125 GeV Higgs Boson and Gauge Higgs Unification

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1 125 GeV Higgs Boson and Gauge Higgs Unification Nobuchika Okada The University of Alabama Miami 2013, Fort Lauderdale, Dec , 2013

2 Discovery of Higgs boson at LHC! 7/04/2012 Standard Model Higgs boson has been discovered at LHC through a variety of decay modes. CMS

3 Electroweak symmetry breaking Higgs potential: The vacuum expectation value breaks the electroweak gauge symmetry

4 Implications of the Higgs boson discovery Higgs mass is determined: GeV Higgs self coupling is determined Higgs boson mass generation

5 What happens for Higgs potential at high energies? Assuming the SM is valid up to, say, Planck scale, Quantum Field Theory allows us to calculate the Higgs potential at very high energies. Renormalization group improved effective high energies : Effective Higgs self coupling including quantum corrections, calculable in the SM

6 1 loop renormalization group equation of the Higgs quartic EW scale:

7 RGE extrapolation of the Higgs quaric coupling Higgs self coupling becomes negative around 10^10 GeV << M_Pl for mh=125 GeV

8 Implication? Veff V=246 GeV Our vacuum is NOT true vacuum! Quantum tunneling is possible to the true minimum. EW Vacuum stability problem if

9 New Physics which takes place at E < 10^10 GeV can solve this problem. RGE running of Higgs self coupling is altered by new particle effects Example: Seesaw extension of SM SM RGE running SM + new physics RGE running Type II Seesaw: Gogoladze, NO &Shafi, PRD 78, (2008) Dev, Gosh, NO, Saha, JHEP 1303 (2013) 150 Type III Seesaw: Gogoladze, NO &Shafi, PLB 668 (2008) 121 He, NO, Shafi, PLB B716 (2012) 197

10 Another picture for the stability bound? mh =125 GeV Effective Low Energy Theory = Standard Model BSM? Special meaning of?

11 Gauge Higgs Unification (GHU) Scenario 5D Standard Model 5 dim. theory compactified on orbifold Manton, NPB 158 (1979) 141 Fairlie, PLB 82 (1979) 97 Hosotani, PLB 126 (1983) 309 PLB129 (183) 193 SM y All SM fields reside in the bulk Higgs boson is unified into 5 th component of gauge fields in higher dimension

12 Basic structure 5 dim SU(3) gauge theory (toy model) SU(3) gauge = adj doublet doublet singlet Impose non trivial boundary conditions (parity assignment) are Z2 even fields, others odd fields Zero modes for odd fields are project out, So SU(3) is broken to SU(2) times U(1) by this parity assignment

13 5D SU(3) GHU Lagrangian 5D SU(3) gauge kinetic term SU(2) x U(1) EW gauge kinetic term Higgs doublet kinetic term No Higgs tree level Higgs potential is generated at quantum level with Kaluza Klein fields

14 Properties (1) The SM Higgs doublet is identified as the 5 th component of 5D bulk gauge field (2) Mass term and Higgs self coupling are protected to be zero by the 5D gauge invariance (3) 5D gauge invariance is broken by the boundary conditions and as a result, Higgs mass and self coupling are induced through quantum corrections at low energies (4) However, there is no quadratic divergence in the theory

15 (5) Low energy effective theory of the model is equivalent to the SM with a certain boundary condition Gauge Higgs condition: Haba, Matsumoto, N.O. & Yamashita, JHEP 02 (2006) 073 5D flat GHU at E < mkk = SM + GH condition for Higgs self coupling 1 loop effective potential in 5D GHU 1 loop effective potential in SM with a cutoff RGE solution

16 UV completion of the Standard Model with GHU model 50 mh =125 GeV Effective Low Energy Theory = Standard Model 5D GHU Compactification scale ~ 10^10 GeV Higgs mass as a function of the compactification scale Gogoladze, NO, Shafi, PLB 665 (2007) (2008) 319

17 Compactification scale can be lower, say, 1 TeV? Need extra fermions to reproduce mh= GeV Realistic SU(3) x U(1) GHU with bulk fermions Bulk fermions with half periodic BC & bulk mass Maru & N.O., PRD 87 (2013) Maru & N.O., arxiv: Quantum numbers: n=0,1,2,3,. U(1) charge in the electroweak SU(3) alpha: coupling with Higgs boson : determined once the SU(3) repr. is fixed M: bulk mass term

18 Example: 10 plet under the EW SU(3) SU(2) representation U(1) charge in SU(3) Free parameters: mkk & M, and Q

19 Higgs mass with color triplet bulk fermions With color triplet 6 plet/10 plet/15 plet Maru & N.O., arxiv:

20 Higgs mass with color triplet bulk fermions With color triplet 6 plet/10 plet/15 plet Maru & N.O., arxiv: Once the rep. and m_kk are fixed, bulk mass is determined so as to reproduce Higgs mass 125 GeV SM RGE 10 plet 15 plet 6 plet GH condition

21 Contributions to effective Higgs boson couplings Kaluza Klein modes of the SM particle and new bulk fermions contribute Higgs to digluon, diphoton couplings gluon top quark loop gluon top quark loop + Kaluza Klein top + new colored fermion W boson loop + KK fermions + KK W boson

22 1. Main production mode: gluon fusion gluon top quark loop gluon + Kaluza Klein top Opposite signs! Maru & Okada, PRD 77 (2008)

23 2. Primary discovery mode: Higgs decay to diphoton top quark loop W boson loop + KK fermions + KK W bosons + New Fermions

24 SU(3) x U(1) GHU model Maru & N.O., arxiv: with 10 plet bulk color triplet fermion realizing mh=125 GeV The KK mode contribution to Higgs digluon coupling alters the Higgs boson production cross section at LHC KK fermions can be tested at LHC Run II

25 The KK mode contribution to Higgs digphoton coupling alters the signal strength of Higgs to diphoton channel Lightest KK QEM= 1/3 Lightest KK QEM=+2/3 For Rgg > 0.9 (mkk > 2.5 TeV), the deviation is less than 10%.

26 KK fermion contributions to Higgs Z gamma? KK fermion mass splitting: Z Interaction vertices between mass eigenstates Maru & N.O., PRD 88 (2013) No contribution to h Z loop!

27 Interactions between KK modes & W, Z Example: 10 plet: Maru & N.O., arxiv: (+2, 0mw) 4(+1, 1 mw) 3(1, +1 mw) 3(0, 2 mw) 2(0, 0 mw) 4(0, +2 mw) 3( 1, 3 mw) 1( 1, 1 mw) 2( 1, +1 mw) 4( 1, +3mw)

28 Heavy fermion LHC Run II Maru & N.O., arxiv: (+2, 0mw) 4(+1, 1 mw) 3(1, +1 mw) 3(0, 2 mw) 2(0, 0 mw) 4(0, +2 mw) 3( 1, 3 mw) 1( 1, 1 mw) 2( 1, +1 mw) 4( 1, +3mw) Heavy top/bottom quarks with suitable Q charge assignments

29 Conclusions The Higgs boson is finally discovered! Higgs physics, one of the most important research area in particle physics, has just begun. There are many things to do to test the SM Higgs sector. Observed Higgs boson properties have lots of implications to new physics beyond the SM.

30 Gauge Higgs unification as UV completion of the Standard Model Quadratic divergence free KK mode mass as an effective cutoff Gauge Higgs condition new interpretation of a vanishing Higgs quartic coupling Reproducing Higgs mass GeV with half periodic fermions GH condition at TeV New contribution to Higgs diphoton coupling No contribution (@1 loop) to Higgs Z gamma Hunting LHC Run II