4.- Littlest Higgs Model with T-parity. 5.- hhh at one loop in LHM with T-parity

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2 1.- Introduction. 2.- Higgs physics 3.- hhh at one loop level in SM 4.- Littlest Higgs Model with T-parity 5.- hhh at one loop in LHM with T-parity 7.- Conclusions

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4 Higgs Decay modes at LHC Direct measurement h 0 ZZ * h 0 γγ * 4 4 h 0 WW * ν ν = e,µ h 0 τ νν ττ, τ had.+ν h 0 bb Upper bound h 0 µµ h 0 µµ(ee) ATLAS, Phys.Lett. B 716, 1 (2012) ATLAS, Phys.Rev.D 90, (2014) m h = ± 0.4 ± 0.4GeV m h = ± 0.41GeV CMS, Phys.Rev.Lett (2015) m h = ± 0.21± 0.11GeV CMS, Phys.Lett.B 716, 30 (2012) m h = ± 0.4 ± 0.5GeV CMS, Nature Phys (2014) m h = 125GeV ATLAS, JHEP 1504, 117 (2015) m h = GeV ATLAS, JHEP 1501, 069 (2015) m h = GeV CMS, Phys.Rev.D (2015) m h = 125GeV ATLAS, Phys.Lett.B 738, 68 (2014) m h = 125GeV CMS, Phys.Rev.D (2015) m h = GeV h 0 Zγ Z ATLAS, Phys.Lett.B 732, 8 (2014) m h = GeV CMS, Phys.Lett.B (2016) m h = 125GeV

5 Higgs Decay modes at LHC Direct measurement h 0 ZZ * h 0 γγ * 4 4 h 0 WW * ν ν = e,µ h 0 τ νν ττ, τ had.+ν h 0 bb Τηε δατα αρε φουνδ το βε χοµπατιβλε ωιτη τηε Στανδαρδ Μοδελ εξπεχτατιονσ φορ α Ηιγγσ βοσον ατ α µασσ οφ Γες Τογετηερ τηεψ αχχουντ φορ αππροξιµατελψ 88 % οφ αλλ δεχαψσ οφ α ΣΜ Ηιγγσ βοσον. ATLAS, Eur. Phys. J. C (2016) 76:6 Exploring electroweak symmetry breaking at the LHC. Upper bound h 0 µµ h 0 µµ(ee) h 0 Zγ Z L ME+h = L Fermionic + L Gauge V(Φ) Higgs sel-couplings V(Φ) = λv 2 Φ Φ + λ(φ Φ) 2 = λv 2 h 2 + λvh λh 4

6 Direct measurement h 0 ZZ * h 0 γγ * 4 4 h 0 WW * ν ν = e,µ h 0 τ νν ττ, τ had.+ν h 0 bb Upper bound h 0 µµ h 0 µµ(ee) h 0 Zγ Z Higgs Decay modes at LHC Τηε δατα αρε φουνδ το βε χοµπατιβλε ωιτη τηε Στανδαρδ Μοδελ εξπεχτατιονσ φορ α Ηιγγσ βοσον ατ α µασσ οφ Γες Τογετηερ τηεψ αχχουντ φορ αππροξιµατελψ 88 % οφ αλλ δεχαψσ οφ α ΣΜ Ηιγγσ βοσον. ATLAS, Eur. Phys. J. C (2016) 76:6 Exploring electroweak symmetry breaking at the LHC. Σεαρχηεσ φορ βοτη ρεσοναντ ανδ νονρεσοναντ Ηιγγσ βοσον παιρ προδυχτιον Νο εϖιδενχε οφ τηειρ προδυχτιον ισ οβσερϖεδ. ATLAS, Phys. Rev. D 92, (2015) Higgs sel-couplings V(Φ) = λv 2 Φ Φ + λ(φ Φ) 2 = λv 2 h 2 + λvh λh 4

7 Sel-coupling hhh at tree and one loop level in SM h At tree level the sel-coupling hhh is independent o the higgs bosons 4-momentum. h * (q) h h 3m 2 h v q + p 1 + p 2 = 0 q 2 p 1 2 p 2 2 m h 2 At one loop level and with o-shell Higgs, we need more driagram to satisy the Bose symmetry. h * (p 1 ) h * (p 2 ) + q p 1 p 2 + q p 1 p 2 + q p 2 p 1 + p 1 p 2 q p 1 + p 1 p 2 q p 2 = Γ h (q 2, p 2 * h * h * 1, p 2 2 ) = 3m 2 h v λ hhh Here λ ηηη is the correction to sel-coupling hhh.

8 Sel-coupling hhh at tree and one loop level in SM The leading one loop contribution o the top quark to sel-coupling is derived as: λ ME t (q 2 ) = gm 2 t s 2 t N 1 1 x c 18 Ξ ME 3!16π 2 2 t (x, y,s t,s q ) m x=0 y=0 W dxdy SM Re Λ top λ ME top (m 2 h ) % SM Im Λ top q 2 = 4m t q GeV Previous results: q GeV λ ME top (m 2 h ) % Phys. Lett. B558, 157 (2003) λ top ME (m h 2 ) % Eur. Phys. J. C23, 163 (2002)

9 Sel-coupling hhh at tree and one loop level in SM The leading one loop contribution o the top quark to sel-coupling is derived as: λ ME t (q 2 ) = gm 2 t s 2 t N 1 1 x c 18 Ξ ME 3!16π 2 2 t (x, y,s t,s q ) m x=0 y=0 W dxdy SM Re Λ top λ ME top (m 2 h ) % SM Im Λ top q 2 = 4m t q GeV Another contributions: λ b ME (m h 2 ) % + i % λ τ ME (m h 2 ) % + i % q GeV λ ME Z+W (m 2 h ) % λ ME h (m 2 h ) %

10 Main ideas 1.- Little higgs models are based on a collective symmetry breaking pattern. (Gauged) O(TeV ) (Global) SU(5) [SU(2) 1 U(1) 1 ] [SU(2) 2 U(1) 2 ] W a a 1µ W 2µ SO(5) SU(2) U(1) 2.- There are 14 Goldstone bosons, and are parametrized by a nonlinear sigma model. v SM U(1) EM 3.- Ater the irst symmetry breaking there are our heavy gauge boson: Z H, A H, W H±. 4.- Ater the second symmetry breaking we have the SM ields, and seven additional scalars ields. 5.- The LHM had an alternative to hierarchy problem. 6.- The heavy photon is a dark matter candidate. 7.- A natural way to deine the action o T-parity on the gauge ields is: B a a 1µ B 2µ Phys. Rev. D 88, (2013) 8.- The constraints rom Higgs couplings results rom the 8 TeV run at the LHC exclude up to 694 GeV. JHEP02 (2014) 053

11 Mirror ermions 1.- Little higgs models are based on a collective symmetry breaking pattern. (Gauged) O(TeV ) (Global) SU(5) [SU(2) 1 U(1) 1 ] [SU(2) 2 U(1) 2 ] SO(5) SU(2) U(1) v SM U(1) EM For each SM SU(2) L ermion doublet, a ermion doublet under SU(2) 1 another under SU(2) 2 are introduced. The T-parity even linear combination is associated with the SM, while the T-odd combination is given a mass o order the scale. The mirror ermion acquire mass through the SU(5) and T invariant Yukawa interaction. L = κ (Ψ i ξ + Ψ i mirror ii 2 1 Σ 0 Ωξ i Ω)Ψ R Then the masses and the Higgs coupling or the u mirror quark and the mirror neutrino are. d H and l H do not have direct m = m H dh = 2κ ii couplings with the Higgs boson. m ν = m H uh = 2κ ii 1 v2 8 2 h hν H ν H iκ ii v 2 2

12 LHM λ +T uh,v H (q 2 ) = N cκ 2 ii m uh,v H m W 3π !gm 2 h v x 18 Ξ ME 3 uh (x, y,s uh,v H,s q ) dxdy x=0 y=0 h * (q) λ ME Z+W (m 2 h ) % LHM+T l q 2 = m h 2 ν H m ν H = m uh = 2κ ii 1 v ν H h(p 1 ) h hν H ν H iκ ii 2 2 v h(p 2 ) Making the decay q H -->V H q kinematically allowed, this corresponds to κ ii >0.45. JHEP02 (2014) 053

13 LHM λ +T uh,v H (q 2 ) = N cκ 2 ii m uh,v H m W 3π !gm 2 h v x 18 Ξ ME 3 uh (x, y,s uh,v H,s q ) dxdy x=0 y=0 LHM T Re Λ hhh = 700GeV = 500GeV q GeV LHM T Im Λ hhh = 500GeV = 700GeV q GeV m ν = m H uh = 2κ ii 1 v2 8 2 q 2 2 = 4m uh h hν H ν H iκ ii 2 2 v

14 1.- To test the electroweak symmetry breaking sector o the SM, not only should the couplings o the Higgs boson to gauge boson and ermions be measured, but also the sel-couplings o the Higgs boson. 2.- In the SM, the one-loop contribution to sel-couplings hhh is 11%, where the top quark contribution is 9.14% 3.- In the LHM+T, the one-loop contribution o mirror ermions to sel-coupling hhh is or =700 GeV.