Nobuchika Okada The University of Alabama Miami 2015, Fort Lauderdale, Dec , GeV Higgs Boson mass from 5D gauge-Higgs unification In collaboration with Jason Carson (University of Alabama) Nobuhito Maru (Osaka City University) Ref: Carson & NO, arXiv: Maru & NO, arXiv: ; ;

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

Higgs boson mass measurement: ATLAS & CMS combined ATLAS + CMS collaborations, March, 2015

Higgs boson properties observed at LHC (ATLAS + CMS) Signal strength fits  consistent with SM predictions ProductionsDecays

The Gauge Hierarchy Problem Higgs mass corrections are quadratically sensitive to UV physics  The last particle, Higgs boson, is discovered  Measured properties are consistent with the SM predictions  Higgs mass ~ VEV =EW scale  How to protect the corrections? Ex) Supersymmetry: fermions  bosons  Chiral symmetry SUSY

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

Basic structure 5D SU(3) gauge theory (toy model) adj doublet singlet SU(3) gauge = Impose non-trivial boundary conditions (parity assignment) are Z 2 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

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

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 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 Actual mass corrections highly depend on bulk fermion contents

(5) Low energy effective theory of the model is equivalent to the SM with a certain boundary condition Gauge-Higgs condition: Haba, Matsumoto, NO & Yamashita, JHEP 02 (2006) 073 5D flat GHU at E < M KK = 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

UV completion of SM by 5D GH  SM with Before Higgs boson discovery  Higgs boson mass prediction in 5D GHU Gogoladze, NO, Shafi, PLB 665 (2007) (2008) 319 Effective Low Energy Theory = Standard Model 5D GHU Mt(GeV) = 

ATLAS & CMS combined (2015) Tevatron & LHC combined (2014)  After Higgs boson discovery ``Instability Problem’’ in SM  In 5D GHU,

Can we lower the KK mass scale to O(1 TeV), while reproducing m h =125 GeV?  Need extra bulk fermions Realistic SU(3) x U(1)’ GHU with bulk fermions Maru & NO, arXiv: ; arXiv: ; arXiv: Examples: with bulk mass Color singlet/triplet Periodic/Antiperiodic boundary condition SU(2) representation U(1) charge in SU(3)

125 GeV Higgs boson mass from GH condition Carson & NO, arXiv: Example 1: PB fermion: n=0, 1, 2, 3, …. HP fermion: n  n+1/2 M: bulk mass E = M kk

Example 2: PB fermion: n=0, 1, 2, 3, …. HP fermion: n  n+1/2 M: bulk mass E = M kk

RG Analysis  Gauge Higgs Condition:  Relation between Yukawa & gauge E = M kk 6-plet case: 10-plet case:  Solving RGEs with the above boundary conditions Free parameters: : # of bulk fermions

6-plet case: modifications of SM RGEs for SM RGEs for SM + lightest KK modes for

Results for 6-plet case Nf=2, color singlet Q’=2/3 Nf=1, color triplet Q’=4/3 SM RG evolution ATLAS & CMS combined (2015) Tevatron & LHC combined (2014)

Nf=2, color singlet Q’=2/3

M KK V.S m 0 in order to reproduce m h = GeV 10-plet case Color triplet Color singlet

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 + Kaluza-Klein top + new colored bulk fermions W boson loop top quark loop + KK fermions+ KK W boson

1. Main production mode: gluon fusion gluon top quark loop + KK top + new bulk fermions Opposite signs! Maru & Okada, PRD 77 (2008)

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

SU(3) x U(1)’ GHU model with 10-plet bulk color triplet-fermion realizing mh= GeV The KK mode contribution to Higgs-digluon coupling alters the Higgs boson production cross section at LHC Carson & NO., arXiv: ATLAS + CMS bound Lightest KK colored fermion Mass > 700 GeV – 1.4 TeV 10-plet case

The KK mode contribution to Higgs-digphoton coupling alters the signal strength of Higgs-to-diphoton channel ATLAS + CMS bound

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.

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 125 GeV with (half)periodic fermions GH condition at TeV New contributions to Higgs-diguon/diphoton coupling Measured Higgs properties constrain KK mass ~> 1 TeV. Hunting LHC Run 2

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

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