the spectra of yang-mills gauge theories with novel, non
TRANSCRIPT
Introduction Features Results
The Spectra of Yang-Mills Gauge Theories withnovel, non QCD-like dynamics
Eoin Kerrane
University of Edinburgh
May 15, 2009
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Table of contents
Introduction
Features
Results
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Outline
Introduction
Features
Results
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Motivation
I Why non QCD-like?
I Why not?I Several BSM applications relevant to LHC:
I TechnicolorI Unparticles
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Motivation
I Why non QCD-like?
I Why not?
I Several BSM applications relevant to LHC:I TechnicolorI Unparticles
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Motivation
I Why non QCD-like?
I Why not?I Several BSM applications relevant to LHC:
I TechnicolorI Unparticles
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Motivation
I Why non QCD-like?
I Why not?I Several BSM applications relevant to LHC:
I Technicolor
I Unparticles
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Motivation
I Why non QCD-like?
I Why not?I Several BSM applications relevant to LHC:
I TechnicolorI Unparticles
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
I SU(N) Yang-Mills theory, Nf fermions in representation R
β(g) = −β0(N,Nf ,R)g3
16π2− β1(N,Nf ,R)
g5
(16π2)2
I β0,1 > 0 for Nf small
I For QCD
β1 = 0 Nf ∼ 8
β0 = 0 Nf ∼ 16
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
I SU(N) Yang-Mills theory, Nf fermions in representation R
β(g) = −β0(N,Nf ,R)g3
16π2− β1(N,Nf ,R)
g5
(16π2)2
I β0,1 > 0 for Nf small
I For QCD
β1 = 0 Nf ∼ 8
β0 = 0 Nf ∼ 16
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
I SU(N) Yang-Mills theory, Nf fermions in representation R
β(g) = −β0(N,Nf ,R)g3
16π2− β1(N,Nf ,R)
g5
(16π2)2
I β0,1 > 0 for Nf small
I For QCD
β1 = 0 Nf ∼ 8
β0 = 0 Nf ∼ 16
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Beta function
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theory
I Concluded that theory with IR fixed pointI is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariant
I does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Bank-Zaks
I Non-trivial IR fixed-point first investigated in 1982 [BZ82]
I Began with observation that β0 < 0 for Nf > N∗ (N∗ ∼ 16)for QCD
I Then noticed:I that b1 < 0 for Nf > N ′f < N∗
I that form of β function is scheme dependent.
I Built an expansion in (Nf − N∗) of RG quantities forNf . N∗, where there is a weakly coupled IR fixed point
I Posited phase diagram of such a theoryI Concluded that theory with IR fixed point
I is scale invariantI does not admit a particle interpretation
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Unparticles [Geo07]
I Proposed possibility of existence of BZ sector with IR fixedpoint, coupled to SM via particles of mass MU
I Below ΛU scale invariance emerges in BZ sector
I Analyses matrix elements of BZ operators
I Concludes that “unparticle stuff with scale dimension dU lookslike a non-integral number dU of invisible particles”
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Unparticles [Geo07]
I Proposed possibility of existence of BZ sector with IR fixedpoint, coupled to SM via particles of mass MU
I Below ΛU scale invariance emerges in BZ sector
I Analyses matrix elements of BZ operators
I Concludes that “unparticle stuff with scale dimension dU lookslike a non-integral number dU of invisible particles”
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Unparticles [Geo07]
I Proposed possibility of existence of BZ sector with IR fixedpoint, coupled to SM via particles of mass MU
I Below ΛU scale invariance emerges in BZ sector
I Analyses matrix elements of BZ operators
I Concludes that “unparticle stuff with scale dimension dU lookslike a non-integral number dU of invisible particles”
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Unparticles [Geo07]
I Proposed possibility of existence of BZ sector with IR fixedpoint, coupled to SM via particles of mass MU
I Below ΛU scale invariance emerges in BZ sector
I Analyses matrix elements of BZ operators
I Concludes that “unparticle stuff with scale dimension dU lookslike a non-integral number dU of invisible particles”
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Suggested [LO06, Lut09] as alternative to Walking Technicolor
I Again, proposes BZ sector with IR fixed point
I 2 massless fermions forming minimal technicor sector
I Nf − 2 electroweak singlet fermions , charged under BZ withexplicit mass terms
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Suggested [LO06, Lut09] as alternative to Walking Technicolor
I Again, proposes BZ sector with IR fixed point
I 2 massless fermions forming minimal technicor sector
I Nf − 2 electroweak singlet fermions , charged under BZ withexplicit mass terms
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Suggested [LO06, Lut09] as alternative to Walking Technicolor
I Again, proposes BZ sector with IR fixed point
I 2 massless fermions forming minimal technicor sector
I Nf − 2 electroweak singlet fermions , charged under BZ withexplicit mass terms
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Suggested [LO06, Lut09] as alternative to Walking Technicolor
I Again, proposes BZ sector with IR fixed point
I 2 massless fermions forming minimal technicor sector
I Nf − 2 electroweak singlet fermions , charged under BZ withexplicit mass terms
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Theory is in conformal phase above TeV scale
I Fermion masses cause flow away from fixed point below TeV
I Scale-invariance broken, theory becomes confining, breakingEW
I Proximity to IR fixed point ensures condensate has largeanomalous dimension
I Fermion masses are enhanced, as in Walking Technicolor
I Argued in [San08] that CT is equivalent to Partially GaugedTechnicolor [DST06], but needs new mass scale for EWSB
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Theory is in conformal phase above TeV scale
I Fermion masses cause flow away from fixed point below TeV
I Scale-invariance broken, theory becomes confining, breakingEW
I Proximity to IR fixed point ensures condensate has largeanomalous dimension
I Fermion masses are enhanced, as in Walking Technicolor
I Argued in [San08] that CT is equivalent to Partially GaugedTechnicolor [DST06], but needs new mass scale for EWSB
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Theory is in conformal phase above TeV scale
I Fermion masses cause flow away from fixed point below TeV
I Scale-invariance broken, theory becomes confining, breakingEW
I Proximity to IR fixed point ensures condensate has largeanomalous dimension
I Fermion masses are enhanced, as in Walking Technicolor
I Argued in [San08] that CT is equivalent to Partially GaugedTechnicolor [DST06], but needs new mass scale for EWSB
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Theory is in conformal phase above TeV scale
I Fermion masses cause flow away from fixed point below TeV
I Scale-invariance broken, theory becomes confining, breakingEW
I Proximity to IR fixed point ensures condensate has largeanomalous dimension
I Fermion masses are enhanced, as in Walking Technicolor
I Argued in [San08] that CT is equivalent to Partially GaugedTechnicolor [DST06], but needs new mass scale for EWSB
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Theory is in conformal phase above TeV scale
I Fermion masses cause flow away from fixed point below TeV
I Scale-invariance broken, theory becomes confining, breakingEW
I Proximity to IR fixed point ensures condensate has largeanomalous dimension
I Fermion masses are enhanced, as in Walking Technicolor
I Argued in [San08] that CT is equivalent to Partially GaugedTechnicolor [DST06], but needs new mass scale for EWSB
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Conformal Technicolor
I Theory is in conformal phase above TeV scale
I Fermion masses cause flow away from fixed point below TeV
I Scale-invariance broken, theory becomes confining, breakingEW
I Proximity to IR fixed point ensures condensate has largeanomalous dimension
I Fermion masses are enhanced, as in Walking Technicolor
I Argued in [San08] that CT is equivalent to Partially GaugedTechnicolor [DST06], but needs new mass scale for EWSB
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Outline
Introduction
Features
Results
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Critical Line
I Yang-Mills spectra measured non-perturbatively in a latticeformulation
, Wilson fermions
I Chiral symmetry broken m0 6= mq
κ =1
8 + 2am0β =
4
g20
I Chirally symmetric phase has mπ,ρ,... → 0 as mq → 0
I Chirally broken phase has mπ ∼√
mq, mρ,... 9 0 as mq → 0
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Critical Line
I Yang-Mills spectra measured non-perturbatively in a latticeformulation, Wilson fermions
I Chiral symmetry broken m0 6= mq
κ =1
8 + 2am0β =
4
g20
I Chirally symmetric phase has mπ,ρ,... → 0 as mq → 0
I Chirally broken phase has mπ ∼√
mq, mρ,... 9 0 as mq → 0
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Critical Line
I Yang-Mills spectra measured non-perturbatively in a latticeformulation, Wilson fermions
I Chiral symmetry broken m0 6= mq
κ =1
8 + 2am0β =
4
g20
I Chirally symmetric phase has mπ,ρ,... → 0 as mq → 0
I Chirally broken phase has mπ ∼√
mq, mρ,... 9 0 as mq → 0
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Critical Line
I Yang-Mills spectra measured non-perturbatively in a latticeformulation, Wilson fermions
I Chiral symmetry broken m0 6= mq
κ =1
8 + 2am0β =
4
g20
I Chirally symmetric phase has mπ,ρ,... → 0 as mq → 0
I Chirally broken phase has mπ ∼√
mq, mρ,... 9 0 as mq → 0
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Critical Line
I Yang-Mills spectra measured non-perturbatively in a latticeformulation, Wilson fermions
I Chiral symmetry broken m0 6= mq
κ =1
8 + 2am0β =
4
g20
I Chirally symmetric phase has mπ,ρ,... → 0 as mq → 0
I Chirally broken phase has mπ ∼√
mq, mρ,... 9 0 as mq → 0
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Outline
Introduction
Features
Results
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
[CS07]
Figure: Fundamental quarks Figure: Adjoint quarks
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
[DDPP08]
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
[DDPP08]
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
[HRRT09]
Figure: Phase diagram of SU(2) adjoint theory
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
[HRRT09]
Figure: Fundamental Figure: Adjoint
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
[HRRT09]
Figure: Fundamental Figure: Adjoint
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
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Light composite Higgs and precision electroweakmeasurements on the Z resonance: An update.
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Phys. Rev., D73:037701, 2006.
Howard Georgi.Unparticle Physics.Phys. Rev. Lett., 98:221601, 2007.
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Markus A. Luty and Takemichi Okui.Conformal technicolor.JHEP, 09:070, 2006.
Markus A. Luty.Strong Conformal Dynamics at the LHC and on the Lattice.JHEP, 04:050, 2009.
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics
Introduction Features Results
Francesco Sannino.(Near) Conformal Technicolor: What is really new?2008.
Eoin Kerrane University of Edinburgh
The Spectra of Yang-Mills Gauge Theories with novel, non QCD-like dynamics