Dynamical Mass Generation by Strong Yukawa Interactions Tom Brauner and Jir Hoek, Phys'Rev'D72: 0450

1
Dynamical Mass Generation by Strong Yukawa
InteractionsTomá Brauner and Jirí Hoek,
Phys.Rev.D72 045007(2005)Petr Bene, Tomá
Brauner and Jirí Hoekhep-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

2
1. Lagrangian and its propertiesremember
arrows of the fields
3
Symmetry
4

• 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)

5
II. Fermion mass generation and scalar boson mass
splitting

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

6
THEN Yukawa interactions generate the
symmetry-breaking scalar proper self-energy ?
7
Yukawa interactions GENERATE SProvided solutions
for anomalous proper self-energies ? exist
8
Explicit form of the coupled Schwinger-Dyson
equations (not very illuminating)
9
NICELY CONVERGENT KERNEL (corresponding counter
terms prohibited by symmetry)

• By dimensional argument
• Compare with Higgs

10
Boson mass splitting

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

11
Solutions found for LARGE YUKAWA COUPLINGS
numerically (exploratory stage (!!!))1. Line of
critical couplings
12
2.Typical shape of UV-finite solutions S and ? .
They are found numerically upon Wick rotation in
SD equations.
13
3. Large amplification of the fermion mass ratios
14

• 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

15
III. Where is the Nambu-Goldstone boson ?

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

16
For S, ? non-zero the identities imply the
massless pole in proper vertices G
17
Basic quantities to be calculated are the UV
finite vectorial tadpoles I
18
Effective NG couplings are related to S and ?
19
The overall normalization is given by tadpoles I
20
IV. Gauge boson mass generation

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

21

• In Higgs (complete polarization tensor)

22
In strongly coupled models no control on the
bound-state spectrum except NG. Consequently,
only the longitudinal part can be computed. By
transversality
23
V. Symmetry-breaking loop-generated UV-finite
vertices genuine (albeit gedanken) predictions
24
An illustration Three-gluon vertex (G is
computed)
25
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