The Higgs Boson: Window to the Unknown? Barbara Jäger, University of Tübingen

Transcription

1 The Higgs Boson: Window to the Unknown? Barbara Jäger, University of Tübingen

2 the plan for today our current picture: the Standard Model of Elementary Particles the Higgs mechanism the search for the Higgs boson ongoing efforts: Higgs production at colliders from discovery to precision physics theory talks to experiment epilogue: the quest for deeper insight

3 what we (think) we know...

4 what we (think) we know... electromagnetism U(1) EM interactions described by local gauge theories quantum chromodynamics SU(3) color

5 ... but: experimental fact: mediators of the weak force (W ± and Z bosons) are massive! theoretical problem: explicit mass terms in Lagrangian violate local gauge invariance

6 ... but: experimental fact: mediators of the weak force (W ± and Z bosons) are massive! theoretical problem: explicit mass terms in Lagrangian violate local gauge invariance the solution: spontaneous symmetry breaking

7 digression: spontaneous symmetry breaking Goldstone s theorem: Each spontaneously broken continuous symmetry gives rise to a massless scalar particle. Nambu-Goldstone boson Jeffrey Goldstone ( 1933) (first discussed by Yoichiro Nambu in the context of BCS superconductivity)

8 The Nobel Prize in Physics 2008 Yoichiro Nambu: for the discovery of the mechanism of spontaneously broken symmetry in subatomic physics

9 spontaneous breaking of local gauge symmetry Physical Review Letters (1964)

10 spontaneous breaking of local gauge symmetry basic concept: gauge boson sector of the SM: L = L gauge + L Higgs gauge fields (W ±, Z, γ) extra massive, neutral, scalar field full Lagrangian invariant vacuum state not invariant under electroweak symmetry symmetry is spontaneously broken!

11 spontaneous symmetry breaking within the SM complex scalar field φ = ( φ + φ 0 with self interaction potential ) V (φ) = µ 2 φ φ + λ 4 (φ φ) 2, λ > 0 crucial point: µ 2 > 0 specific choice φ 0 = ( 0 v 2 V (φ) minimal for φ = ) 2µ 2 λ v 2 > 0 breaks gauge invariance spontaneously

12 the Englert-Brout-Higgs-Hagen-Guralnik-Kibble mechanism recall Goldstone s theorem: each spontaneously broken symmetry gives rise to one massless Goldstone boson Standard Model: complex scalar doublet with four degrees of freedom photon remains massless three (real) longitudinal polarization states of massive W ± and Z bosons one component real scalar particle: Higgs boson

13 the Englert-Brout-Higgs-Hagen-Guralnik-Kibble mechanism recall Goldstone s theorem: each spontaneously broken symmetry gives rise to one massless Goldstone boson Standard Model: complex scalar doublet with four degrees of freedom photon remains massless three (real) longitudinal polarization states of massive W ± and Z bosons one component real scalar particle: Higgs boson???

14 the full picture (?)

15

16 experimental bounds on the Higgs mass information on the Higgs boson is obtained via indirect searches: Higgs boson affects various observables indirectly via quantum corrections direct searches for explicit Higgs production in e + e collisions hadronic collisions

17 Higgs couplings gauge boson V fermion f self interaction M 2 V m f M 2 H coupling of the Higgs boson to any particle proportional to its mass only free parameter of the Standard Model: M H

18 indirect searches Higgs boson affects electroweak precision data (e.g. gauge boson mass determination) via quantum corrections + corrections proportional to ln M2 H M 2 Z constrain M H by precision data from various experiments (LEP, SLC, CDF, D0): M H % CL [LEP EWWG, July 2010]

19 direct search in electron-positron collisions M 2 V m f reminder: Higgs coupling particle mass! direct Higgs production at e + e colliders e Z Z mainly via Higgs-strahlung e + H

20 LEP? the Large Electron-Positron Collider (LEP) at CERN: operated until 2000 at c.m.s. energy of S 209 GeV Higgs search mainly via e + e ZH 4jets M H GeV excluded at 95% confidence level, slight preference for M H 116 GeV but: combined statistics too low for conclusive interpretation

21 e + e vs. hadron collider ALEPH event well-defined, but moderate c.m.s. energy (LEP: 200 GeV) clean environment clean signature LHC simulation H µ + µ µ + µ broad energy reach [only fraction of hadronic collision energy available for hard scattering event] complex environment large event rate

22 needed: high-energy hadron colliders Superconducting Super Collider (SSC) location: Texas, USA design energy: 40 TeV Tevatron Large Hadron Collider (LHC) location: Fermilab, USA energy: 2 TeV location: CERN, design energy: 14 TeV Switzerland

23 needed: high-energy hadron colliders Superconducting Super Collider (SSC) location: Texas, USA design energy: 40 TeV cancelled: 1993 Tevatron Large Hadron Collider (LHC) location: Fermilab, USA energy: 2 TeV location: CERN, design energy: 14 TeV Switzerland

24 the first hadron collider at the Terascale the Tevatron at Fermilab: high energy synchrotron with proton anti-proton collisions at c.m.s. energy S 2 TeV

25 combined experimental bounds on the Higgs mass

26 the world s largest hadron collider the Large Hadron Collider (LHC) at CERN

27 the world s largest hadron collider smashes proton or heavy-ion beams tunnel crosses border between France and Switzerland circumference: 27 km more than 1600 superconducting magnets 96 tons of liquid helium to keep operating temperature of C design energy S = 14 TeV (3 m/s slower than the speed of light) interactions between colliding beams: every 25 ns

28 the world s largest hadron collider and its four major experiments... Compact Muon Solenoid CMS A Large Ion Collider Experiment ALICE ATLAS LHCb LHC-beauty A Toroidal LHC Apparatus

29 CERN: July 4, 2012

30 Higgs and Englert before the seminar

31 Higgs event in CMS

32 Higgs signal

33 Higgs signal

34 CERN: Higgs seminar on July 4, 2012

35 reactions to the announcement

36 Higgs and Englert after the seminar

37 Spiegel Online, 4. Juli 2012

38 the CMS experiment reports the observation of a new boson with a mass of ± 0.6 GeV the ATLAS experiment reports the observation of an excess of events at a mass of GeV latest combination: ± 0.24 GeV

39 The Nobel Prize in Physics for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN s Large Hadron Collider.

40 hadron-hadron collision

41 hadron-hadron collision foundation for predictive power of perturbative QCD: long-distance structure of hadrons can be separated from hard partonic scattering factorization

42 parton-parton collision

43 Higgs LHC 10 σ(pp H+X) [pb] Higgs cross section WG s= 8 TeV gluon fusion (GF) LHC HIGGS XS WG 2012 pp H (NNLO+NNLL QCD + NLO EW) pp qqh (NNLO QCD + NLO EW) pp WH (NNLO QCD + NLO EW) pp tth (NLO QCD) pp ZH (NNLO QCD +NLO EW) M H [GeV]

44 Higgs LHC 10 σ(pp H+X) [pb] Higgs cross section WG LHC HIGGS XS WG 2012 s= 8 TeV gluon fusion (GF) t th production pp H (NNLO+NNLL QCD + NLO EW) pp qqh (NNLO QCD + NLO EW) pp WH (NNLO QCD + NLO EW) pp tth (NLO QCD) pp ZH (NNLO QCD +NLO EW) M H [GeV]

45 Higgs LHC 10 σ(pp H+X) [pb] Higgs cross section WG LHC HIGGS XS WG 2012 s= 8 TeV gluon fusion (GF) t th production pp H (NNLO+NNLL QCD + NLO EW) pp qqh (NNLO QCD + NLO EW) pp WH (NNLO QCD + NLO EW) pp tth (NLO QCD) pp ZH (NNLO QCD +NLO EW) M H [GeV] vector boson fusion (VBF)

46 Higgs LHC 10 σ(pp H+X) [pb] Higgs cross section WG LHC HIGGS XS WG 2012 s= 8 TeV gluon fusion (GF) t th production pp H (NNLO+NNLL QCD + NLO EW) pp qqh (NNLO QCD + NLO EW) pp WH (NNLO QCD + NLO EW) pp tth (NLO QCD) pp ZH (NNLO QCD +NLO EW) M H [GeV] vector boson fusion (VBF) W, Z bremsstrahlung

47 Higgs decay some prominent decay modes: Higgs cross section WG Higgs BR + Total Uncert ττ cc bb gg WW ZZ LHC HIGGS XS WG 2011 branching fractions γγ Zγ [GeV] M H

48 Higgs production & decay

49 Higgs production & decay Higgs cross section WG the full picture: combine with cross section for production branching ratio of decay mode BR [pb] σ τ + τ VBF H τ + τ ± WH l νbb ZH l l bb l = e, µ ν = ν e,ν µ,ν τ q = udscb tth ttbb = 8TeV γγ s ± WW l νqq + - WW l νl ν + - ZZ l l qq + - ZZ l l νν + - ZZ l l + - l l M H [GeV] LHC HIGGS XS WG 2012

50 the perturbationist s task provide precise predictions for experimentally accessible observables as pre-requisites for accurate determination of physics parameters (couplings, masses, PDFs,... ) discovery of new particles and physics scenarios

51 hard scattering: the perturbative approach high energies: (ideally) series expansion in α s (or α) σ = N n=n 0 α n s σ(n) + O(α N+1 s ) truncation at fixed order α N s ( LO, NLO,... ) order N provided by theoretician ( # of loops ) depends on: complexity of the problem kinematic properties of the reaction multiplicity of the final state ( # of legs ) mass scales of involved particles... accuracy which can be achieved in experiment computational skills of the perturbationist

52 loops and legs at the LHC # legs realistic description of complex final state # loops accurate description of elementary interaction, small scale uncertainty Higgs event recorded by CMS

53 loops and legs at the LHC: examples loops legs gluon fusion loop diagrams already at lowest perturbative order technically challenging top-associated production including decay chains advanced theoretical developments needed to match precision of experimental measurements

54 multi leg processes at the LHC: pp t th experimental signature of pp t th: not tops, but their decay products (e.g. from t Wb lνb decay chains) but: full NLO-QCD calculation of pp l + νbl ν bh very demanding

55 multi leg processes at the LHC: pp t th simplified prescription [Frixione et al. (2007)]: 1) perform NLO-QCD calculation for on-shell t th production, 2) add decays of tops at LO in narrow-width approximation, 3) re-instate off-shell effects of the tops can be incorporated in POWHEG-BOX tool that provides interface to parton-shower generators like PYTHIA

56 multi leg processes at the LHC: pp t th Hartanto, Reina, B.J., Wackeroth (2015) modern Monte Carlo tools provide fully differential predictions top-associated production including decay chains

57 frontiers of NLO QCD exact NLO calculation of multi-leg processes possible accurate treatment of off-shell configurations (narrow-width approximation no longer necessary) example: t th (with t Wb lνb) [Beenakker et al.; Dawson et al. ( )] pp e + ν e µ ν µ b bh [Denner, Feger (2015)] ν e g t t t H W + e + b g b ū u g t t t ν e W + e + b H µ W ν µ b g g t t t ν e W + e + b H g b g t W µ ν µ u g b g W µ ν µ

58 pp e + ν e µ ν µ b bh at NLO QCD ] [ dσ fb dmb 1 b 2 GeV K factor Denner, Feger (2015) M b1 b 2 [GeV] LO NLO tremendous complexity: amplitudes generated with the help of automated tool RECOLA loop integrals are evaluated with the COLLIER library bottle neck: efficient phase-space integration gain: full control on final-state particles (realistic cuts on leptons and b-jets, access to decay correlations,... )

59 t th,h b b at the LHC ATLAS TDR (1999): In conclusion, the extraction of a Higgs-boson signal in the t th, H b b channel appears to be feasible over a wide range in the low Higgs-boson mass region [... ].

60 realistic search: signal and background the t th,h b b signal: need to search for t tb b final states, but same final state can arise from different processes Higgs signal QCD background

61 the bad news: backgrounds Events / 10 GeV Cammin et al. (2003) tth(120) ttjj ttbb (QCD) ttbb (EW) m bb (GeV) overwhelming backgrounds: S/B 1/6, differences in shape only marginal

62 improved backgrounds CMS NOTE 2006/119: In contrast to earlier studies, the global picture for this analysis is substantially more pessimistic. This change is due mainly to the greater degree of realism that was made possible for this study by use of more advanced tools for event generation, detector simulation and physics reconstruction, which were not available to previous (fast-)simulation studies.

63 CMS NOTE 2006/119: improved backgrounds In contrast to earlier studies, the global picture for this analysis is substantially more pessimistic. This change is due mainly to the greater degree of realism that was made possible for this study by use of more advanced tools for event generation, detector simulation and physics reconstruction, which were not available to previous (fast-)simulation studies. note added: significant improvements attainable via new jet-substructure techniques Plehn, Salam, Spannowsky (2009)

64 combination: ATLAS and CMS tth ZH WH VBF ggf γγ ZZ WW ττ γγ ZZ WW ττ γγ WW ττ bb γγ WW ττ bb γγ WW ττ ATLAS and CMS LHC Run 1 Observed ±1σ Th. uncert. bb σ B norm. to SM prediction combination of results at 7 and 8 TeV for various production and decay modes within statistical uncertainties all results compatible with SM

65 multi-loop calculations for the LHC: gg H loop diagrams already at lowest perturbative order gluon fusion via heavy quark loop higher order corrections require computation of multi-loop integrals (and multi-parton-emission at same perturbative order) technically challenging resort to approximations such as expansion in heavy quark mass

66 gluon fusion at higher orders in QCD does the perturbative expansion converge?

67 gluon fusion at higher orders in QCD convergence properties and uncertainties much improved at NNLO QCD

68 very new: gg H at N 3 LO QCD only collider process known to such high orders in QCD outstanding complexity: O(10 3 ) three-loop master integrals, O(10 5 ) interference diagrams, O(10 7 ) phase-space integrals immediate implications on physics at the LHC

69 gg H at N 3 LO QCD Anastasiou et al. (2016) perturbative result stabilized scale dependence reduced

70 backgrounds again: pp W + W 4f pp W + W 4f constitutes important class of background processes to the Higgs search in the mode pp H W + W 4f precision achieved in experiment requires NNLO QCD and NLO electroweak corrections (incuding full access to kinematics of final-state leptons)

71 pp NNLO QCD! Gehrmann et al. (08/2014) σ[pb] pp W + W +X ATLAS CMS 80 note: improved agreement with LHC data gg H WW added to all predictions σ/σ NLO 7 8 s[tev] NNLO+gg NLO+ggN NLON+gg LONN+gg 13 14

72 pp WW 4f: full NLO EW calculation δ[%] Biedermann et al. (05/2016) LO EW qγ qq γγ p T,e [GeV] dσ dp T,e pp ν µ µ + e ν e +X spp = 13TeV ATLAS WW setup µ treated coll. unsafe 700 [ ] fb GeV flexible Monte-Carlo approach gives full control on lepton distributions and correlations with realistic selection cuts: EW corrections small for total XS, but large and negative at high scales systematic enhancement due to EW Sudakov logarithms ln(m W /Q)

73 EW corrections: generic features naive expectation: α α 2 s NLO EW NNLO QCD? but: systematic enhancements possible, e.g.: kinematic effects photon emission mass-singular logs, e.g. α π ln ( Q m µ ) high energies EW Sudakov logs, e.g. α π ln2( Q M W )

74 EW corrections: Sudakov logarithms typical 2 2 process: at high energy EW corrections enhanced by large logs ln 2( ) Q 2 energy scale of 1 TeV MW 2 universal origin of leading EW logs: mass singularities in virtual corrections related to external lines soft and collinear virtual gauge bosons: double logs soft or collinear virtual gauge bosons: single logs

75 EW corrections: Sudakov logarithms compare to QED / QCD: IR singularities of virtuals canceled by real-emission contributions electroweak bosons massive real radiation experimentally distinguishable non-abelian charges of W,Z are open Bloch-Nordsieck theorem not applicable M. Ciafaloni, P. Ciafaloni, Comelli; Beenakker, Werthenbach; Denner, Pozzorini; Kühn et al., Baur;...

76 VBF event topology p jet Z,W H Z,W p jet suppressed color exchange between quark lines gives rise to little jet activity in central rapidity region scattered quarks two forward tagging jets (energetic; large rapidity) Higgs decay products typically between tagging jets

77 tagging jets: properties rapidity separation of the tagging jets jj 1/σ dσ/d η Klämke, Zeppenfeld (2007) gluon fusion VBF tt+jets QCD-WW η jj jets more central in QCD- than in EW-induced production processes

78 why VBF Higgs production? distinctive signature very useful for signal extraction and background suppression suppressed color exchange between quark lines gives rise to little jet activity in central rapidity region scattered quarks two forward tagging jets Higgs decay products typically between tagging jets allows a determination of couplings and CP-properties of the Higgs boson

79 tensor structure of the HV V coupling µ most general HV V vertex: V V q 1 q 2 H T µν = a 1 g µν + ( a 2 q1 q 2 g µν q ν 1 2) qµ + ν a 3 ǫ µνρσ q 1ρ q 2σ physical interpretation: SM Higgs scenario: L HV µ V µ a 1 CP even scenario: L eff HV µν V µν a 2 CP odd scenario: L eff HV µν Ṽ µν a 3

80 CP properties of the Higgs boson azimuthal angle between tagging jets dip structure at 90 (CP even) or 0/180 (CP odd) only depends on tensor structure of HV V vertex (little dependence on actual size of form factor, QCD corrections, Higgs mass etc.) 1/ σ dσ / d φ jj Figy et al. (2006) CP-even CP-odd SM φ jj

81 Higgs production in NLO QCD NLO QCD: inclusive cross section: Han, Valencia, Willenbrock (1992) distributions: Figy, Oleari, Zeppenfeld (2003) Berger, Campbell (2004) NLO QCD corrections moderate and well under control (order 10% or less) publicly available parton-level Monte Carlos: VBFNLO MCFM

82 Higgs production in NLO EW Ciccolini, Denner, Dittmaier (2007): NLO EW corrections to inclusive cross sections and distributions NLO EW corrections non-negligible, modify K factors and distort distributions by up to 10% dσ dσ LO 1[%] pp Hjj + X EW+QCD EW QCD publicly available parton-level Monte Carlo: HAWK [Denner, Dittmaier, Kallweit, Mück] M H = 200GeV p j1,t [GeV]

83 higher orders of QCD in VBF Harlander, Vollinga, Weber (2007): gauge invariant, finite sub-class of virtual two-loop QCD corrections to pp Hjj via VBF important due to large gluon luminosity at LHC? gg q qh, q q ggh, qg qgh, qg qgh minimal set of cuts: σ 2 loop gluon 2 % of σ LO VBF VBF cuts: relative suppression by additional order of magnitude

84 higher orders of QCD in VBF Bolzoni, Maltoni, Moch, Zaro (2010): subset of the NNLO QCD contributions to the total cross section for pp Hjj via VBF in the structure function approach 1 µ P 1 X 1 q 1 V 1 q 2 V 2 P 2 X 2 ρ

85 higher orders of QCD in VBF Bolzoni et al. (2011) 1 σ (pb) at LHC s = 7 TeV LO NLO NNLO NNLO predictions are in full agreement with NLO results 10-1 scale choice: Q/4 µ R,µ F 4Q residual scale uncertainties are reduced from 4% to 2% σ(µ R,µ F )/σ NNLO (Q) m H (GeV) NNLO PDF uncertainties are at the 2% level

86 NNLO: exclusive results Cacciari, Dreyer, Karlberg, Salam, Zanderighi (2015) σ (no cuts) [pb] σ (VBF cuts) [pb] LO NLO NNLO relative NNLO corrections 1% relative NNLO corrections 6% NNLO QCD corrections are much larger in VBF setup than for inclusive cuts

87 NNLO: exclusive results Cacciari et al. (2015)

88 NNLO: exclusive results NNLO corrections make jets softer fewer events pass VBF cuts Cacciari et al. (2015)

89 Steckbrief Vorname: Higgs Nachname: Boson Geburtsdatum: 4. Juli 2012 Geburtsort: CERN Geschwister: noch keine meine besten Freunde: Top-Quarks Lieblingsfarbe: leider bin ich farbenblind Gewicht: ca. 125,1 GeV Lebensdauer: ca sec.

90 Steckbrief Vorname: Higgs Nachname: Boson Geburtsdatum: 4. Juli 2012 Geburtsort: Geschwister: meine besten Freunde: Lieblingsfarbe: Gewicht: Lebensdauer: CERN noch keine Top-Quarks leider bin ich farbenblind ca. 125,1 GeV ca sec. IS IT THE STANDARD-MODEL HIGGS??

91 alternatives

92 Higgs properties need precise information on properties of Higgs boson to determine its nature: mass charge spin CP properties couplings to other particles

93 Higgs properties: angular correlations Djouadi (2005) angular correlations of decay particles (e.g. leptons in H ZZ 4l) info on spin and CP properties of mother particle

94 Å À Ö µ» ½ À Å ¼¼ Î Å Ö Higgs properties: angular correlations Djouadi (2005) ½º ½ µ» ½º Å ¼¼ Î ½º ½º¾ ½º¾ ½ ½ ¼º ¼º À Ï Ï À Ï Ï ¼º ¼º ½ ¼ ¾ ¼ ¾ ½ CP-even (H) versus CP-odd (A) Higgs boson

95 Higgs couplings g SM V = 2M2 V v λ SM f = m f v Standard Model: Higgs couplings determined by particle mass

96 determination of Higgs couplings V V Z Z observables: combination of production and decay channel product of Higgs couplings in production and decay in practice: measure all combinations of production and decay modes that are experimentally accessible

97 Higgs couplings g SM V = 2M2 V v λ SM f = m f v Standard Model: Higgs couplings determined by particle mass test of Standard Model hypothesis: scale factors parameterize deviation from Standard Model value g V = κ V g SM V λ f = κ f λ SM f

98 Higgs couplings κ Z ATLAS and CMS LHC Run 1 ATLAS+CMS ATLAS CMS 1σ interval 2σ interval κ W κ t κ τ κ b κ µ scale factors κ i : deviation of various Higgs couplings from Standard Model value (1) Parameter value

99 Higgs couplings v V m κ V 1 ATLAS and CMS LHC Run 1 W Z t or v F m 1 10 κ F µ τ b ATLAS+CMS SM Higgs boson [M, ε] fit 68% CL 95% CL Standard Model: linear relation between particle masses and Higgs couplings Particle mass [GeV] 2

100 the future: more powerful colliders? International Linear Collider (ILC), Japan Future Circular Collider (FCC), CERN

101 future colliders HL-LHC: ILC: 14 TeV, 1000 GeV, 3000 fb fb 1 HE-LHC: CLIC: 33 TeV, 3000 GeV, 3000 fb fb 1 VLHC: 100 TeV, 3000 fb 1 TLEP: 350 GeV, fb 1

102 Higgs couplings future prospects Snowmass Study (2013)

103 Higgs precision physics why is precision in determination of Higgs couplings so important? experimental fact: M H = 125 GeV new physics effects (if any) small in accessible region; could result in tiny deviations from SM values specific models with one or more Higgs boson(s) model-independent effective analysis: L eff = L SM + c (6) i Λ 2 O(6) i +...

104 new interactions in the electroweak sector [fb/gev] d σ/d p T,l hardest Karlberg, Zanderighi, B.J. (2013) ratio to SM s = 14 TeV c WWW =0 NLO c WWW =-5 NLO p T,l hardest [GeV] allow for non-zero dimension-six operator coefficients (compatible with exp. limits) tails of transverse momentum distributions enhanced but: very demanding at LHC14 because of small signal rates (much better limits possible with 33 or 100 TeV) hardest lepton stemming from decay

105 supersymmetric partner with different spin for each SM particle 5 Higgs bosons that differ in mass and CP properties (lightest one could be the observed Higgs boson)

106 supersymmetry? lightest SUSY-Higgs boson could be the observed Higgs boson how can we distinguish SUSY Higgs from SM Higgs? observation of additional Higgs bosons observation of other SUSY particles deviations in couplings from SM expectation...

107 news from the experiments? Events / 40 GeV Data - fitted background ATLAS Preliminary Data Background-only fit -1 s = 13 TeV, 3.2 fb [GeV] m γγ December 2015: indications (from ATLAS and CMS) for a new heavy particle with a mass of 750 GeV? open issues: sufficient number of events? statistical fluctuations? what s the physics behind?

108 are data significant? Events / 40 GeV ATLAS Preliminary Data Background-only fit -1 s = 13 TeV, 3.2 fb 10 1 Data - fitted background [GeV] m γγ new particle at 750 GeV? Higgs signal (125 GeV)

109 open questions Is there a grand unified theory? How does gravity fit in? What is dark matter and dark energy? Why is there an asymmetry of matter and anti-matter? What is the origin of mass?

110

111 backup slides for details and supplementary material

112 digression: spontaneous symmetry breaking ground state of a system doesn t share the full symmetry of the underlying theory e.g.: isotropic ferromagnet: H 1 2 i,j S i S j lowest energy state: all spins aligned, but: direction of alignment is arbitrary degenerate ground state

113 digression: spontaneous symmetry breaking ground state of a system doesn t share the full symmetry of the underlying theory e.g.: isotropic ferromagnet: H 1 2 i,j S i S j lowest energy state: all spins aligned, but: direction of alignment is arbitrary degenerate ground state consequence: Nambu-Goldstone bosons (here: spin waves)