1. Review of gauge-Higgs unification models Naoyuki Haba ( 波場直之 ) TIS2005, Taiwan, 6/10/2005 (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. →5 th component of gauge field ( A 5 ) ＝ 4D scalar in eff. theo. ⇒ Regard “Higgs”! regard it adjoint Higgs which breaks SU(5) GUT (Hosotani, etal) μ (ex) What we want is not Σ but SM Higgs doublet which breaks SU(2)×U(1) today. （ radi:10 -29 mm （ 10 16 GeV) ）

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

5. 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 in base of (Kubo,Lim,Yamashita, Hall,Nomura,Smith, Burdman,Nomura,….)

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

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

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

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 NH, Y. Hosotani, Y. Kawamura and T. Yamashita, Phys.Rev.D70:015010, 2004 NH and T. Yamashita, JHEP 0402:059,2004 wanted potential is (at least) up to λ 2 、 λ 4 at tree level However, since it is originally gauge field, Let’s estimate quantum corrections !

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

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

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

19. is physical d.o.f. ？ Q: （ cf. is not! It is gauged away (would-be NG) ） ： Wilson line phase is the order parameter of symmetry breaking A: is remaining. is preferable since A 5 = Higgs doublet picture is good. more accurately, gauge symmetry which satisfies (Abe, NH, Matsunaga etal)

20. If the vacuum exist at a=1, mean the remaining gauge symmetry is （ although ≠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.!

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

22. effective potential:

23. (ex)

24. effective potential: (ex)

25. effective potential: (ex)

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

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

28. effective potential: (ex)

29. effective potential: (ex)

30. (3). Introduction of SUSY 5D N=1 SUSY odd dim.=vector-like ⇔ 4D N=2 SUSY Yukawa interaction ( ｇ ～ y top ～ 0.7 when 1/R ～ GUT) motivation of introducing SUSY ： ☆ write all couplings by gauge coupling ☆ dark matter ☆ forbidden dangerous higher order operators (Yukawa among extra bulk fields) 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), ･･･

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

32. 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) N f (±) (fund.) & N a (±) (adjo.) gauge quarks/ leptons extra matters We have seen (by introducing extra bulk field) A 5 can play a role of Higgs doublet, S U(2)×U(1)→U(1)em So how about inducing Yukawa int. （ｇ＝ｙ） ? (this is 2 nd motivation)] For this perpose, assuggests quark/lepton must be in the bulk. （ ex. ） A 5 can’t couple with ４ D brane field If we set then it is possible (but in this case Higgs is non-local field.)

33. 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

34. fund. rep. bulk field SU(2) doublet SU(2) singlet gauge sector SU(3) c ×SU(3) W model Yukawa

35. fund. rep. bulk field SU(2) doublet SU(2) singlet gauge sector SU(3) c ×SU(3) W model Yukawa

36. fund. rep. bulk field SU(2) doublet SU(2) singlet gauge sector SU(3) c ×SU(3) W model Yukawa

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

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

39. effective potential: (ex)

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

41. 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

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

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

44. tend to be small comparing to SM ( ～ 10%) (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

45. D-flat NH, K.Takenaga,T.Yamashita, Phys.Rev.D71:025006,2005 (3). Mass spectrum at tree level at S 1 case probably (radiative induced mass ～ O(100)GeV) ☆ gauginos mass~higgsinos mass ～ β/R ☆ (preliminary ）

46. 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” (A 5 ) 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 5 ． summary & discussion

47. 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 (g 4 ～ O(1), (M * R) 1/2 ≫ 1 (M * ≫ 1/R)) ● wall-localized kinetic terms, g 4 2 > λ -1, (we take g 4 ～ 1), and expect ● introduction of additional U(1)’, extending U(3)×U(3), etc. (SU(3) symmetry 無い )

48. future works ☆ gauge-Higgs unification １． more realistic model にする （ Weinberg angle ： U(1)’ 、 U(3)×U(3) 、 Yukawa の階層性？） ２． 量子効果を含めた mass spectrum の計算 (m h, m H, m A,…) ３． ● 摂動の正当性： 2 loop effective potential ● brane field の eff.pot. への効果 (brane-bulk mixing mass, kinetic term ） ４． Higgs doublet 以外の効果の効果（ triplet VEV,…ρ 等で観測？） ５． RGE analysis ● 1/R の scale up ６． 境界条件のある（ MS)SM としての取り扱い（ｃｆ. top mode) ７． Warp back ground に拡張 (Higgs mass 重く、 Higgs-less model との繋が り） ☆ composite Higgs (fat Higgs) (NH, Okada, ph/0409113) Higgs は M Z より十分重い（ >10TeV ）が、 246 GeV の VEV を取れるか？ １．現象論（ STU からの制限、 self coupling, etc.) ☆ invisible TC (NH, Okada, Kitazawa, 準備中） ～〈 ψψ 〉 |φ| 2 １． pNG の現象論

49. ☆ gauge-Higgs unification in E 6, E 7 GUTs on （ good point ）： don’t need many representation to obtain quark/lepton Yukawa ints. E 6 : bulk matters ⇒ adjoint & fund. E 7 : bulk matters ⇒ adjoint quark/lepton favor structure ← effects of brane-localized extra fields (NH and Y. Shimizu, Phys.Rev.D67:095001,2003, Erratum-ibid.D69:059902,2004) related work （ 1 ） gauge extra matters quark/lepton cf. ３，６，１０，８ rep. are needed in SU(3)×SU(3) model

50. 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) releted works （２） ☆ RGE analyses （ analyses of MSSM with boundary condidtion ） mass 2 logE