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Review of gauge-Higgs unification models

Review of gauge-Higgs unification models. TIS2005, Taiwan, 6/10/2005. Naoyuki Haba ( 波場直之 ). (Tokushima Univ.). Plan of talk. 1. models of gauge-Higgs unification. 2. electro-weak symmetry breaking （１）. 3. electro-weak symmetry breaking （２）. 4. Higgs phenomenology.

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Review of gauge-Higgs unification models

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  1. Review of gauge-Higgs unification models TIS2005, Taiwan, 6/10/2005 Naoyuki Haba(波場直之) (Tokushima Univ.)

  2. Plan of talk 1. models of gauge-Higgs unification 2. electro-weak symmetry breaking （１） 3. electro-weak symmetry breaking （２） 4. Higgs phenomenology 5. summary & discussion

  3. Q: Can origin of Higgs be extra component of gauge field?→gauge invariance guarantees the smallness of “Higgs” mass (against quantum c)! A: Yes, we can do it in the extraD gauge theory. →5th component of gauge field (A5)＝4D scalar in eff. theo. 　　　　　　　　　　　　　　　　　　　　　　　　　　　　 ⇒ Regard “Higgs”! （radi:10-29mm （1016 GeV)） (ex) μ (Hosotani, etal) regard it adjoint Higgs which breaks SU(5) GUT What we want is not Σ but SM Higgs doublet which breaks SU(2)×U(1) today.

  4. （radi:10-１６mm （1TeV)） (ex) μ ⇒ origin of “Higgs doublet” (zero mode) ⇒ origin ofYukawa interaction “Higgs doublet” mass is finite. (～1/R) 5D gauge symmetry Gauge-Higgs unification

  5. preparation（notation）

  6. preparation（notation）

  7. preparation（notation）

  8. perparation（notation） zero mode (remaining field in the low energy）

  9. preparation（notation）

  10. 1. models of gauge-Higgs unification (1). SU(3)×SU(3) model (2). SU(6) model

  11. (1). SU(3)c×SU(3)W model (Kubo,Lim,Yamashita, Hall,Nomura,Smith, Burdman,Nomura,….) in base of

  12. (1). SU(3)c×SU(3)W model (Kubo,Lim,Yamashita, Hall,Nomura,Smith, Burdman,Nomura,….) in base of Higgs doublet Higgs doublet

  13. (2). SU(6) model (Hall,Nomura,Smith, Burdman,Nomura) in base of

  14. (2). SU(6) model (Hall,Nomura,Smith, Burdman,Nomura) in base of Higgs doublet Higgs doublet

  15. 2. electro-weak symmetry breaking （１） -“Higgs doublet” can really take VEV or not?- (1). SU(3)×SU(3) model (2). SU(6) model (3). Introduction SUSY wanted potential is (at least) up to λ2、λ4 However, since it is originally gauge field, at tree level Let’s estimate quantum corrections ! NH, Y. Hosotani, Y. Kawamura and T. Yamashita, Phys.Rev.D70:015010, 2004 NH and T. Yamashita, JHEP 0402:059,2004

  16. ’s 1 loop quantum corrections (method） Sum of infinite# of diagram （KK） → obtain →　search the vacuum of 　　　　　　 →　whether “Higgs”

  17. (1).SU(3)c×SU(3)W model effective potential (gauge contribution）: a=1 is acceptable if life time of universe is long enough? no symmetry breaking!

  18. Q: （cf. is not! It is gauged away (would-be NG)） is physical d.o.f. ？ (Abe, NH, Matsunaga etal) ：Wilson line phase A: is the order parameter of symmetry breaking remaine!. more accurately, gauge symmetry which satisfies

  19. If the vacuum exist at a=1, mean the remaining gauge symmetry is （although <A5>≠0） It is no good! base also shows region is good order parameter. Since “Higgs doublet” picture (STU) is good & 246 GeV ≪ 1/R is consistent. Anyhow, only the gauge contribution is not enough for the suitable vacuum.!

  20. ☆ let us introduce extra bulk fields. fermion (adj. & fund.) scalar (fund.) term is added.

  21. effective potential:

  22. effective potential: (ex)

  23. effective potential: (ex)

  24. effective potential: (ex)

  25. effective potential: (ex) OK ! effects of extra bulk field

  26. (2). SU(6) model effective potential (gauge contribution）: not good! → introduction extra bulk field

  27. effective potential: (ex)

  28. effective potential: (ex)

  29. (3). Introduction of SUSY SUSY: introducing particles which have the same masses but different spin as 1/2 (ex.) gauge (1) ⇔ gaugino (1/2), Higgs (0) ⇔ higgsino (1/2), quark (1/2) ⇔ squark (0), ･･･ motivation of introducing SUSY： ☆ write all couplings by gauge coupling ☆ dark matter ☆ forbidden dangerous higher order operators (Yukawa among extra bulk fields) 5D N=1 SUSY odd dim.=vector-like ⇔4D N=2 SUSY Yukawa interaction (ｇ ～ ytop～ 0.7 when 1/R ～ GUT)

  30. ☆ Higgs doublets:SUSY requires ２ HD (anomaly cancellation, holomorphy) at tree level if SUSY is not broken, potential is flat → Scherk-Schwarz SUSY breaking twist of SU(2)R as exp(2πiβσ2)

  31. 1 loop effective potential → EWSB is not realized only by gauge contribution also in SUSY case → introduction of extra bulk fields (hyper-multiplet) can do (ex.) (SS SUSY breaking parameter β=0.1) Nf(±) (fund.) & Na(±) (adjo.) We have seen (by introducing extra bulk field) A5 can play a role of Higgs doublet, SU(2)×U(1)→U(1)em So how about inducing Yukawa int.（ｇ＝ｙ）? (this is 2nd motivation)] For this perpose, as suggests quark/lepton must be in the bulk. quarks/ leptons （ex.）A5 can’t couple with ４D brane field gauge extra matters If we set then it is possible (but in this case Higgs is non-local field.)

  32. 3. electro-weak symmetry breaking （2） -Can “Higgs” take VEV when quark/lepton are in bulk?- show here example of SUSY SU(3)×SU(3) model NH and T. Yamashita, JHEP 0404 (2004) 016

  33. SU(3)c×SU(3)W model fund. rep. bulk field Yukawa gauge sector 3 → down-Yukawa 6 → up-Yukawa 10 → charged lepton-Yukawa 8 → ν-Yukawa (Burdman-Nomura)

  34. quark/lepton’s contribution to the effective potential : effective potential of gauge sector & quark/lepton： (Ng: generation#) not good! → extra bulk field in bulk

  35. effective potential: (ex)

  36. effective potential: (ex) SU(6) modelの例

  37. 4. Higgs phenomenology (1). soft scalar mass (2). 3-point self coupling (3). Mass spectrum NH, K.Takenaga and T.Yamashita, Phys.Rev.D71:025006,2005 NH, K.Takenaga and T.Yamashita, hep-ph/0411250

  38. (1). soft scalar mass We add soft scalar mass, m (z=mR) in addition to SS term as SUSY breaking. SU(3) × SU(3) model (例) ｍφcan be heavy even the same matter content

  39. (ex) SU(3) × SU(3) model m (z=mR) SU(6) model m (z=mR) O(1) # of extra bulk field can realize EWSB !

  40. (2). 3-point self coupling （motivation）：measurement of λis important to know the mechanism of EWSB, and deviation from the Standard Model can be significant. ILC実験 ☆ higher order operators a few TeV → suppression scale → suppressed enough ☆ effective 3-point coupling deviation from SM tend to be small comparing to SM(～10%)

  41. (3). Mass spectrum (preliminary） ☆ gauginos mass~higgsinos mass～β/R D-flat NH, K.Takenaga,T.Yamashita, Phys.Rev.D71:025006,2005 at tree level at S1 case ☆ probably (radiative induced mass～O(100)GeV)

  42. 5．summary & discussion origin of Higgs：extraD component of extraD gauge field → “doublet Higgs” → Yukawa int. Higgs mass is finite (1/R) (← extraD gauge invariance) 1 loop effective potential of “Higgs doublets” (A5) in SU(3)×SU(3) model & SU(6) model (quark/lepton blane & bulk) ↓ EW DSB can be possible by extra bulk matters (suitable rep. & #) ☆ gauginos mass ～ higgsinos mass ～β/R ☆ 3-point self coupling: -10 % deviation from SM ☆ extra bulk fields～O (100) GeV ★ (mass spectrum (now calculating)) tanβ～1

  43. problems (1): SU(6) model 　　☆ how to break extra U(1) ? ☆ how to forbid rapid proton-decay when 1/R～ TeV? ← U(1)B (2): SU(3)×SU(3) model ☆Winberg angle 5D gauge kinetic term→4D Higgs kinetic term ● wall-localized kinetic terms, (SU(3) symmetry無い) g42 > λ-1, (we take g4～1), and expect (g4～O(1), (M*R)1/2≫1 (M*≫1/R)) ● introduction of additional U(1)’, extending U(3)×U(3), etc.

  44. related work （1） ☆ gauge-Higgs unification in E6, E7 GUTs on (NH and Y. Shimizu, Phys.Rev.D67:095001,2003, Erratum-ibid.D69:059902,2004) （good point）：don’t need many representation to obtain quark/lepton Yukawa ints. E6: bulk matters ⇒ adjoint & fund. E7: bulk matters ⇒ adjoint cf. ３，６，１０，８ rep. are needed in SU(3)×SU(3) model quark/lepton favor structure ← effects of brane-localized extra fields extra matters quark/lepton gauge

  45. releted works（２） ☆ RGE analyses　（analyses of MSSM with boundary condidtion） gaugino mass ⇔ higgsino mass at tree level at 1/R Analyze radiative breaking (EWSB) is possible or not including SGGRA effects. (Choi, N.H., Jeong, Okumura, Shimizu, Yamaguchi, JHEP 0402:037,2004) mass2 logE

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