The Higgs boson and its mass
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Transcript of The Higgs boson and its mass
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The Higgs boson and its mass
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LHC : Higgs particle observation
CMS 2011/12
ATLAS 2011/12
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a prediction…
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Higgs boson found
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standard model Higgs boson
T.Plehn, M.Rauch
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Spontaneous symmetry breaking confirmed at
the LHC
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Higgs mechanism verified
Higgs Brout Englert
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Spontaneous symmetry breaking
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Physics only describes probabilities
Gott würfelt
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Physics only describes probabilities
Gott würfelt Gott würfelt nicht
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Physics only describes probabilities
Gott würfelt
Gott würfelt nicht
humans can only deal with probabilities
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Spontaneous symmetry breaking
Fermi scale
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Scalar potential
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Radial mode and Goldstone mode
expand around minimum of potential
mass term for radial mode
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massless Goldstone mode
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Abelian Higgs mechanism
supraconductivitycoupling of complex scalar field to photon
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Abelian Higgs mechanism
supraconductivity
massive photon !
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Gauge symmetry
Goldstone boson is gauge degree of freedomno physical particlecan be eliminated by gauge transformationin favor of longitudinal component of massive photon
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Photon mass m=e φ
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Standard – Model of electroweak
interactions :Higgs - mechanism
The masses of all fermions and gauge bosons are proportional to the ( vacuum expectation ) value of a scalar field φH ( Higgs scalar )
For electron, quarks , W- and Z- bosons :
melectron = helectron *
φH etc.
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lessons
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1
Vacuum is complicated
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mass generated by vacuum properties
particles: excitations of vacuum
Their properties depend on properties of vacuum
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vacuum is not empty !
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2
Fundamental “constants” are not
constant
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Have coupling constants in the early Universe other values than today ?Yes !
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Masses and coupling constants are determined by properties of vacuum !Similar to Maxwell – equations in matter
Fundamental couplings in quantum field theory
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Condensed matter physics :
laws depend on state of the system
Ground state , thermal equilibrium state …
Example : Laws of electromagnetism in superconductor are different from Maxwells’ laws
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Standard model of particle physics :
Electroweak gauge symmetry is spontaneously broken by expectation value of Higgs scalar
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Cosmology :
Universe is not in one fixed state
Dynamical evolutionLaws are expected to depend
on time
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Restoration of symmetryat high temperature in the early Universe
High TSYM <φ>=0
Low TSSB<φ>=φ0 ≠ 0
high T :Less orderMore symmetry
Example:Magnets
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Standard – Model of electroweak
interactions :Higgs - mechanism
The masses of all fermions and gauge bosons are proportional to the ( vacuum expectation ) value of a scalar field φH ( Higgs scalar )
For electron, quarks , W- and Z- bosons :
melectron = helectron *
φH etc.
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In hot plasma of early Universe :
masses of electron und muon
not different!
similar strength of electromagnetic and weak
interaction
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electromagnetic phase transition in early
universe
10-12 s after big bang
most likely smooth crossover
could also be moreviolent first ordertransition
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Varying couplings
How strong is present variation of couplings ?
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Can variation of fundamental “constants” be
observed ?
Fine structure constant α (electric charge)
Ratio electron mass to proton mass
Ratio nucleon mass to Planck mass
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Time evolution of couplings and scalar fields
Fine structure constant depends on value of
cosmon field : α(φ)
in standard model: couplings depend on value of Higgs scalar field
Time evolution of φ Time evolution of α
Jordan,…
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Static scalar fieldsIn Standard Model of particle physics : Higgs scalar has settled to its present
value around 10-12 seconds after big bang. Chiral condensate of QCD has settled at
present value after quark-hadron phase transition around 10-6 seconds after big bang .
No scalar with mass below pion mass. No substantial change of couplings after
QCD phase transition. Coupling constants are frozen.
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Observation of time- or space- variation of
couplings
Physics beyond Standard Model
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Particle masses in quintessence cosmology
can depend on value of cosmon field
similar to dependence on value of Higgs field
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3
Standard model of particle physics could be valid down to the Planck
length
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The mass of the Higgs boson, the great
desert, and asymptotic safety of gravity
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a prediction…
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key points
great desert solution of hierarchy problem at
high scale high scale fixed point vanishing scalar coupling at fixed
point
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no supersymmetry
no low scale higher dimensions
no technicolorno multi-Higgs model
Planck scale, gravity
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Quartic scalar coupling
prediction of mass of Higgs boson
=
prediction of value of quartic scalar coupling λ
at Fermi scale
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Radial mode = Higgs scalar
expansion around minimum of potential
mass term for radial mode
Fermi scale
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Running couplings, Infrared interval,UV-IR mapping
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renormalization
couplings depend on length scale,or mass scale k
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Running quartic scalar coupling λ
and Yukawa coupling of top quark h
neglect gauge couplings g
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running SM couplings
Degrassi et al
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Partial infrared fixed point
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infrared interval
allowed values of λ or λ/h2 at UV-scale Λ :
between zero and infinity are mapped to finite infrared interval of
values of λ/h2 at Fermi scale
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infrared interval
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realistic mass of top quark (2010),
ultraviolet cutoff: reduced Planck mass
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ultraviolet- infrared map
Whole range of small λ at ultraviolet scale is mapped
byrenormalization flow to lower bound of infrared
interval !Prediction of Higgs boson
mass close to 126 GeV
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high scale fixed point
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high scale fixed point
with small λ
predicts Higgs boson mass close to 126 GeV
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key points
great desert solution of hierarchy problem at
high scale high scale fixed point vanishing scalar coupling at fixed
point
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fixed point in short-distance theory
short-distance theory extends SM minimal: SM + gravity higher dimensional theory ? grand unification ? ( almost) second order electroweak phase
transition guarantees ( approximate ) fixed point of flow
needed : deviation from fixed point is an irrelevant parameter (A>2)
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asymptotic safety for gravity
Weinberg , Reuter
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running Planck mass
infrared cutoff scale k ,
for k=0 :
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fixed point for dimensionless ratio M/k
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scaling at short distances
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infrared unstable fixed point:
transition from scaling to constant Planck mass
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modified running of quartic scalar coupling in presence of
metric fluctuations
for a > 0 and small h :
λ is driven fast too very small values !
e.g. a=3 found in gravity computations
+…
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short distance fixed point at λ=0
interesting speculation
top quark mass “predicted” to be close to minimal value , as found in experiment
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running quartic scalar coupling
Degrassi et al
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Sensitivity to Higgs boson mass
for given top quark mass
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top “prediction” for known Higgs boson mass
for mH =126 Gev :
mt = 171.5 GeV
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conclusions
observed value of Higgs boson mass is compatible with great desert
short distance fixed point with small λ predicts Higgs boson mass close to 126 GeV
prediction in SM+gravity, but also wider class of models
desert: no new physics at LHC and future colliders
relevant scale for neutrino physics may be low or intermediate ( say 1011 GeV ) - oasis in desert ?
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end
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gauge hierarchy problemand
fine tuning problem
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quantum effective potential
scalar field χ with high expectation value M,say Planck mass
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anomalous mass dimension
one loop, neglect gauge couplings g
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fixed point for γ = 0 zero temperature electroweak phase
transition (as function of γ ) is essentially second order
fixed point with effective dilatation symmetry
no flow of γ at fixed point
naturalness due to enhanced symmetry small deviations from fixed point due to
running couplings: leading effect is lower bound on Fermi scale by quark-antiquark condensates
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critical physics
second order phase transition corresponds to critical surface in general space of couplings
flow of couplings remains within critical surface
once couplings are near critical surface at one scale, they remain in the vicinity of critical surface
gauge hierarchy problem : explain why world is near critical surface for electroweak phase transition
explanation can be at arbitrary scale !
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critical physics in statistical physics
use of naïve perturbation theory ( without RG – improvement ) would make the existence of critical
temperature look “unnatural”
artefact of badly converging expansion
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self-tuned criticality deviation from fixed point is an irrelevant
parameter (A>2) critical behavior realized for wide range
of parameters in statistical physics : models of this type
are known for d=2 d=4: second order phase transitions
found , self-tuned criticality found in models of
scalars coupled to gauge fields (QCD), Gies…
realistic electroweak model not yet found
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SUSY vs Standard Model
natural predictions baryon and lepton number conservation
SM flavor and CP violation described by CKM
matrix SM absence of strangeness violating neutral
currents SM g-2 etc.
SM dark matter particle (WIMP)
SUSY
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gravitational running
a < 0 for gauge and Yukawa couplings asymptotic freedom
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bound on top quark massquartic scalar coupling has to remain positive during flow( otherwise Coleman-Weinberg symmetry breaking at high scale)
~170 GeV