . . . . . . . . . . . . 447
M.7 The relation between SU(2) and SO(3) . . . . . . . . . . . . 450
N Geometrical Aspects of Gauge Fields
453
N.1 Covariant derivatives and coordinate transformations . . . . 453
N.2 Geometrical curvature and the gauge field strength tensor . . 460
O Dimensional Regularization
463
P Grassmann Variables
467