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Spontaneous breakdown (SB) of symmetry

Spontaneous breakdown (SB) of symmetry. real scalar j. v.e.v. Z 2 symmetry. SB. mass of x :. field redefinition. +fermion y. chiral symmetry. mass term. :forbidden. mass of y :. fermion mass generation by SB. complex scalar field f. global U(1) symmetry. v.e.v. SB.

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Spontaneous breakdown (SB) of symmetry

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  1. Spontaneous breakdown (SB) of symmetry real scalarj v.e.v. Z2 symmetry SB mass of x : field redefinition +fermion y chiral symmetry mass term :forbidden mass of y : fermion mass generation by SB complex scalarfield f global U(1) symmetry v.e.v. SB field redefinition masses of x, c : c : Nambu-Goldstone boson

  2. Goldstone Theorem If a symmetry under continuous group is broken spontaneously, the system includes a massless field. The massless particle is called Nambu- Goldstone field. +fermiony mass term : forbidden chiral U(1)×U(1) symmetry mass of y : fermion mass generation by SB Higgs mechanism complex scalar field f, U(1)gauge field Am v.e.v. U(1) gauge symmetry SB field redefinition mass of A' The gauge boson mass is generated. mass of x The NG boson c is absorbed byA'.

  3. Non-Abelian Gauge Theory SU(2) gaugefield SU(2) gauge symmetry transformation invariant Lagrangian density

  4. Spontaneous Breakdown of Non-Abelian Gauge Symmetry SU(2) gaugefield SU(2) doublet complex scalar real field SU(2) gauge symmetry transformation (t i ： Paulimatrix) invariant Lagrangian density + potential = V V

  5. + potential = V V

  6. 微分　 2m2|f|+4l|f|3=0 the lowest energy state If m2<0 (the vacuum state) occurs at The vacuum violates SU(2) gauge symmetry spontaneously. vacuum expectation value (v.e.v.) redefinition x, c i : real Then

  7. redefinition x, c i : real Then

  8. ]22 (v+x)2 gtjW'mjgtiW'jm [

  9. mass of W' The gauge boson mass is generated. mass of x The gauge boson becomes massive by absorbing NG boson c.

  10. Weinberg Salam Model SU(2)×U(1)gauge symmetry SU(2) gaugefield U(1) gaugefield Higgsfield complex scalar,SU(2) doublet Yf=1 quark lepton Lorentz group SU(3) U(1)hypercharge SU(2) quark lepton quark lepton -1 1 1/3 2 3 0 4/3 1 1 3 -2 -2/3 Lagrangian density

  11. Lagrangian density

  12. the vacuum is at If m2<0 SU(2)×U(1)gauge sym. is broken spontaneously v.e.v.

  13. = gauge field mixing Weinberg angle mass of gauge fields W & Z get massive absorbing c. mass of x

  14. Am:electromagnetic field The electromagnetic U(1) gauge symmetry is preserved. , electromagnetic coupling constant = gauge field mixing Weinberg angle mass of gauge fields W & Z get massive absorbing c. mass of x

  15. Am:electromagnetic field The electromagnetic U(1) gauge symmetry is preserved. , electromagnetic coupling constant electroweak boson kinetic terms and self-interactions

  16. gauge-boson fermion interaction terms

  17. gauge-boson fermion interaction terms (QCD含む)

  18. Yukawa interaction fermion mass term

  19. diagonalization diagonal Cabibbo-Kobayashi-Maskawa matrix Maki-Nakagawa-Sakata matrix +h.c. +h.c.

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