A model of soft mass generation

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A model of soft mass generation

• Jirí Hošek
• Department of Theoretical Physics
• Nuclear Physics Institute
• Rež (Prague)
• hosek_at_ujf.cas.cz

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1. AN OLD-FASHIONED REASONING

• In (mysterious) SU(2)LxU(1)Y IF fermion masses
  are generated dynamically without elementary
  scalars by a new interaction the intermediate
  masses follow (Schwinger). Hence, fermion masses
  are of primary concern. L-R and interfamily
  connections needed.
• Composite (bound state) would-be NG bosons gt
  New interaction must be strong.
• Massiveness is a low-momentum phenomenon
  Dynamical mass generation should be low-momentum
  dominated. Right choice of the degrees of
  freedom Massive complex vector field.

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2. THE MODEL

• LSM is the SM Lagrangian of three fermion
  families supplemented with neutrino right-handed
  singlets
• LF Heavy complex vector field Cµ interacting
  with family-changing current of the left- and
  right-handed fermion electroweak multiplets

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• SU(2)LxU(1)Y invariance is manifest
• NEW GLOBAL U(1)F

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• Renormalizability
• No one-loop vertex corrections
• Hard right-handed Majorana mass term only for one
  family
• Mgt107 GeV CHALLENGE !!!

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3. FERMION MASS GENERATIONself-consistent
variational (nonperturbative)

• ASSUME S are dynamically
  generated

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S implies nondiagonal part of C boson propagator
D

• effective bilinear Lagrangian
• Nondiagonal part of the propagator

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FERMION SCHWINGER-DYSON EQUATIOS extra convergent
kernels all fermion masses in the world related
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A HOPE

• Approximations hard fermion masses p0 ?M
• Integral equations turn into UV finite calculable
  integrals

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System of implicit coupled equations for the
fermion masses can be analyzed

• abbreviate

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Once we solve the equation f(y)0 the fermion
masses are given. Solutions are found.
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4. W AND Z BOSON MASS GENERATION

• Dynamically generated S break SU(2)LxU(1)Y down
  to U(1)em
• The would-be NGs (composite !) are visualized
  in WT identities

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From the pole terms we extract the effective
vertices between the gauge and three
multicomponenet NG bosons. These vertices give
rise to the longitudinal parts of W and Z
polarization tensors with massless poles
(Schwinger). Their residues are
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• W and Z boson masses are related to the fermion
  masses by sum rules
• From a model of S the sum rules are saturated by
  the top quark mass
• Weinbergs relation tolerably violated

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5. SPONTANEOUS BREAKDOWN OF THE GLOBAL U(1)F
SYMMETRY

• S and ? dynamically generated by strong C
  boson-fermion interaction break spontaneously the
  global U(1)F
• Massless NG pseudoscalar phenomenologically
  dangerous

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• Multicomponent bound state of both fermions and
  Ciµ
• Effective couplings to fermions negligibly small
  due to C admixture
• Weinberg-Wilczek axion ?

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6. CONCLUDING COMMENTS (work in progress)

• We believe in stiff dynamics underlying SM
• Admiration for Wilson
• Strongly coupled model of Kroll, Lee, Zumino
• Model requires several families

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