Toshifumi Yamashita MISC, Kyoto Sangyo U. Aichi Medical U. 愛知医科大学

1. Toshifumi Yamashita MISC, Kyoto Sangyo U. Aichi Medical U.愛知医科大学 grand gauge-Higgs unification& doublet-triplet splitting 2012/3/17@GUT2012 based on : [1] PRD84, 051701 (2011) (arXiv:1103.1234) w/ K. Kojima (Kyushu) & K. Takenaga (Kumamoto Health Science) [2] PRD84, 115016 (2011) (arXiv:1106.3229)

2. Outline GUT-breaking via Hosotani mechanism = “grand gauge-Higgs unification” adjoint [1] K.Kojima, K.Takenaga & T.Y. • naturalDoublet-Triplet (DT) splitting by a “missing VEV” even inSU(5)models • general & testableprediction [2] T.Y. We may get a hint of the GUT-breaking @LHC.

3. Plan Outline Hosotani mech. & DT splitting grand GHU low energy predictions summary

4. Hosotani mechanism & DT Splitting zero-mode of A5 symmetry breaking by a continuous Wilson loop Y. Hosotani (1983) gauge-Higgs unification talks by Maru & Hosotani • The order parameter, , is valued on the group(instead of the algebra). special traceless (inversely) missing VEV DT Splitting [2] T.Y.

5. Hosotani mechanism & DT Splitting 5 : • BCs around are modified: ex) “anti-periodic” 5 chiral massless doublet • basis transformation Kawamura’s talk (broken) gauge transformation w/ symmetry breaking by BCs, as in the orbifold breaking • DT splitting [2] T.Y.

6. Plan Outline Hosotani mech. & DT splitting grand GHU low energy predictions summary

7. grand gauge-Higgs unification • difficulty [1] K.Kojima, K.Takenaga & T.Y. • orbifold action projects out adjoint scalars due to the opposite orbifold BCs. • this difficulty is shared w/ heterotic string • very well studied,classified w/ Kac-Moody level • ``diagonal embedding” method Kuwakino’s talk K.R.Dienes & J.March-Russel (1996) We borrow this in our pheno. models.

8. grand gauge-Higgs unification • diagonal embedding (in field theory) [1] K.Kojima, K.Takenaga & T.Y. This provides a way to “introduce” chiral fermions in S1 models!! ex) has a zero-mode. chiral fermions • deconstruction similar to S1 model

9. grand gauge-Higgs unification • SU(5) example [1] K.Kojima, K.Takenaga & T.Y. w/ appropriate bulk fermions SU(5) GSMon a local minimum where DT Splitting [2] T.Y.

10. grand gauge-Higgs unification • matter content • bulk fields Hu& Hd • similar to S1 model : vector-like • couple to W.L. : SU(5)incomplete multiplets • boundary fields chiral matter • essentially 4D fields : chiral • not couple to W.L. : SU(5)full multiplets

11. Plan Outline Hosotani mech. & DT splitting grand GHU low energy predictions summary

12. low energy predictions We may observe . to remain perturbative [2] T.Y. • light adjoint chiral multiplets • A5is massless @tree level, & acquires a mass of O(mSB)via loop. Its superpartners can have masses of O(mSB). • gauge coupling unification • The adjoint matters : recovered w/

13. low energy predictions [2] T.Y. • recovery of GCU ex) additional matters for : 5 10(in the bulk) - MSSM - MSSM + adj - MSSM + adj + add

14. low energy predictions Preliminary • phenomenology of adjoints • SU(3) is no longer asymptotically free, & remains strong @high energy squarks & octet become rather heavy. • colorless fields may be produced @LHC. (SUSY) triplet/(doublet)/singlet Higgs model. e.g. • these may increase thehiggs mass. NMSSM-like and/or through loop heavier higgs : now working M.Kakizaki, S.Kanemura, H.Tanigucji & T.Y.

15. summary Hosotani-breaking of GUT symmetry • PRD84, 051701 (2011)w/ K.Kojima & K.Takenaga • proposed this possibility, grand gauge-Higgs unification. • a (local) vacuum : SU(5) GSM • PRD84, 115016 (2011) • SUSY version : DT splitting realized naturally • general prediction : light adjoint chiral w/ may be tested @LHC e.g. direct production of a weak triplet, heavy squarks & higgs