Amplifications & Corrections

Supplemental references:

§ 1.3: Add at the bottom of page 9, after “observed.” — The exotic J^{PC} = 1^{-+} states π1(1400) and π1(1600) are now established, and considered candidates for q\bar{q}g hybrids. See the brief discussion in §4 of C. Amsler, “non-q\bar{q} mesons,” in the 2006 Review of Particle Physics. For a discussion of the many recently reported multiquark meson candidates, many of which have exotic non-q\bar{q} quantum numbers, see S. L. Olsen, “XYZ Meson Spectroscopy,”  arXiv:1511.01589.
Add at the end of the first complete sentence on page 10 — Reported evidence for light qqqq\bar{q} “pentaquark” states has not been sustained. For a perspective on the searches, see K. H. Hicks, “On the Conundrum of the Pentaquark,” Eur. Phys. J. H 37, 1 (2012). Evidence for heavy pentaquarks, though with nonexotic N^* quantum numbers, was reported by R. Aaij et al. (LHCb Collaboration), “Observation of J\!/\!\psi p Resonances Consistent with Pentaquark States in \Lambda^0_b \to J\!/\!\psi K^- p Decays,” Phys. Rev. Lett. 115, 072001 (2015).

§ 1.References: Add at the end of Ref. 6 — G. Zweig, “Concrete Quarks: The Beginning of the End,” CERN Colloquium video (September 13, 2013); and article; CERN interview. M. Gell-Mann, Closing remarks at the Caltech Celebration of Murray Gell-Mann’s Quark Model of Hadrons, December 10, 2013. See also A. Petermann, “Propriétés de l’étrangeté et une formule de masse pour les mésons vectoriels,” Nucl. Phys. 63, 349–352 (1965), in which a spinor isodoublet and more massive spinor isoscalar are proposed to explain the pattern of vector-meson masses. 50 Years of Quarks, edited by H. Fritzsch and M. Gell-Mann, World Scientific, Singapore, 2015, contains a wealth of information about how the influence of the quark model spread.

Lagrangian formulation of quantum field theory, pp. 35–36: Add after first entry (Wilczek) — Also see G. ‘t Hooft, “The Evolution of Quantum Field Theory, From QED to Grand Unification,” arXiv:1503.05007.
Add below last entry — A comprehensive treatment of the logic and structure of field theory is given by A. Duncan, The Conceptual Framework of Quantum Field Theory, Oxford University Press, Oxford, 2012.

Conservation Laws, p. 36: Add after the Kosmann-Schwarzbach entry — See also D. E. Neuenschwander, Emmy Noether’s Wonderful Theorem, revised and updated edition, Johns Hopkins University Press, Baltimore, 2017.

Gauge Invariance, p. 54: Add after the Jackson–Okun reference — Also see C. N. Yang, “The conceptual origins of Maxwell’s equations and gauge theory,” Physics Today 67 (11), 45–51 (November 2014).

Problem 5.7: R. P. Feynman, “The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity,” chapter 21 of The Feynman Lectures on Physics, vol III, Quantum Mechanics.

Spontaneous symmetry breaking in other physical contexts, p. 92: Add after the Tinkham reference — For an accessible discussion of the exclusion of magnetic flux in superconductors, see A. A. Abrikosov, “Type-II Superconductors and the Vortex Lattice,” 2003 Nobel Lecture. The development of the Ginzburg–Landau theory is presented in V. L. Ginzburg, “Superconductivity and superfluidity (what was done and what was not),” Usp. Fiz. Nauk 167, 429 (1997); [Physics — Uspekhi 40 (4), 407 – 432 (1997)].

Add after the Dixon reference on p. 93 — M. Endres et al. “The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition,” Nature 487, 454–458 (2012). R. Matsunaga et al., “Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor,” Science 345, 1145-1149 (2014) and A. Pashkin and A. Leitenstorfer, “Particle physics in a superconductor,” Science 345, 1121-1122 (2014); M. A. Méasson et al., “Amplitude Higgs mode in the 2H−NbSe2 superconductor,” Phys. Rev. B 89, 060503(R) (2014). Philip W. Anderson, “Superconductivity: Higgs, Anderson and all that,” Nature Physics (2015); D. Sherman et al., “The Higgs mode in disordered superconductors close to a quantum phase transition,” Nature Physics (2015). D. Pekker and C. M. Varma, “Amplitude / Higgs Modes in Condensed Matter Physics,” Ann. Rev. Cond. Matt. Phys. 6, 269-297 (2015) [arXiv:1406.2968];A. Jain et al., “Higgs mode and its decay in a two-dimensional antiferromagnet,” Nature Physics 13, 633–637 (2017); Tao Hong et al., “Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point,” Nature Physics 13, 638–642 (2017).

Spontaneously broken symmetries in particle physics, p. 94: Class for Physics of the Royal Swedish Academy of Sciences, “The BEH-Mechanism, Interactions with Short Range Forces and Scalar Particles,” Scientific Background on the Nobel Prize in Physics 2013; Popular Science Background; François Englert, “The BEH Mechanism and Its Scalar Boson,” Nobel Lecture, and Rev. Mod. Phys. 86, 843 (2014); Peter Higgs, “Evading the Goldstone Theorem,” Nobel Lecture, and Rev. Mod. Phys. 86, 851 (2014).

Also see G. S. Guralnik and C. R. Hagen, “Where Have All the Goldstone Bosons Gone?”

Several of the leading actors have described their personal involvement.

§ 6.7 Neutrino Mixing and Neutrino Mass: Updated global fits to neutrino mixing data. Class for Physics of the Royal Swedish Academy of Sciences, “Neutrino Oscillations,” Scientific Background on the Nobel Prize in Physics 2015; Popular Science Background, “The chameleons of space.” Takaaki Kajita, “Nobel Lecture: Discovery of atmospheric neutrino oscillations,” Rev. Mod. Phys. 88, 030501 (2016); Arthur B. McDonald, “Nobel Lecture: The Sudbury Neutrino Observatory: Observation of flavor change for solar neutrinos,” Rev. Mod. Phys. 88, 030502 (2016). For a review, see M. Wurm, “Solar Neutrino Spectroscopy,” arXiv:1704.06331.

Neutrino Oscillations, p. 181: Add after final entry — For a survey of long-baseline experiments based at accelerators, see T. Nakaya and R. K. Plunkett, “Neutrino Oscillations with the MINOS, MINOS+, T2K, and NOvA Experiments,” arXiv:1507.08134. Direct evidence for \nu_\mu \to \nu_\tau oscillations is reported in N. Agafonova et al. [OPERA Collaboration], “Discovery of \tau Neutrino Appearance in the CNGS Neutrino Beam with the OPERA Experiment,” Phys. Rev. Lett. 115, 121802 (2015) [arXiv:1507.01417].

Neutrinoless double-beta decay, p. 182: M. Agostini et al. [GERDA Collaboration], “Results on Neutrinoless Double-β Decay of 76Ge from Phase I of the GERDA Experiment,” Phys. Rev. Lett. 111, 122503 (2013); The EXO-200 Collaboration, “Search for Majorana neutrinos with the first two years of EXO-200 data,” Nature 510, 229 (2014); R. Arnold et al. [NEMO-3 Collaboration], “Search for neutrinoless double-beta decay of 100Mo with the NEMO-3 detector,” Phys. Rev. D 89, 111101R (2014); K. Alfonso et al. [CUORE Collaboration], “Search for Neutrinoless Double-Beta Decay of 130Te with CUORE-0,” arXiv:1504.02454; M. Agostini et al. [GERDA Collaboration], “Background free search for neutrinoless double beta decay with GERDA Phase II,” Nature 544, 47–52 (2017) [arXiv:1703.00570]; J. B. Albert et al. (EXO-200 Collaboration), “Searches for Double Beta Decay of 134Xe with EXO-200,” arXiv:1704.05042.

Majorana Fermions, p. 182: Add to first entry (Wilczek) “Majorana and Condensed Matter Physics.”
Add new entry: For a tour of Majorana fermions in diverse settings, see S. R. Elliott and M. Franz, “Colloquium: Majorana fermions in nuclear, particle, and solid-state physics,” Rev. Mod. Phys. 87, 137 (2015).

Charged-lepton flavor violation, p. 183: Add after final entry — R. H. Bernstein and P. S. Cooper, “Charged Lepton Flavor Violation: An Experimenter’s Guide,” Phys. Rept. 532, 27 (2013) [arXiv:1307.5787].

§ 6.References: Add at the end of Ref. 25 — Updated values are given in S. Heinemeyer et al. [LHC Higgs Cross Section Working Group Collaboration], “Handbook of LHC Higgs Cross Sections: 3. Higgs Properties,” CERN-2013-004 [arXiv:1307.1347]. Tables of Higgs-boson branching fractions are given at

§ 7.7 A Brief Look at Quantum Corrections: D. Androic et al. [Qweak Collaboration], “First Determination of the Weak Charge of the Proton,” Phys. Rev. Lett. 111, 141803 (2013). Cf. Problems 6.17, 6,18.

K. S. Kumar, S. Mantry, W. J. Marciano, and P. A. Souder, “Low-Energy Measurements of the Weak Mixing Angle,” Ann. Rev. Nucl. Part. Sci. 63, 237 (2013). Cf. Figure 7.23.

A. Sirlin and A. Ferroglia, “Radiative corrections in precision electroweak physics: A historical perspective,” Rev. Mod. Phys. 85, 263 (2013).

§ 7.9 Search for the Higgs Boson: M. Della Negra, P. Jenni, and T. S. Virdee, Science 338, 1560 (2102); The CMS Collaboration, Science 338, 1569 (2012); The ATLAS Collaboration, Science 338, 1576 (2012).

S. Chatrchyan et al. [CMS Collaboration], “Observation of a new boson with mass near 125 GeV in pp collisions at √s = 7 and 8 TeV,” JHEP 1306, 081 (2013).
V. Khachatryan et al. [CMS Collaboration], “Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV,” arXiv:1412.8662.
G. Aad et al. [ATLAS Collaboration], “Measurements of Higgs boson production and couplings in diboson final states with the ATLAS detector at the LHC,” Phys. Lett. B726, 88 (2013).

G. Aad et al. [ATLAS Collaboration], “Evidence for the spin-0 nature of the Higgs boson using ATLAS data,” Phys. Lett. B726, 120 (2013}.
S. Chatrchyan et al. [CMS Collaboration], “Study of the Mass and Spin-Parity of the Higgs Boson Candidate Via Its Decays to Z Boson Pairs,” Phys. Rev. Lett. 110, 081803 (2013).
V. Khachatryan et al. [CMS Collaboration], “Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV,” arXiv:1411.3441.
For comparison, see E. Abouzaid et al. [KTeV Collaboration], “Determination of the Parity of the Neutral Pion via the Four-Electron Decay,” Phys. Rev. Lett. 100, 182001 (2008).

The ATLAS and CMS Collaborations, “Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \sqrt{s} = 7 and 8 TeV,” ATLAS-CONF-2015-044 / CMS-PAS-HIG-15-002, September 15, 2015.

ATLAS Higgs-boson publications and other public results.
CMS Higgs-boson documents.

For an overview of the search and discovery, see A. Nisati and V. Sharma (editors), Discovery of the Higgs Boson (World Scientific, Singapore, 2016).

F. Wilczek, “Triumph, Window, Clue, and Inspiration: The Higgs Particle in Context,” MIT Physics Annual 2013, pp. 38-47.

M. Carena, C. Grojean, M. Kado, and V. Sharma, “Status of Higgs Boson Physics,” for the 2014 Review of Particle Physics, Chin. Phys. C38, 090001 (2014).

G. Bernardi and M. Herndon, “Standard model Higgs boson searches through the 125 GeV boson discovery,” Rev. Mod. Phys. 86, 479 (2014).

T. Aaltonen et al. [CDF and D0 Collaborations], “Higgs Boson Studies at the Tevatron,” Phys. Rev. D 88, 052014 (2013).

T. R. Junk and A. Juste, “Review of Physics Results from the Tevatron: Higgs Boson Physics,” Int. J. Mod. Phys. A 30, 1541006 (2015) [arXiv:1409.5043].

§ 7.11 The Hierarchy Problem: M. Dine, “Naturalness Under Stress,” Annual Review of Nuclear and Particle Science 65 (2015).

Problem 7.23: Add at end — For an update, see LHCb Collaboration, “Determination of the quark coupling strength |V_{ub}| using baryonic decays,” Nature Physics (2015).

CP Violation, p. 258: Add after last entry — A comprehensive account of the research carried out by the BaBar and BELLE Collaborations is given in A. J. Bevan et al., The Physics of the B Factories, arXiv:1406.6311.

Quark-mixing matrix elements, p. 259: Add at the end of the second entry—For updates, see F. C. Porter, “Experimental Status of the CKM Matrix,” arXiv:1604.04940, and P. Koppenburg & S. Descotes-Genon, “The CKM Parameters,” arXiv:1702.08834.

Misgivings about elementary scalars, p. 262: Add at end — For a revealing counterpoint, see §5 of K. G. Wilson, Nucl. Phys. Proc. Suppl. 140,3 (2005) [hep-lat/0412043], passage beginning with “The final blunder … .”

§ 7.References: Add at end of Ref. 29 — J. Erler, C. J. Horowitz, S. Mantry and P. A. Souder, “Weak Polarized Electron Scattering,” Ann. Rev. Nucl. Part. Sci.
64, 269-298 (2014)
[arXiv:1401.6199]. The Jefferson Lab PVDIS Collaboration, “Measurement of parity violation in electron–quark scattering,” Nature 506, 67 (2014), significantly improves the precision with which the parity-violating eq interaction is known.

Add at end of Ref. 102 — D. Buttazzo et al., “Investigating the near-criticality of the Higgs boson,” JHEP 1312, 089 (2013) [arXiv:1307.3536].

Add at end of Ref. 107 (Schellekens) Rev. Mod. Phys. 85, 1491 (2013). J. Polchinski, “String theory to the rescue,” arXiv:1512.02477.

§ 8.7 Two-Photon Processes and the Photon-Structure Function: Ch. Berger, “Photon Structure Function Revisited,” arXiv:1404.3551. See especially the discussion surrounding Figures 8 and 9.

§ 8.11 Strong-Interaction Symmetries: Page 353, add at end of first paragraph — The competition between electromagnetic and mass isospin breaking effects has been demonstrated in lattice QCD by Sz. Borsanyi et al., “Ab initio calculation of the neutron-proton mass difference,”  Science 347, 1452 (2015) [extended version at arXiv:1406.4088].

Add at end of section — J. Jaeckel and A. Ringwald, “The Low-Energy Frontier of Particle Physics,” Ann. Rev. Nucl. Part. Sci. 60, 405 (2000).

Problem 8.19: Replace \hat{\sigma} by d\hat{\sigma}/d\hat{t}.

Problem 8.22: The quantity tabulated here as \hat{\sigma}, following the notation of “Supercollider Physics” (EHLQ), is (\hat{s}/\pi)d\hat{\sigma}/d\hat{t}, in the (corrected) notation of Problem 8.19. Thanks to Alex Sherman for calling my attention to the confusion!

Renormalization group methods, p. 372: Add at end of first entry — The Stueckelberg–Petermann article (in French) is available at For a brief description in English, see “The Renormalization Group in Quantum Theory,”  Helvetica Physica Acta 24, 317–319 (1951).

Parton distribution functions, p. 373–4: Add after final entry (Martin et al.) — APFEL is a computer library specialized in the solution of evolution equations up to NNLO in QCD and to LO in QED. See V. Bertone, S. Carrazza and J. Rojo, “APFEL: A PDF Evolution Library with QED corrections,” Comput. Phys. Commun. 185, 1647 (2014), [arXiv:1310.1394]. APFEL WEB, a web-based application, is documented in S. Carrazza et al., “APFEL Web: a web-based application for the graphical visualization of parton distribution functions”, J. Phys. G: Nucl. Part. Phys. 42, 057001 (2014) and [arXiv:1410.5456]. The HERAFitter project, an open source QCD fit framework to extract PDFs and assess the impact of new data, is documented in S. Alekhin et al., “HERAFitter, Open Source QCD Fit Project,” Eur. Phys. J. C75, 304 (2015) [arXiv:1410.4412]. For definitive results from HERA, see H. Abramowicz et al. [H1 and ZEUS Collaborations], “Combination of Measurements of Inclusive Deep Inelastic e^{\pm}p Scattering Cross Sections and QCD Analysis of HERA Data,” arXiv:1506.06042. For a new treatment of the photon parton distribution within the proton, see A. Manohar et al., “How bright is the proton? A precise determination of the photon PDF,” arXiv:1607.04266.

Jet physics at hadron colliders, p. 374: Add after final entry — For a thorough historical account, with extensive experimental detail, see J. Rak and M. Tannenbaum, High-pT Physics in the Heavy Ion Era (Cambridge University Press, 2013).

Modern Computational Methods, p. 374: Add to final entry — L. Dixon, “Amplitudes: the Untold Story of Loops and Legs.”

§ 8.References: Add to Ref. 124 — For an accessible modern treatment, see T. Becher, A. Broggio, and A. Ferroglia, “Introduction to Soft-Collinear Effective Theory,” arXiv:1410.1892, Springer Lecture Notes in Physics 896 (2015).

Figure 9.5: For an improved bound (\tau_p >5.9\times10^{33} years at 90% CL), see K. Abe et al. [Super-Kamiodande Collaboration], “Search for Proton Decay via p\to \nu K^+ using 260 kiloton⋅year data of Super-Kamiokande,” Phys. Rev. D 90, 072005 (2014).

Problem 9.11: How the evolution of the SU(3)c, SU(2)L, and (properly normalized) U(1)Y couplings depends on the scale at which a full spectrum of superpartners becomes active is illustrated in this animation.

§ 9.References: Add to Ref. 9: Tantalizing hints of deviations from lepton universality are reviewed by G. Ciezarek et al., “A challenge to lepton universality in B-meson decays,”  Nature 546, 227–233 (2017).

B.1 Phase-Space Formulas: Decay Rates and Cross Sections: Add at the end of the section — In a standard notation, \mathcal{S}_{ij} = \left[s - (m_i + m_j)^2\right]^{1/2}\left[s - (m_i - m_j)^2\right]^{1/2}.

B. Regularization and renormalization, p. 454: Add after final entry — For an interesting perspective on renormalization and renormalizable (in contrast to cutoff) theories, see G. P. Lepage, “What is renormalization?,” arXiv:hep-ph/0506330.

B. Computer-enabled techniques, p. 454-455: Add at end of MadGraph entry — J. Alwall et al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,” JHEP 1407, 079 (2014).

C. Système International d’Unités, p. 458: Add at end of entry — How the SI will evolve is described in D. B. Newell, “A more fundamental International System of Units,” Physics Today 67 (7), 35 (2014).

New editions:

A second edition (2014) of Dynamics of the Standard Model, by Donoghue, Golowich, and Holstein, cited on pages 24, 89, 94, and 183, has been published by Cambridge University Press.


Equation (2.3.4): On the far right-hand side, \delta_\mu should read \partial_\mu.

Equation (6.1.71): The first equation should read q_1 \cdot p_1 = mE, not me. Noted by Kaushik Roy.

Equations (6.5.8) and (6.5.9): The factors of x resp. x^\prime in the denominators are spurious. The rates for a heavy Higgs boson into a pair of intermediate vector bosons should read
\begin{array}{rclcr} {{\Gamma(H \rightarrow W^+ W^-)}} & = & \displaystyle{\frac{G_{\mathrm{F}} M_H^3} {32\pi\sqrt{2}}} {(1-x)^{1/2}} (3x^2 - 4x+4) , & \qquad & (6.5.8) \\[18pt] {\Gamma(H \rightarrow Z^0 Z^0)} & = & \displaystyle{\frac{G_{\mathrm{F}} M_H^3} {64\pi\sqrt{2}}} {(1-x^\prime)^{1/2}} (3x^{\prime 2} - 4x^\prime +4) ,& \qquad & (6.5.9) \end{array}
where x = 4M_W^2/M_H^2 and x^\prime = 4M_Z^2/M_H^2 = x/\cos^2 \theta_{\mathrm{w}}. Thanks to Matthew Low for noticing!

Equation (7.4.70): The factor E^\prime E on the right-hand side should read {\displaystyle\frac{E^\prime}{E}}\,. Thanks to Ken Lane for noticing!

Equation (B.1.4): The denominator should contain m_\alpha^3, not m_\alpha^2, so that
\displaystyle{\frac{d\Gamma_{\beta\alpha}}{d\Omega_{\rm{cm}}}} = \displaystyle{\frac{|{\cal{M}}_{\beta\alpha}|^2}{64\pi^2}}\displaystyle{\frac{{\cal{S}}_{12}}{m_\alpha^3}} \cdot S. \qquad\mathrm{(B.1.4)}
Thanks to Lukas Pritchett for noticing!

Subject Index: Einstein, E. should read Einstein, A.
Add in first column of page 479: Meissner effect, 90, 92, 93, 341.