The Physics Of Yang-Mills-Higgs Systems

Transcription

1 The Physics Of Yang-Mills-Higgs Systems Beyond Perturbation Theory Axel Maas 9 th of January 2014 University of Heidelberg Germany

2 Overview Yang-Mills-Higgs theory

3 Overview Yang-Mills-Higgs theory Physical states from the lattice

4 Overview Yang-Mills-Higgs theory Physical states from the lattice Quantum phase diagram

5 Overview Yang-Mills-Higgs theory Physical states from the lattice Quantum phase diagram Excited states from the lattice

6 Overview Yang-Mills-Higgs theory Physical states from the lattice Quantum phase diagram Excited states from the lattice Experimental signatures Summary

7 Yang-Mills-Higgs Theory

8 The Higgs sector as a gauge theory The Higgs sector is a gauge theory

9 The Higgs sector as a gauge theory The Higgs sector is a gauge theory L= 1 4 W a μ ν W a μ ν W a μ ν = μ W a a ν ν W μ W Ws W μ a

10 The Higgs sector as a gauge theory The Higgs sector is a gauge theory L= 1 4 W a μ ν W a μ ν W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν W W W Ws W μ a abc Coupling g and some numbers f

11 The Higgs sector as a gauge theory The Higgs sector is a gauge theory L= 1 4 W a μ ν W a μ ν W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν W W W Ws W μ a No QED: Ws and Zs are degenerate h h abc Coupling g and some numbers f

12 The Higgs sector as a gauge theory The Higgs sector is a gauge theory L= 1 4 W a μ ν μ W ν a +(D ij μ h j ) + D μ ik h k W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν W W W Ws W μ a D μ ij =δ ij μ h Higgs h i No QED: Ws and Zs are degenerate abc Coupling g and some numbers f

13 The Higgs sector as a gauge theory The Higgs sector is a gauge theory L= 1 4 W a μ ν μ W ν a +(D ij μ h j ) + D μ ik h k Ws W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν D ij μ =δ ij μ igw a ij μ t a a W μ h i Higgs h W W W h W No QED: Ws and Zs are degenerate Coupling g and some numbers f abc and t a ij

14 The Higgs sector as a gauge theory The Higgs sector is a gauge theory L= 1 4 W a W a D ij h j D ik h k h a h a v 2 2 Ws Higgs W a = W a W a gf a bc W b c W D ij = ij igw a ij t a a W μ h i No QED: Ws and Zs are degenerate h W W W h W h h Couplings g, v, λ and some numbers f abc and t a ij

15 Symmetries L= 1 4 W a μ μ νw ν a +(D ij μ h j ) + D μ ik h k +λ(h a h + a v 2 ) 2 W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν D ij μ =δ ij μ igw a ij μ t a

16 Symmetries L= 1 4 W a μ ν μ W ν a +(D ij μ h j ) + D μ ik h k +λ(h a h + a v 2 ) 2 W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν D ij μ =δ ij μ igw a ij μ t a Local SU(2) gauge symmetry Invariant under arbitrary gauge transformations a x W a W a a b g f a bc W c b h i h i g t a ij a h j

17 Symmetries L= 1 4 W a μ ν μ W ν a +(D ij μ h j ) + D μ ik h k +λ(h a h + a v 2 ) 2 W a μ ν = μ W a ν ν W a μ +gf a bc W b c μ W ν D ij μ =δ ij μ igw a ij μ t a Local SU(2) gauge symmetry Invariant under arbitrary gauge transformations W a W a a b g f a bc W c b Global SU(2) Higgs flavor symmetry h i h i g t a ij a h j Acts as right-transformation on the Higgs field only W μ a W μ a a x h i h i +a ij h j +b ij h j

18 Classical analysis [Bohm et al. 2001] L= 1 4 W a μ ν μ W ν a +(D ij μ h j ) + D μ ik h k +λ(h a h + a v 2 ) 2

19 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Classical analysis of the Higgs sector

20 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Shape depends on parameters Classical analysis of the Higgs sector

21 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Shape depends on parameters Experiments decides - Higgs mass is tachyonic Classical analysis of the Higgs sector

22 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Shape depends on parameters Experiments decides - Higgs mass is tachyonic Classical minima h h h h h Classical analysis of the Higgs sector

23 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Shape depends on parameters Experiments decides - Higgs mass is tachyonic Classical minimum h h h Global gauge choice h h Classical analysis of the Higgs sector

24 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Shape depends on parameters Experiments decides - Higgs mass is tachyonic Classical minimum h h h Global gauge choice h h Classical analysis of the Higgs sector Non-zero condensate shifts Higgs mass to an ordinary mass

25 Classical analysis [Bohm et al. 2001] L=λ(h a h a + v 2 ) 2 Shape depends on parameters Experiments decides - Higgs mass is tachyonic Classical minimum h h h Global gauge choice h h Classical analysis of the Higgs sector Non-zero condensate shifts Higgs mass to an ordinary mass Perform perturbative expansion around the classical vacuum

26 Standard approach [Bohm et al. 2001] Minimize action classically Yields hh =v 2 - Higgs vev

27 Standard approach [Bohm et al. 2001] Minimize action classically Yields - Higgs vev hh =v 2 Assume quantum corrections to this are small

28 Standard approach [Bohm et al. 2001] Minimize action classically Yields - Higgs vev Assume quantum corrections to this are small Perform global gauge transformation such that h x = hh =v 2 1 x i 2 x v x i 3 x h = 0 v

29 Standard approach [Bohm et al. 2001] Minimize action classically Yields - Higgs vev Assume quantum corrections to this are small Perform global gauge transformation such that h x = hh =v 2 1 x i 2 x v x i 3 x h = 0 v mass depends at tree-level on v

30 Standard approach [Bohm et al. 2001] Minimize action classically Yields - Higgs vev Assume quantum corrections to this are small Perform global gauge transformation such that h x = hh =v 2 1 x i 2 x v x i 3 x h = 0 v mass depends at tree-level on Perform perturbation theory v

31 Implications of global transformation Not all charge directions equal

32 Implications of global transformation Not all charge directions equal This is not physical, but merely a choice of gauge

33 Implications of global transformation Not all charge directions equal This is not physical, but merely a choice of gauge Spontaneous gauge symmetry breaking

34 Implications of global transformation Not all charge directions equal This is not physical, but merely a choice of gauge Spontaneous gauge symmetry breaking Broken by the transformation, not by the dynamics Dynamics only affect the length of the Higgs field Local symmetry intact and cannot be broken [Elitzur PR'75]

35 Implications of global transformation Not all charge directions equal This is not physical, but merely a choice of gauge Spontaneous gauge symmetry breaking Broken by the transformation, not by the dynamics Dynamics only affect the length of the Higgs field Local symmetry intact and cannot be broken [Elitzur PR'75] Consequence: Symmetry in charge space not manifest (hidden) Complicated charge tensor structures

36 Implications of global transformation Not all charge directions equal This is not physical, but merely a choice of gauge Spontaneous gauge symmetry breaking Broken by the transformation, not by the dynamics Dynamics only affect the length of the Higgs field Local symmetry intact and cannot be broken [Elitzur PR'75] Consequence: Symmetry in charge space not manifest (hidden) Complicated charge tensor structures Symmetry expressed in STIs/WTIs

37 Masses from propagators Masses are determined by poles of propagators

38 Masses from propagators Masses are determined by poles of propagators 2 propagators W/Z D ab μ ν ( x y)= <W a μ ( x)w b ν ( y)> Degenerate without QED

39 Masses from propagators Masses are determined by poles of propagators 2 propagators W/Z Degenerate without QED Scalar D ab μ ν ( x y)= <W a μ ( x)w b ν ( y)> D H ij (x y)= <h i (x)h j+ ( y)>

40 Masses from propagators Masses are determined by poles of propagators 2 propagators W/Z Degenerate without QED Scalar D ab μ ν ( x y)= <W a μ ( x)w b ν ( y)> D H ij (x y)= <h i (x)h j+ ( y)> (Tree-level/perturbative) poles at Higgs and W mass

41 Masses from propagators Masses are determined by poles of propagators 2 propagators W/Z Degenerate without QED Scalar D ab μ ν ( x y)= <W a μ ( x)w b ν ( y)> D H ij (x y)= <h i (x)h j+ (Tree-level/perturbative) poles at Higgs and W mass But only in a fixed gauge ( y)> Elementary fields are gauge-dependent

42 Masses from propagators Masses are determined by poles of propagators 2 propagators W/Z Degenerate without QED Scalar D ab μ ν ( x y)= <W a μ ( x)w b ν ( y)> D H ij (x y)= <h i (x)h j+ (Tree-level/perturbative) poles at Higgs and W mass But only in a fixed gauge ( y)> Elementary fields are gauge-dependent Without gauge fixing propagators are δ(x y)

43 Physical states [Fröhlich et al. PLB 80, 't Hooft ASIB 80, Bank et al. NPB 79] Elementary fields depend on the gauge Except right-handed neutrinos

44 Physical states [Fröhlich et al. PLB 80, 't Hooft ASIB 80, Bank et al. NPB 79] Elementary fields depend on the gauge Except right-handed neutrinos Experiments measure peaks in cross-sections for particular quantum numbers E.g. hadrons in QCD

45 Physical states [Fröhlich et al. PLB 80, 't Hooft ASIB 80, Bank et al. NPB 79] Elementary fields depend on the gauge Except right-handed neutrinos Experiments measure peaks in cross-sections for particular quantum numbers E.g. hadrons in QCD Gauge-invariance requires composite operators in gauge theories Not asymptotic states in perturbation theory

46 Physical states [Fröhlich et al. PLB 80, 't Hooft ASIB 80, Bank et al. NPB 79] Elementary fields depend on the gauge Except right-handed neutrinos Experiments measure peaks in cross-sections for particular quantum numbers E.g. hadrons in QCD Gauge-invariance requires composite operators in gauge theories Not asymptotic states in perturbation theory Higgs-Higgs, W-W, Higgs-Higgs-W etc. h h W W W h h

47 Lattice and Physical States

48 Lattice calculations Take a finite volume usually a hypercube L

49 Lattice calculations Take a finite volume usually a hypercube Discretize it, and get a finite, hypercubic lattice a L

50 Lattice calculations Take a finite volume usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral Can be done numerically Uses Monte-Carlo methods a L

51 Lattice calculations Take a finite volume usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral Can be done numerically Uses Monte-Carlo methods Artifacts Finite volume/discretization a L

52 Lattice calculations Take a finite volume usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral Can be done numerically Uses Monte-Carlo methods Artifacts Finite volume/discretization Masses vs. wave-lengths L a

53 Lattice calculations Take a finite volume usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral Can be done numerically Uses Monte-Carlo methods Artifacts Finite volume/discretization Masses vs. wave-lengths L a

54 Lattice calculations Take a finite volume usually a hypercube Discretize it, and get a finite, hypercubic lattice Calculate observables using path integral Can be done numerically Uses Monte-Carlo methods Artifacts Finite volume/discretization Masses vs. wave-lengths a Euclidean formulation L

55 Masses from Euclidean propagators

56 Masses from Euclidean propagators D( p)= O + ( p)o( p) Masses can be inferred from propagators

57 Masses from Euclidean propagators D( p)= O + ( p)o( p) 1 p 2 +m 2 Masses can be inferred from propagators

58 Masses from Euclidean propagators D( p)= O + ( p)o( p) 1 p 2 +m 2 C (t)= O + (x)o( y) exp( m Δ t) Masses can be inferred from propagators

59 Masses from Euclidean propagators D( p)= O + ( p)o( p) a i Masses can be inferred from propagators Long-time behavior relevant No exact results on time-like momenta p 2 +m i 2 C (t)= O + (x)o( y) a i exp( m i Δ t) a i =1 m 0 <m 1 <...

60 Masses from Euclidean propagators Masses can be inferred from propagators Long-time behavior relevant No exact results on time-like momenta

61 Masses from Euclidean propagators Masses can be inferred from propagators Long-time behavior relevant No exact results on time-like momenta

62 Masses from Euclidean propagators Masses can be inferred from propagators Long-time behavior relevant No exact results on time-like momenta

63 Higgsonium h h Simpelst 0+ bound state h + (x)h(x)

64 Higgsonium h h Simpelst 0+ bound state Same quantum numbers as the Higgs No weak or flavor charge h + (x)h(x)

65 Higgsonium [Maas et al. '13] h h Simpelst 0+ bound state Same quantum numbers as the Higgs No weak or flavor charge h + (x)h(x)

66 Higgsonium [Maas et al. '13] Influence of heavier states h h Finite-volume effects Finite-volume effects Simpelst 0+ bound state Same quantum numbers as the Higgs No weak or flavor charge h + (x)h(x)

67 Higgsonium [Maas et al. '13] h h Finite-volume effects Simpelst 0+ bound state h + (x)h(x) Same quantum numbers as the Higgs No weak or flavor charge Mass is about 120 GeV

68 Higgsonium [Maas et al. '13] h h Finite-volume effects Finite-volume effects Simpelst 0+ bound state h + (x)h(x) Same quantum numbers as the Higgs No weak or flavor charge Mass is about 120 GeV

69 Higgsonium [Maas et al. '13] Influence of heavier states h h Finite-volume effects Finite-volume effects Simpelst 0+ bound state h + (x)h(x) Same quantum numbers as the Higgs No weak or flavor charge Mass is about 120 GeV

70 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV

71 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence?

72 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No.

73 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No. Duality between elementary states and bound states [Fröhlich et al. PLB 80]

74 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No. Duality between elementary states and bound states [Fröhlich et al. PLB 80] (h + h)(x)(h + h)( y)

75 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No. Duality between elementary states and bound states [Fröhlich et al. PLB 80] (h + h)(x)(h + h)( y) h=v+η

76 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No. Duality between elementary states and bound states [Fröhlich et al. PLB 80] (h + h)(x)(h + h)( y) h=v+η const.+ h + (x)h( y) +O(η 3 )

77 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No. Duality between elementary states and bound states [Fröhlich et al. PLB 80] (h + h)(x)(h + h)( y) Same poles to leading order h=v+η const.+ h + (x)h( y) +O(η 3 )

78 Mass relation - Higgs [Fröhlich et al. PLB 80 Maas'12, Maas & Mufti'13] Higgsonium: 120 GeV, Higgs at tree-level: 120 GeV Scheme exists to shift Higgs mass always to 120 GeV Coincidence? No. Duality between elementary states and bound states [Fröhlich et al. PLB 80] (h + h)(x)(h + h)( y) Same poles to leading order Deeply-bound relativistic state Mass defect~constituent mass h=v+η const.+ h + (x)h( y) +O(η 3 ) Cannot describe with quantum mechanics Very different from QCD bound states

79 Comparison to Higgs [Maas et al. '13]

80 Comparison to Higgs [Maas et al. '13] Same mass Different influence at short times Can be traced back to Higgs mechanism

81 Isovector-vector state W h h Vector state 1- with operator tr t a h + h + h D h μ h + h Only in a Higgs phase close to a simple particle Higgs-flavor triplet, instead of gauge triplet

82 Isovector-vector state [Maas et al. '13] W h h Vector state 1- with operator tr t a h + h + h D μ Only in a Higgs phase close to a simple particle Higgs-flavor triplet, instead of gauge triplet h h + h

83 Isovector-vector state [Maas et al. '13] W h h Vector state 1- with operator Only in a Higgs phase close to a simple particle Higgs-flavor triplet, instead of gauge triplet Mass about 80 GeV tr t a h + h + h D μ h h + h

84 Mass relation - W [Fröhlich et al. PLB 80 Maas'12] Vector state: 80 GeV W at tree-level: 80 GeV W not scale or scheme dependent

85 Mass relation - W [Fröhlich et al. PLB 80 Maas'12] Vector state: 80 GeV W at tree-level: 80 GeV W not scale or scheme dependent Same mechanism (h + D μ h)(x)(h + D μ h)( y)

86 Mass relation - W [Fröhlich et al. PLB 80 Maas'12] Vector state: 80 GeV W at tree-level: 80 GeV W not scale or scheme dependent Same mechanism (h + D μ h)(x)(h + D μ h)( y) h=v+η const.+ W μ (x)w μ ( y) +O(η 3 ) v=0

87 Mass relation - W [Fröhlich et al. PLB 80 Maas'12] Vector state: 80 GeV W at tree-level: 80 GeV W not scale or scheme dependent Same mechanism (h + D μ h)(x)(h + D μ h)( y) h=v+η const.+ W μ (x)w μ ( y) +O(η 3 ) v=0 Same poles at leading order At least for a light Higgs

88 Mass relation - W [Fröhlich et al. PLB 80 Maas'12] Vector state: 80 GeV W at tree-level: 80 GeV W not scale or scheme dependent Same mechanism (h + D μ h)(x)(h + D μ h)( y) h=v+η const.+ W μ (x)w μ ( y) +O(η 3 ) v=0 Same poles at leading order At least for a light Higgs Remains true beyond leading order

89 Comparison to W [Maas et al. '13]

90 Comparison to W [Maas et al. '13] Same mass Different influence at short times Not a hard mass, but decreases at high energies

91 Ground state spectrum [Maas et al. Unpublished, PoS'12] ~ Higgs ~ W

92 Ground state spectrum [Maas et al. Unpublished, PoS'12] ~ Higgs ~ W Many states No simple relation to elementary states besides Higgs and W

93 Ground state spectrum [Maas et al. Unpublished, PoS'12] ~ Higgs ~ W Many states No simple relation to elementary states besides Higgs and W

94 Ground state spectrum [Maas et al. Unpublished, PoS'12] ~ Higgs ~ W Many states No simple relation to elementary states besides Higgs and W

95 Ground state spectrum [Maas et al. Unpublished, PoS'12] ~ Higgs ~ W Many states No simple relation to elementary states besides Higgs and W

96 Ground state spectrum [Maas et al. Unpublished, PoS'12] ~ Higgs ~ W Many states No simple relation to elementary states besides Higgs and W Can mimic new physics Note: Depends on parameters

97 Ground states For W and Higgs exist gauge-invariant composite/bound states of the same mass Play the role of the experimental signatures True physical states Reason for the applicability of perturbation theory for electroweak physics

98 Ground states For W and Higgs exist gauge-invariant composite/bound states of the same mass Play the role of the experimental signatures True physical states Reason for the applicability of perturbation theory for electroweak physics Is this always true? Full standard model: Probably Other parameters?

99 Quantum Phase Diagram

100 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a

101 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem

102 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale

103 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale Numerical procedure: Calculate for several a with all independent observables fixed - Lines of constant physics

104 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale Coupling(s) Numerical procedure: Calculate for several a with all independent observables fixed - Lines of constant physics Mass(es)

105 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale Coupling(s) Numerical procedure: Calculate for several a with all independent observables fixed - Lines of constant physics Mass(es)

106 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale Coupling(s) a decreases Numerical procedure: Calculate for several a with all independent observables fixed - Lines of constant physics Mass(es)

107 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale Coupling(s) a decreases Numerical procedure: Calculate for several a with all independent observables fixed - Lines of constant physics Mass(es) Full theory

108 Lines of constant physics Lattice simulations have an intrinsic cutoff the lattice spacing a Full theory reached at zero lattice spacing If it exists: Triviality problem Masses, couplings, and actions are specified at this scale Numerical procedure: Calculate for several a with all independent observables fixed - Lines of constant physics Different starting points yield different physics Coupling(s) a decreases Mass(es) Full theory

109 Phase diagram [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] (Lattice-regularized) phase diagram f(classical Higgs mass) g(classical gauge coupling)

110 Phase diagram (Lattice-regularized) phase diagram f(classical Higgs mass) [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase g(classical gauge coupling)

111 Phase diagram (Lattice-regularized) phase diagram f(classical Higgs mass) [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase Confinement phase g(classical gauge coupling)

112 Phase diagram (Lattice-regularized) phase diagram f(classical Higgs mass) [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase Confinement phase g(classical gauge coupling)

113 Phase diagram (Lattice-regularized) phase diagram f(classical Higgs mass) [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase 1 st order Confinement phase g(classical gauge coupling)

114 Phase diagram (Lattice-regularized) phase diagram continuous f(classical Higgs mass) Crossover [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase 1 st order Confinement phase g(classical gauge coupling)

115 Phase diagram (Lattice-regularized) phase diagram continuous Separation only in fixed gauges f(classical Higgs mass) Crossover Landau gauge [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase 1 st order Confinement phase g(classical gauge coupling)

116 Phase diagram (Lattice-regularized) phase diagram continuous Separation only in fixed gauges f(classical Higgs mass) Crossover Coulomb gauge Landau gauge [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] Higgs phase 1 st order Confinement phase g(classical gauge coupling)

117 Phase diagram [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] (Lattice-regularized) phase diagram continuous Separation only in fixed gauges f(classical Higgs mass) Same asymptotic states in confinement and Higgs pseudo-phases Crossover Higgs phase Confinement phase g(classical gauge coupling) 1 st order

118 Phase diagram [Fradkin & Shenker PRD'79 Caudy & Greensite PRD'07] (Lattice-regularized) phase diagram continuous Separation only in fixed gauges Same asymptotic states in confinement and Higgs pseudo-phases g(classical gauge coupling) Same asymptotic states irrespective of coupling strengths f(classical Higgs mass) Crossover Higgs phase 1 st order Confinement phase

119 Typical spectra [Maas, Mufti PoS'12, unpublished, Evertz et al.'86, Langguth et al.'85,'86] Higgs Higgs W

120 Typical spectra [Maas, Mufti PoS'12, unpublished, Evertz et al.'86, Langguth et al.'85,'86] Higgs QCD Higgs W

121 Typical spectra [Maas, Mufti PoS'12, unpublished, Evertz et al.'86, Langguth et al.'85,'86] Higgs QCD Higgs W Generically different low-lying spectra 0++ lighter in QCD-like region 1-- lighter in Higgs-like region

122 Typical spectra [Maas, Mufti PoS'12, unpublished, Evertz et al.'86, Langguth et al.'85,'86] Higgs QCD Higgs W Generically different low-lying spectra 0++ lighter in QCD-like region 1-- lighter in Higgs-like region Use as operational definition of phase

123 Phase diagram [Maas, Mufti, unpublished]

124 Phase diagram [Maas, Mufti, unpublished] Higgs QCD Complicated real phase diagram

125 Phase diagram [Maas, Mufti, unpublished] Higgs QCD Complicated real phase diagram QCD-like behavior even for negative bare mass

126 Phase diagram [Maas, Mufti, unpublished] Higgs QCD Complicated real phase diagram QCD-like behavior even for negative bare mass Similar bare couplings for both physics types

127 Phase diagram [Maas, Mufti, unpublished] Higgs QCD Complicated real phase diagram QCD-like behavior even for negative bare mass Similar bare couplings for both physics types Lower Higgs (0+ ) mass bound: W (1 - ) mass

128 Limits of perturbation theory [Maas, Mufti'13] Naively: Too large couplings Landau poles around electroweak scale

129 Limits of perturbation theory [Maas, Mufti'13] Naively: Too large couplings Landau poles around electroweak scale Mass relation W to 1- may break earlier

130 Limits of perturbation theory [Maas, Mufti'13] Naively: Too large couplings Landau poles around electroweak scale Mass relation W to 1- may break earlier

131 Limits of perturbation theory [Maas, Mufti'13] QCD-like Naively: Too large couplings Landau poles around electroweak scale Mass relation W to 1- may break earlier

132 Limits of perturbation theory [Maas, Mufti'13] QCD-like Naively: Too large couplings Landau poles around electroweak scale Mass relation W to 1- may break earlier Threshold in the 0+ channel at twice the 1 - mass

133 Limits of perturbation theory [Maas, Mufti'13] QCD-like Naively: Too large couplings Landau poles around electroweak scale Mass relation W to 1- may break earlier Threshold in the 0+ channel at twice the 1 - mass No reliable identification of asymptotic states

134 Limits of perturbation theory [Maas, Mufti'13] QCD-like Naively: Too large couplings Landau poles around electroweak scale Mass relation W to 1- may break earlier Threshold in the 0+ channel at twice the 1 - mass No reliable identification of asymptotic states Depends on dynamics right LCP?

135 Comparability to the standard model 2 correct masses only fix two parameters, but 3 parameters needed

136 Comparability to the standard model 2 correct masses only fix two parameters, but 3 parameters needed Comparison to standard model complicated States stable, no W/Z splitting

137 [Maas, Mufti'13] Comparability to the standard model 2 correct masses only fix two parameters, but 3 parameters needed Comparison to standard model complicated States stable, no W/Z splitting Couplings run differently proceed with caution

138 Lattice and Excited States

139 (Speculative) Consequences Composite states can have excitations Not necessarily [Wurtz et al. '13]

140 (Speculative) Consequences Composite states can have excitations Not necessarily [Wurtz et al. '13] Could mimic additional Higgs or Z'

141 (Speculative) Consequences Composite states can have excitations Not necessarily [Wurtz et al. '13] Could mimic additional Higgs or Z' Will be suppressed as higher orders in the expansion around the vacuum field Small couplings, perhaps 1% or less of gauge couplings Consistent with experimental bounds

142 (Speculative) Consequences Composite states can have excitations Not necessarily [Wurtz et al. '13] Could mimic additional Higgs or Z' Will be suppressed as higher orders in the expansion around the vacuum field Small couplings, perhaps 1% or less of gauge couplings Consistent with experimental bounds Possibly only sigma-like bumps Distinction from scattering states

143 (Speculative) Consequences Composite states can have excitations Not necessarily [Wurtz et al. '13] Could mimic additional Higgs or Z' Will be suppressed as higher orders in the expansion around the vacuum field Small couplings, perhaps 1% or less of gauge couplings Consistent with experimental bounds Possibly only sigma-like bumps Distinction from scattering states Requires confirmation or exclusion

144 Excited states on the lattice Each quantum number channel has a spectrum Discreet in a finite volume

145 Excited states on the lattice Each quantum number channel has a spectrum Discreet in a finite volume States can be either stable, excited states, Elastic Excited state Ground state

146 Excited states on the lattice Each quantum number channel has a spectrum Discreet in a finite volume States can be either stable, excited states, resonances Resonances Inelastic Elastic Excited state Ground state

147 Excited states on the lattice Each quantum number channel has a spectrum Discreet in a finite volume States can be either stable, excited states, resonances or scattering states Inelastic Resonances or scattering states Elastic Excited state Ground state

148 Excited states on the lattice [Luescher'85,'86,'90,'91] Inelastic Resonances or scattering states Exponential volume dependency - if stable against decays into other channels Elastic Excited state Ground state

149 Excited states on the lattice [Luescher'85,'86,'90,'91] Polynominal (inverse) volume dependence Width and nature from phase shifts below the inelastic threshold Exponential volume dependency - if stable against decays into other channels Inelastic Resonances or scattering states Elastic Excited state Ground state

150 Excited states on the lattice [Luescher'85,'86,'90,'91] Above inelastic threshold still complicated Polynominal (inverse) volume dependence Width and nature from phase shifts below the inelastic threshold Exponential volume dependency - if stable against decays into other channels Inelastic Resonances or scattering states Elastic Excited state Ground state

151 Excited states on the lattice [Luescher'85,'86,'90,'91]

152 Excited states on the lattice [Luescher'85,'86,'90,'91] Ground state

153 Excited states on the lattice [Luescher'85,'86,'90,'91] Inelastic threshold: H->2H Elastic threshold: H->2W Ground state

154 Excited states on the lattice [Luescher'85,'86,'90,'91] Scattering states Inelastic threshold: H->2H Elastic threshold: H->2W Ground state

155 Excited states on the lattice [Luescher'85,'86,'90,'91] Scattering states Inelastic threshold: H->2H Avoided level crossing Identification and widths from phase shifts Elastic threshold: H->2W Ground state

156 Excited Higgs [Maas et al. unpublished] Scattering states Inelastic threshold Elastic threshold Ground state NB: weakly coupled

157 Excited Higgs [Maas et al. unpublished] Scattering states Inelastic threshold Elastic threshold Possible excited Higgs ~150 GeV Ground state NB: weakly coupled

158 Z' Scattering states Inelastic threshold Elastic threshold Ground state NB: weakly coupled

159 Z' Scattering states Inelastic threshold Identification unclear Elastic threshold Ground state NB: weakly coupled

160 Experimental Signals

161 Weakly coupled experimental signals? Similar or identical to standard model Higgs sector

162 Weakly coupled experimental signals? Similar or identical to standard model Higgs sector Full non-perturbative matrix elements can be expanded in Higgs quantum fluctuations

163 Weakly coupled experimental signals? Similar or identical to standard model Higgs sector Full non-perturbative matrix elements can be expanded in Higgs quantum fluctuations Order <~1% in the standard model weakly coupled and thus strongly suppressed

164 Weakly coupled experimental signals? Similar or identical to standard model Higgs sector Full non-perturbative matrix elements can be expanded in Higgs quantum fluctuations Order <~1% in the standard model weakly coupled and thus strongly suppressed Near W/Z or Higgs pole by construction identical to the perturbative result

165 Weakly coupled experimental signals? Similar or identical to standard model Higgs sector Full non-perturbative matrix elements can be expanded in Higgs quantum fluctuations Order <~1% in the standard model weakly coupled and thus strongly suppressed Near W/Z or Higgs pole by construction identical to the perturbative result Excited states or different quantum numbers possible best signal channel

166 Weakly coupled experimental signals? Similar or identical to standard model Higgs sector Full non-perturbative matrix elements can be expanded in Higgs quantum fluctuations Order <~1% in the standard model weakly coupled and thus strongly suppressed Near W/Z or Higgs pole by construction identical to the perturbative result Excited states or different quantum numbers possible best signal channel Example experimental signal: Excited Higgs 190 GeV mass, 19 GeV width

167 Impact on quartic gauge coupling

168 Impact on quartic gauge coupling [Maas et al. Unpublished] (Singlet) quartic gauge coupling and resonance formation in the same channel W/Z W/Z W/Z W/Z

169 Impact on quartic gauge coupling [Maas et al. Unpublished] (Singlet) quartic gauge coupling and resonance formation in the same channel W/Z W/Z W/Z W/Z + W/Z W/Z W/Z W/Z

170 Impact on quartic gauge coupling [Maas et al. Unpublished] (Singlet) quartic gauge coupling and resonance formation in the same channel W/Z W/Z W/Z W/Z + W/Z W/Z W/Z W/Z

171 Impact on quartic gauge coupling [Maas et al. Unpublished] (Singlet) quartic gauge coupling and resonance formation in the same channel W/Z W/Z W/Z W/Z + Resonance W/Z W/Z W/Z W/Z Resonance peak in final state invariant mass?

172 Impact on quartic gauge coupling [Maas et al. Unpublished] (Singlet) quartic gauge coupling and resonance formation in the same channel W/Z W/Z W/Z W/Z + Resonance W/Z W/Z W/Z W/Z Resonance peak in final state invariant mass? Estimate using effective theory+sherpa: Too small to be seen (less than 1% at peak)

173 Experimental accessibility [Maas et al. Unpublished] Parton 1 Z Z W + Parton 2 W -

174 Experimental accessibility [Maas et al. Unpublished] Parton 1 Z Z Parton 2 Ordinary: e.g. Higgs W + W -

175 Experimental accessibility [Maas et al. Unpublished] Parton 1 Z Z Non-perturbative: 0 ++*,... W + Parton 2 Ordinary: e.g. Higgs W - E.g. excited Higgs: Decay channel: 2W

176 Experimental accessibility [Maas et al. Unpublished] Parton 1 Z Z Non-perturbative: 0 ++*,... Additional 1% effect W + Parton 2 Ordinary: e.g. Higgs W - E.g. excited Higgs: Decay channel: 2W

177 Experimental accessibility [Maas et al. Unpublished] SPECULATIVE Parton 1 Z Z Non-perturbative: 0 ++*,... Additional 1% effect W + Parton 2 Perturbative: Higgs, Z, γ W - [Low-energy effective Lagrangian, MC by Sherpa 1.4.2] E.g. excited Higgs: Decay channel: 2W

178 Experimental accessibility [Maas et al. Unpublished] SPECULATIVE Parton 1 Z Z Non-perturbative: 0 ++*,... Additional 1% effect W + Parton 2 Perturbative: Higgs, Z, γ W - [Low-energy effective Lagrangian, MC by Sherpa 1.4.2] E.g. excited Higgs: Decay channel: 2W

179 Experimental accessibility [Maas et al. Unpublished] SPECULATIVE Parton 1 Z Z Non-perturbative: 0 ++*,... Additional 1% effect W + Parton 2 Perturbative: Higgs, Z, γ W - [Low-energy effective Lagrangian, MC by Sherpa 1.4.2] E.g. excited Higgs: Decay channel: 2W Decides whether present in the standard model If present standard-model physics this would be a gateway to new physics

180 Experimental accessibility [Maas et al. Unpublished] SPECULATIVE Parton 1 Z Z Non-perturbative: 0 ++*,... Additional 1% effect W + Parton 2 Perturbative: Higgs, Z, γ 20 fb fb fb -1 W - [Low-energy effective Lagrangian, MC by Sherpa 1.4.2] E.g. excited Higgs: Decay channel: 2W Decides whether present in the standard model If present standard-model physics this would be a gateway to new physics

181 Summary Higgs sector with light Higgs successfully described by perturbation theory around classical physics

182 Summary Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality

183 Summary Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality Highly relativistic bound states Unusual structure

184 Summary Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality Highly relativistic bound states Unusual structure Permits physical interpretation of resonances in cross sections

185 Summary Higgs sector with light Higgs successfully described by perturbation theory around classical physics Bound-state/elementary state duality Highly relativistic bound states Unusual structure Permits physical interpretation of resonances in cross sections Possibility of new excitations of bound states Background for new physics searches If existing likely accessible at LHC/ILC New experimental perspective/program Non-perturbatively interesting even for a light Higgs