Potential Implications of the Higgs Boson
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Potential Implicationsof the Higgs Boson
Christopher T. HillFermilab
Colloquium, Oct. 23, 2013
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Electromagnetic force U(1)
Quark color force SU(3)
Massless Gauge Fields
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All Gauge theories are basedupon charge conservation.
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The continuous symmetry that leads, by Noether’s Theorem, to charge
conservationis called Local Gauge Invariance
All Gauge theories are basedupon charge conservation.
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The continuous symmetry that leads, by Noether’s Theorem, to charge
conservationis called Local Gauge Invariance
Local Gauge Invariancedefines the full structure of
electrodynamics
All Gauge theories are basedupon charge conservation.
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Local Gauge Symmetry U(1):
electron = electron + collinear gauge field
phase of electron’swave function is
strictly unobservable
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Local U(1) Gauge Invariance Wallet Card
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Standard Electroweak Model
u
d
e
nuW
SU(2)L x U(1)
Weak Force
(left-handed fields):
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Weak Force
(left-handed fields):
u
d
e
nuW What gives rise to the masses of
W and Z boson?
SU(2)L x U(1)
Massive Gauge Fields
Standard Electroweak Model
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Can a gauge field have a mass and still have gauge symmetry?
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massless scalar field
Can a gauge field have a mass and still have gauge symmetry?
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Spontaneous Continuous Symmetry Breaking
Where can we find a massless scalar?
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Higgs Boson: small radial oscillations massive mode
Nambu-Goldstone Boson: angular motion with no cost
in energy massless mode
Goldstone TheoremU(1) symmetry
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v = “VEV” = 175 GeV
Radius of hat:
Curvature in brim:mHiggs
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Physicists Find Elusive Particle Seen as Key to Universe
July 4th, 2012
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v = “VEV” = 175 GeV
Radius of hat:
Curvature in brim:mHiggs = 126 GeV
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The Higgs Boson is required to explain fermion mass
(as well as gauge boson mass)
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The Higgs Boson is required to explain fermion mass
(as well as gauge boson mass)
This traces back to parity violation,i.e., the difference between left and right.
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Fermion Mass and Chirality
+z axis
time
light cone
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A massless right-handed fermionsz = +1/2
+z axis
time
spin
momentum
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+z axis
time
spin
momentum
A massless left-handed fermionsz = +1/2
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Couple electron to the photon
+z axis
time
right-handed
right-handed
Chirality is conserved!
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Couple electron to the photon
+z axis
time
left-handed
left-handed
Chirality is conserved
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How do we make a massive electron?
+z axis
time
light cone
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The left-handed and right-handedelectrons have the same electric charge
QED is “vectorlike”ergo, no parity violation
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A massive fermion oscillates inchirality through spacetime:
right-handed
right-handed
right-handed
left-handed
left-handed
Chirality is not conserved by mass!
electric charge isconserved
spin isconserved
m
m
m
m
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But, only left-handed fermions haveelectroweak charge and form doublets
under SU(2)
Right handed’s are “sterile” under SU(2)
Parity is violated
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Helicity of decay products in pion decay:
?
?
Mirror Images
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Parity is violated in pion decay:(Lederman)
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Couple LH fermions to the W-boson
+z axis
time
left-handed
left-handed
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How do we make a massive fermionbut conserve weak charge?
right-handed
right-handed
left-handed
left-handed
left-handed
Mass Violates Electroweak Gauge Symmetry!!!
mass violatesweak charge!!!
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Couple to a “Higgs boson”
+z axis
time
left-handed
right-handed
Weak charge is conserved !
Higgs boson
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Higgs Boson Condenses in vacuum
+z axis
time
Weak charge is hidden in vacuum
Higgs bosonvacuum expectation
value = 175 GeV
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Fermion Masses in Electroweak Theory
right-handed
right-handed
left-handed
left-handed
left-handed
Fermion Mass requires Higgs to maintainElectroweak Gauge Symmetry!!!
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The Higgs Boson Explains the Masses of Elementary Particles
July 4th, 2012
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The Higgs Boson Explains the Masses of Elementary Particles
Or Does it?
July 4th, 2012
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It was hoped that a fundamental Higgs Mechanismwould explain the origin of electroweak mass
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We now know that a fundamental Higgs Bosonexists and explains the masses of quarks, leptons, W and Z
It was hoped that a fundamental Higgs Mechanismwould explain the origin of electroweak mass
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But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale:
Vweak = 175 GeV
We now know that a fundamental Higgs Bosonexists and explains the masses of quarks, leptons, W and Z
It was hoped that a fundamental Higgs Mechanismwould explain the origin of electroweak mass
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i.e., what is the originof the Higgs Boson mass itself?
We now know that a fundamental Higgs Bosonexists and explains the masses of quarks, leptons, W and Z
It was hoped that a fundamental Higgs Mechanismwould explain the origin of electroweak mass
But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale:
Vweak = 175 GeV
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i.e., what is the originof the Higgs Boson mass itself?
We now know that a fundamental Higgs Bosonexists and explains the masses of quarks, leptons, W and Z
It was hoped that a fundamental Higgs Mechanismwould explain the origin of electroweak mass
But, the Higgs Boson does NOT explain the origin of the electroweak mass-scale:
Vweak = 175 GeV
This is either very sobering, or itpresents theoretical opportunities
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The world of masslessnessfeatures a symmetry:
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The world of masslessnessfeatures a symmetry:
Scale Invariance
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The world of masslessnessfeatures a symmetry:
Scale Invariance
Scale Invariance is (almost) always broken by quantum effects
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The world of masslessnessfeatures a symmetry:
Scale Invariance
Scale Invariance is (almost) always broken by quantum effects
Feynman Loops h -
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Scale Symmetry in QCDis broken by quantum loops
and this gives rise to:
The Origin of the Nucleon Mass(most of the visible mass in
the Universe)
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Gell-Mann and Low:
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Khriplovitch (1969); t’ Hooft (1972)Gross, Politzer and Wilczek (1973):
Gell-Mann and Low:
QCD:
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Khriplovitch (1969); t’ Hooft (1972)Gross, Politzer and Wilczek (1973):
“running coupling constant” | |
Gell-Mann and Low:
QCD:
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QCD running coupling constant
| |
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A Puzzle: Murray Gell-Mann lecture ca 1975
Noether current of Scale symmetry
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A Puzzle: Murray Gell-Mann lecture ca 1975
Noether current of Scale symmetry
Current divergence
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A Puzzle: Murray Gell-Mann lecture ca 1975
Noether current of Scale symmetry
Current divergence
Yang-Mills Stress Tensor
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A Puzzle: Murray Gell-Mann lecture ca 1975
Noether current of Scale symmetry
Current divergence
Yang-Mills Stress Tensor
Compute:
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A Puzzle: Murray Gell-Mann lecture ca 1975
Noether current of Scale symmetry
Current divergence
Yang-Mills Stress Tensor
Compute:
QCD is scale invariant!!!???
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Resolution: The Scale Anomaly
gluon
gluon
gluons and quarks
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See Murraypalooza talk:Conjecture on the physical implications of the scale anomaly.
Christopher T. Hill (Fermilab) . hep-th/0510177
Resolution: The Scale Anomaly
Origin of Mass in QCD = Quantum Mechanics
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Murraypalooza Santa Fe July 2005
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‘t Hooft Naturalness:
Small ratios of physical parameters are controlled by symmetries. In the limit that a
ratio goes to zero, there is enhanced symmetry (“custodial symmetry”).
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‘t Hooft Naturalness:
0
Small ratios of physical parameters are controlled by symmetries. In the limit that a
ratio goes to zero, there is enhanced symmetry (“custodial symmetry”).
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‘t Hooft Naturalness:
Small ratios of physical parameters are controlled by symmetries. In the limit that a
ratio goes to zero, there is enhanced symmetry (“custodial symmetry”).
0 h - 0
0
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‘t Hooft Naturalness:
Small ratios of physical parameters are controlled by symmetries. In the limit that a
ratio goes to zero, there is enhanced symmetry (custodial symmetry).
Classical Scale Invariance is the “Custodial Symmetry” of QCD
0 h - 0
0
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‘t Hooft Naturalness:
Small ratios of physical parameters are controlled by symmetries. In the limit that a
ratio goes to zero, there is enhanced symmetry (custodial symmetry).
0 h - 0
0
Large hierarchies are natural!
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Many theories were proposed to imitate QCDfor the electroweak scale.
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Many theories were proposed to imitate QCDfor the electroweak scale.
All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of vWeak <<
MGut, Planck
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Many theories were proposed to imitate QCDfor the electroweak scale.
(1)Technicolor(2)Supersymmetric Technicolor(3)Extended Technicolor(4)Multiscale Technicolor(5)Walking Extended Technicolor(6)Topcolor Assisted Technicolor(7)Top Seesaw(8)Supersymmetric Walking Extended Technicolor(9)Strong dynamics from extra-dimensions(10)….
All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of vWeak <<
MGut, Planck
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Many theories were proposed to imitate QCDfor the electroweak scale.
(1)Technicolor(2)Supersymmetric Technicolor(3)Extended Technicolor(4)Multiscale Technicolor(5)Walking Extended Technicolor(6)Topcolor Assisted Technicolor(7)Top Seesaw(8)Supersymmetric Walking Extended Technicolor(9)Strong dynamics from extra-dimensions(10)….
All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of vWeak <<
MGut, Planck
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Many theories were proposed to imitate QCDfor the electroweak scale.
(1)Technicolor(2)Supersymmetric Technicolor(3)Extended Technicolor(4)Multiscale Technicolor(5)Walking Extended Technicolor(6)Topcolor Assisted Technicolor(7)Top Seesaw(8)Supersymmetric Walking Extended Technicolor(9)Strong dynamics from extra-dimensions(10)….
All of these featured “strong dynamics” and classical scale invariance as the custodial symmetry of vWeak <<
MGut, Planck
Mass extinction of theories on July 4th 2012
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Susy is still alive?
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Susy is still alive?
But, where is it?
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F e me
2
_
e mede = 2
(me/MeV)
( /GeV)2= 0.2 x 10-16 (e-cm) x _______
Current limit: de < 10-27 e-cm
> 1.4 x 105 GeV
Why EDM’s are so powerful:
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Are EDM’s telling us something about SUSY?:
Fe me
_
Mselectron > 6.8 x 103 GeV ( sin)1/2
e e
selectron
wino wino
= sinsin2 1/Mselectron
Future limit: de < 10-29 e-cm -- 10-32 e-cm ?
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It is possible that we need only the strongest coupled SUSY
partners to the Higgs Boson to be nearby in mass
e.g., “The More minimal supersymmetric standard model”A, G. Cohen , D.B. Kaplan, A.E. Nelson Phys.Lett. B388 (1996) 588-598
e.g., “Natural SUSY” : A Light Stop
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Weak Scale SUSY was seriously challengedbefore the LHC turned on (e.g. EDM’s)
MSSM now copes with severe direct limits;Some nMSSM models survive
If SUSY is the custodial symmetrywe should see it in LHC RUN-II
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Bardeen: Classical Scale Invariancecould be the custodial symmetry of a fundamental, perturbatively
light Higgs Boson.
On naturalness in the standard model.William A. Bardeen
FERMILAB-CONF-95-391-T, Aug 1995. 5pp.
The only manifestations of Classical Scale Invariance breaking by
quantum loops are d = 4 scale anomalies
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Can a perturbative Higgs Boson masscome from quantum mechanics?
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v = “VEV” = 175 GeV
Radius of hat:
Curvature in brim:mHiggs = 126 GeV
i.e., can quantum mechanics makea Mexican hat?
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4
2_
v
Start with the Classically Scale Invariant Higgs Potential
Scale Invariance -> Quartic Potential -> No VEV
v
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2
__
Quantum loops generate a logarithmic “running” of the quartic coupling, ala Gell-Mann & Low
(v) log (v/M)
~
running couplings have many possible trajectories, each parameterized by some
M
v
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Quantum loops generate a logarithmic “running” of the quartic coupling
Nature chooses a particular trajectorydetermined by dimensionless cc’s.
v
2
__(v) log (v/M)
~
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v
this is the relevant behavior passing from 0 to 0 requires 0~
2
__(v) log (v/M)
~
Quantum loops generate a logarithmic “running” of the quartic coupling
~ ~
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Result: “Coleman-Weinberg Potential”
2
__(v)
v
v
4
Potential Minimum arises from running ofi.e. Quantum Mechanics
~
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Classical potential
V =
Quantum running of
Expand around a hypothetical VEV, v
runs according to RG equation:
A bit more mathematically:
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The resulting potential:
Demand that v is an extremum:
Demand v is a minimum, boson mass:
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|H|4
2_
<H> = v
Start with the Classically Scale Invariant Higgs Potential
Apply this to the Higgs Boson
Scale Invariance -> Quartic Higgs Potential -> No VEV
v
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Extremum, and curvature of potential (mass):
Higgs mass
Higgs VEV, v
What do we need to make a Mexican Hatfrom quantum mechanics?
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Renormalization Group Equation of Gell-Mann and Low
topH
top
g = top Yukawa cc
What does theory predict for ?
(I am ignoring small EW contributionsfor simplicity of discussion)
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R is negative in Standard Model
No solution !
approximate SM physical values:
Top Yukawa cc:Higgs quartic cc:
We require positive to have aminimum, stable (mh
2 0) potential
v
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Requires New Bosonic physics beyond the standard model
Bardeen, Eichten, CTH, G G Ross …
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Simplest hypothesis:
The missing bosonic matter may bea second Higgs doublet
that has no VEV:
“Dormant” or “Inert” Higgs Boson
Requires New Bosonic physics beyond the standard model
Bardeen, Eichten, CTH, G G Ross …
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Item Type: Thesis (Dissertation (Ph.D.))
Degree Grantor: California Institute of Technology
Division: Physics, Mathematics and Astronomy
Major Option: Physics
Thesis Availability: Public (worldwide access)
Research Advisor(s): •Gell-Mann, Murray
Thesis Committee: •Gell-Mann, Murray (chair)•Tollestrup, Alvin V.•Barish, Barry C.•Ross, Graham•Feynman, Richard Phillips
http://thesis.library.caltech.edu/4505/
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Item Type: Thesis (Dissertation (Ph.D.))
Degree Grantor: California Institute of Technology
Division: Physics, Mathematics and Astronomy
Major Option: Physics
Thesis Availability: Public (worldwide access)
Research Advisor(s): •Gell-Mann, Murray
Thesis Committee: •Gell-Mann, Murray (chair)•Tollestrup, Alvin V.•Barish, Barry C.•Ross, Graham•Feynman, Richard Phillips
http://thesis.library.caltech.edu/4505/
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CTH, C N Leung, S RaoNPB262 (1985) 517
Masslesstwo doublet
potential
Two doubletRG
equations
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CTH, C N Leung, S RaoNPB262 (1985) 517
Masslesstwo doublet
potential
Two doubletRG
equations
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H2
H
H
H
H
Positive can come from the second Higgs Doublet
This modifies the RG equation:
Note: I include the full one-loop RG eqns.with EW cc’s etc in the analysis, but omitit in the discussion for simplicity.
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Can now solve for :
g = gtop 1
Extremum, and curvature of potential (mass):
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M2 is determined heavy “dormant” Higgs doublet
Production, mass, and decay details are model dependent
No VeV but coupled to SU(2) xU(1):
“Dormant” Higgs Doublet (vs. “Inert”)
The New Doublet has a positive M2
If Dormant Higgs couples to SU(2) x U(1) but not fermions
Parity H2 H2 implies stabity:H2 H2
0 + (eif MM0
Then H20
is stable dark matter WIMP
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CalcHEP estimatesvery preliminary!!!
pp -> H0 H0
pp -> H+ H-
pp -> H+ H0
fb
The Dormant Doublet is pair producedabove threshold near 2MH 800 GeV
pp X *, W*, h*) X H H*
H0
-> bb = 45 GeV Assume gb‘ = 1
H+ -> tb = 14 GeV fb
fb More work needed
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The trilinear and quartic Higgs couplings will be significantly different than in SM case
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R Demisek,T H Jung, H D Kim[hep-ph] 1308.0891
Trilinear term = (5/3) x SM
Quartic term = (11/3) x SMThis may be doable at LHC !
The trilinear and quartic Higgs couplings will be significantly different than in SM case
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GeV) = 4.79 (black) GeV) = -0.1 (red) GeV) = 0.1 (green)gtop= 1 (blue)= = 0
Landau Pole = 9.5 TeV
UV instabilityimplying strong scale?
Landau Pole -> Composite H2
New Strong Dynamics
Log(vweak)
Log(vweak)
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Hambye-Strumia model has nice features[hep-ph]1306.2329
H2 develops a Coleman-Weinberg potential and VEV v2
3 is negative and gives the Higgs boson its -m2 |H2 |2
The model does not require large quartic cc’s, hassensible UV behavior
H2 and associatedgauge fields becomeviable dark matter
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I think this is a very important scientific question:
Is the Higgs potential Coleman-Weinberg?
• Examined a “maximally visible” scheme• Requires new bosonic contribution(s) to RG
• Dormant Higgs Boson from std 2-doublet scheme M 400 GeV
• May be observable, LHC run III?• Higgs trilinear and quartic couplngs non-standard
• UV problem -> new strong scale 10 TeV• New bosons may be dark matter
Perhaps we live in a world where allMass comes from quantum effects
No classical mass input parameters.
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QCD and Higgs may be telling ussomething very profound:
All mass in nature may be a quantum phenomenon !
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“All mass is a quantum phenomenon”
Max Planck
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“All mass is a quantum phenomenon”is almost as jolting as being told that
“light comes in quanta!”
Max Planck
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(a heretic)
What if all mass comes from Quantum Physics?
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It’s a very heretical conjecture:
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We live in D=4!
Cosmological constant is zero in classical limit
QCD scale is generated in this way; Hierarchyis naturally generated
Testable in the Weak Interactions!
“Predictions” of the Conjecture:
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We live in D=4!
Cosmological constant is zero in classical limit
QCD scale is generated in this way; Hierarchyis naturally generated
Testable in the Weak Interactions!
String Theory RULED OUT (classical string scale)
“Predictions” of the Conjecture:
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Conjecture on the physical implications of the scale anomaly.Christopher T. Hill (Fermilab) . hep-th/0510177
We live in D=4!
Cosmological constant is zero in classical limit
QCD scale is generated in this way; Hierarchyis naturally generated
Testable in the Weak Interactions!
Weyl Gravity in D=4 is QCD-like:
String Theory RULED OUT (classical string scale)
“Predictions” of the Conjecture:
Weyl Gravity?Weyl Gravity is Renormalizeable!
The Planck Mass Comes From Quantum Mechanics!
See:(and refs.therein)
Predicts D=4!
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The String-o-Centric Universe
-infinity
Planck Scaleat the center
Hubble Scale
QCD Scale
Weak Scale
Log()
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A more Copernican idea:The “Scaloplex”
Log() infinity-infinity
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The classical “Scaloplex” isinfinite, uniform, and isotropic
infinity-infinity
Planck ScaleHubble Scale
Log()
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Physics is determined by local values ofdimensionless coupling constants at any log
infinity-infinity
Planck ScaleHubble Scale
g0 = g
Log()
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infinity-infinity
Planck Scale’Hubble Scale’
an equivalent universe 101000 x
Log()
Physics is determined by local values ofdimensionless coupling constants
g0 = g(101000)
g0 = g’
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infinity-infinity
Planck Scale’’Hubble Scale’’
an equivalent universe 10-1000 x
Log()
Physics is determined by local values ofdimensionless coupling constants
g0 = g(10-1000)
g0 = g’’
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Conjecture: Can a local translational symmetryin the scaloplex enforce ‘t Hooft naturalness
of all small mass ratios?
m
M__ m’
M__
Additive relationships between large and small are then forbidden:
m
m+M
_____ m’ +M
M______ m
M
M
Dilaton?
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We live in D=4!
Cosmological constant is zero in classical limit
QCD scale is generated in this way; Hierarchyis naturally generated
Testable in the Weak Interactions!
Weyl Gravity in D=4 is QCD-like:
String Theory RULED OUT (classical string scale)
“Predictions” of the Conjecture:
Weyl Gravity:Weyl Gravity is Renormalizeable!
The Planck Mass Comes From Quantum Mechanics!
Predicts D=4!
We Live in a Scaloplex !!!
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Amazon.com
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