Dynamical Mass Generation by Strong Yukawa Interactions Tom

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Dynamical Mass Generation by Strong Yukawa
InteractionsTomáš Brauner and Jirí Hošek,
Phys.Rev.D72 045007(2005)Petr Beneš, Tomáš
Brauner and Jirí Hošekhep-ph/0605147 CERN
Yellow Book hep-ph/0608079

• Lagrangian and its properties
• Fermion mass generation and scalar boson mass
  splitting
• Where is the Nambu-Goldstone boson ?
• Gauge boson mass generation
• Symmetry-breaking loop-generated vertices
• SU(2)xU(1) generalization

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1. Lagrangian and its propertiesremember
arrows of the fields
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Symmetry
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• Why two fermion species no axial anomaly
• With M2gtO no symmetry breakdown in scalar sector
  itself
• Comparison with Higgs mechanism by heart (see the
  Lagrangian)

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II. Fermion mass generation and scalar boson mass
splitting

• ASSUME that Yukawa interactions generate the
  chiral-symmetry breaking fermion proper
  self-energies S

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THEN Yukawa interactions generate the
symmetry-breaking scalar proper self-energy ?
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Yukawa interactions GENERATE SProvided solutions
for anomalous proper self-energies ? exist
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Explicit form of the coupled Schwinger-Dyson
equations (not very illuminating)
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NICELY CONVERGENT KERNEL (corresponding counter
terms prohibited by symmetry)

• By dimensional argument
• Compare with Higgs

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Boson mass splitting

• In particular case of real ? found numerically
• the real and imaginary parts of F are the mass
  eigenstates with masses

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Solutions found for LARGE YUKAWA COUPLINGS
numerically (exploratory stage (!!!))1. Line of
critical couplings
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2.Typical shape of UV-finite solutions S and ? .
They are found numerically upon Wick rotation in
SD equations.
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3. Large amplification of the fermion mass ratios
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• Large amplification of fermion mass ratios as a
  response to small changes in Yukawa coupling
  ratios
• Explicit knowledge of non-analytic dependences of
  masses upon couplings
• ULTIMATE DREAM
• Coupling constant ? ignored as unimportant for
• non-perturbative mass generation

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III. Where is the Nambu-Goldstone boson ?

• Axial-vector current
• Axial-vector Ward identities for proper vertices

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For S, ? non-zero the identities imply the
massless pole in proper vertices G
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Basic quantities to be calculated are the UV
finite vectorial tadpoles I
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Effective NG couplings are related to S and ?
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The overall normalization is given by tadpoles I
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IV. Gauge boson mass generation

• Gauge boson mass squared is the residue at the
  massless pole of the gauge field polarization
  tensor
• (Schwinger)

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• In Higgs (complete polarization tensor)

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In strongly coupled models no control on the
bound-state spectrum except NG. Consequently,
only the longitudinal part can be computed. By
transversality
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V. Symmetry-breaking loop-generated UV-finite
vertices genuine (albeit gedanken) predictions
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An illustration Three-gluon vertex (G is
computed)
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VI. Outlook (bona fide)

• - Common source of fermion and gauge-boson mass
  generation
• Hope for natural description of wide, sparse and
  irregular fermion mass spectrum
• Basic SU(2)xU(1) generalization exists
• T. Brauner, J.H., A model of flavors,
• hep-ph/0407339 introduce TWO DISTINCT
  massive scalar SU(2)xU(1) doublets. I LIKE
  SCALARS-THEY FEEL FLAVORS.
• - Phenomenological viability is to be investigated