Chiral freedom and the scale of weak interactions - PowerPoint PPT Presentation

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Chiral freedom and the scale of weak interactions

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chiral couplings to. quarks and leptons ... large chiral coupling for top leads to large effective attractive interaction for top quark ... – PowerPoint PPT presentation

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Title: Chiral freedom and the scale of weak interactions


1
Chiral freedomand the scale ofweak interactions
2
proposal for solution of gauge hierarchy problem
  • model without fundamental scalar
  • new anti-symmetric tensor fields
  • mass term forbidden by symmetry
  • chiral couplings to quarks and leptons
  • chiral couplings are asymptotically free
  • weak scale by dimensional transmutation

3
antisymmetric tensor fields
  • two irreducible representations of Lorentz
    symmetry (3,1) (1,3)
  • complex representations (3,1) (1,3)
  • similar to left/right handed spinors

4
chiral couplings to quarks and leptons
  • most general interaction consistent with Lorentz
    and gauge symmetry ß are weak doublets with
    hypercharge
  • consistent with chiral parity
  • d R , e R , ß - have odd chiral parity

5
no local mass term allowed for chiral tensors
  • Lorentz symmetry forbids (ß) ß
  • Gauge symmetry forbids ß ß
  • Chiral parity forbids (ß-) ß

6
kinetic term
  • does not mix ß and ß
  • consistent with all symmetries, including chiral
    parity

7
quartic couplings
add gauge interactions and gauge invariant
kinetic term for fermions
8
classical dilatation symmetry
  • action has no parameter with dimension mass
  • all couplings are dimensionless

9
consistency of chiral tensors ?
10
B - basis
  • B fields are unconstrained
  • six complex doublets
  • vectors under space rotations
  • irreducible under Lorentz -transformations

11
free propagator
inverse propagator has unusual form
propagator is invertible ! except for pole at q
2 0
12
energy density
positive for longitudinal mode b3 vanishes for
transversal modes b1,2 ( borderline to stability
) unstable secular classical solutions in free
theory quantum theory free Hamiltonian is not
bounded
13
no consistent free theory !
14
interacting chiral tensors can be consistently
quantized
  • Bounded Hamiltonian permits canonical
    quantization
  • Interactions will decide on which side of the
    borderline between stability and instability the
    model lies.
  • Vacuum not perturbative
  • Non perturbative generation of mass
  • stable massive spin one particles !
  • Chirons

15
asymptotic freedom
16
evolution equations for chiral couplings
17
evolution equations for top coupling
fermion anomalous dimension
tensor anomalous dimension
no vertex correction
asymptotic freedom !
Similar observation in abelian model
Avdeev,Chizhov 93
18
dimensional transmutation
  • Chiral coupling for top grows large
  • at chiral scale ?ch
  • This sets physical scale dimensional
    transmutation -
  • similar to ?QCD in strong QCD- gauge interaction

19
spontaneous electroweaksymmetry breaking
20
top anti-top condensate
  • large chiral coupling for top leads to large
    effective attractive interaction for top quark
  • this triggers condensation of top anti-top
    pairs
  • electroweak symmetry breaking effective Higgs
    mechanism provides mass for weak bosons
  • effective Yukawa couplings of Higgs give mass to
    quarks and leptons

cf Miranski Bardeen, Hill, Lindner
21
Schwinger - Dyson equationfor top quark mass
  • solve gap equation for top quark propagator

22
SDE for B-B-propagator
23
gap equation for top quark mass
  • has reasonable solutions for mt somewhat above
    the chiral scale

24
two loop SDE for top-quark mass
contract B- exchange to pointlike four fermion
interaction
tL
tR
25
effective interactions
  • introduce composite field for top- antitop bound
    state
  • plays role of Higgs field
  • new effective interactions involving the
    composite scalar f

26
effective scalar tensor interactions
27
chiral tensor gauge boson - mixing
and more
28
massive chiral tensor fields
29
massive spin one particles
  • new basis of vector fields
  • standard action for massive vector fields
  • classical stability !

Z(q) 1 m2 / q2
30
classical stability
  • massive spin one fields stable
  • free theory borderline stability/instability,
  • actually unstable ( secular solutions , no
    ghosts)
  • mass term moves theory to stable region
  • positive energy density

31
non perturbative mass term
  • m2 local in S - basis , non-local in B basis
  • cannot be generated in perturbation theory in
    absence of electroweak symmetry breaking
  • plausible infrared regularization for divergence
    of inverse quantum propagator as chiral scale is
    approached
  • in presence of electroweak symmetry breaking
    generated by loops involving chiral couplings

32
effective cubic tensor interactions
generated by electroweak symmetry breaking
33
propagator corrections from cubic couplings
non local !
34
effective propagator for chiral tensors
massive effective inverse propagator pole for
massive field
mass term
35
phenomenology
36
new resonances at LHC ?
  • production of massive chirons at LHC ?
  • signal massive spin one resonances
  • rather broad decay into top quarks
  • relatively small production cross section small
    chiral couplings to lowest generation quarks ,
    no direct coupling to gluons

37
mixing of charged spin one fields
  • modification of W-boson mass
  • similar for Z boson
  • watch LEP precision tests !

38
mixing between chiral tensorand photon
39
Pauli term contributes to g-2
  • suppressed by
  • inverse mass of chiral tensor
  • small chiral coupling of muon and electron
  • small mixing between chiral tensor and photon
  • for Mc 300 GeV ?(g-2) 5 10 -9 for muon

40
effective interactions fromchiral tensor exchange
  • solve for Sµ in presence of other fields
  • reinsert solution

41
general solution
propagator for charged chiral tensors
42
electroweak precision tests
  • compatible with LEP experiments
  • for Mc gt 300 GeV

43
mixing of chiral tensors with ? - meson
could contribute to anomaly in radiative pion
decays
44
conclusions
  • chiral tensor model has good chances to be
    consistent
  • mass generation needs to be understood
    quantitatively
  • interesting solution of gauge hierarchy problem
  • phenomenology needs to be explored !
  • if quartic couplings play no major role
  • less couplings than in standard model
    predictivity !

45
end
46
new four fermion interactions
typically rather small effect for lower
generations more substantial for bottom , top !
47
momentum dependent Weinberg angle
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