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Custodial SU(2) Symmetry

Lecture 5:. Custodial SU(2) Symmetry. --- custodial SU(2) symmetry of V(  ).  -parameter in SM. (at tree level). a consequence of custodial SU(2) symmetry of V(  ). Higgs scalar is SU(2) doublet. SU(2) 的基础表示. (loop level). a few percent.  i s SU(2) doublet ：.

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Custodial SU(2) Symmetry

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  1. Lecture 5: Custodial SU(2) Symmetry --- custodial SU(2) symmetry of V()

  2. -parameter in SM (at tree level) a consequence of custodial SU(2) symmetry of V() Higgs scalar is SU(2) doublet SU(2)的基础表示 (loop level) a few percent

  3.  is SU(2) doublet： V() has a custodial SU(2)symmetry SU(2)的基础表示 1 + i 2 3 + i 4  = V()= V(||2) V() has a large symmetry: O(4)  SU(2)  SU(2) O(4) symmetry reduce to: O(3)  SU(2)  get a vev: 3 Goldstone bosons  triplet of O(3) V() has a custodial O(3)  SU(2)symmetry

  4.  is SU(2) doublet： 1 + i 2 3 + i 4  = equal Qup Qdown Qup - Qdown = +1 0 v + 0 SSB  = (Y = +1/2) v 0 0 - SSB  = (Y = -1/2) Q cannot SB only 0 can SB

  5.  is SU(2) doublet： 3 Goldstone bosons – triplet of custodial SU(2) (Y = +1/2) Rotate away 3 Goldstone bosons through a SU(2) rotation gauge boson mass

  6. gauge boson mass (Y = +1/2)

  7. Gauge boson mass 是SU(2) 的基础表示

  8. What about several Higgs doublets ? Will MW=MZ cW still hold ? The answer is: yes ! For each Higgs doublet: the derivation process is same ( with ) finally

  9. gauge boson mass (in detail) = ab ? = 0? think: if Higgs is not doublet, ...... ?

  10. Peskin book: 691, 699-700 global symmetry SSB 3 Goldstone bosons with SU(2) custodial symmetry

  11. (1) talk by V. Pleitez (2) hep-ph/0607144 (3) arXiv: 1011.5228 Custodial SU(2) Symmetry

  12. SM has some accidental global symmetries They are not imposed, they are consequence of: • Lorentz invariance • Gauge invariance • Renormalizability • Representation content of the model Examples: Baryon number, Lepton number, approximate chiral symmetries

  13. SSB: Scalar doublet: Potential: bi-doublet: ?

  14. U(1)Y SU(2)L (x) global and local symmetry:

  15. 扩大为 (x) Then L has a large symmetry 的真空态： SSB A1, A2, A3  Z are in a triplet of SU(2)L+R :

  16. Yukawa couplings: Extending custodial symmetry to Yukawa sector Defining bi-doublets: (right-handed neutrinos are needed)

  17. Yukawa interactions take the form: invariant under SU(2)LSU(2)R SSB Then Yukawa interactions have custodial SU(2)symmetry

  18. tree level: loop level: • Fermion loops This correction vanishes in the limit of mt=mb e.g., Higgs loops:

  19. Summary： a symmetry for V() custodial SU(2) broken by Higgs U(1)Y gauge interaction Yukawainteractions custodial SU(2) symmetry for V() (tree level) Higgs scalar is SU(2) doublet  = 1 +  (loop level) turn off U(1)Y （g’=0） (extend custodial SU(2) to gauge interactions) mu = md(extend custodial SU(2) to Yukawa interactions.) vanish

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