1. Life at the LHC without the Higgs: Models Giacomo Cacciapaglia (UC Davis) 2007 Eötvös-Cornell Workshop Budapest June 28, 2007

2. Life without a Higgs: The Standard Model has been tested very accurately, however… we still don’t know the origin of the Electroweak symmetry breaking (and masses…) The Higgs mechanism is a nice description of such phenomenon, but it suffers from theoretical prejudices (hierarchy problem), and the Higgs boson has not been discovered yet. What if we don’t see the Higgs at the (early) LHC?

3. The role of the Higgs: Weakly coupled doublet H = (h, W L ±, Z L ) The same dof’s can arise as composite states of a strongly interacting sector ( ) → no fundamental scalar Can we decouple h from the theory? What would that imply? W L W L scattering violates Unitarity at ~ 1 TeV scale. Strong coupling appears below 1 TeV → broad resonances (techni-ρ, …), theory out of control (precision EW tests, …)

4. We would like to keep the theory under control up to a safe scale of 5-10 TeV: Let’s consider the contribution of the  -mesons to the W L scattering:  Expanding the scattering amplitude for large Energy: A (W L -W L ) ~ A (4) E 4 + A (2) E 2 + finite terms.  A (4) vanishes due to gauge invariance;  A (2) receives contributions both from the vector resonances and the Higgs: The violation of perturbative unitarity can be delayed up to 10 TeV! We can smoothly go to a Higgsless model (gaugephobic Higgs model) hep-ph/0611385

5. Many models have been proposed:  Higgsless models in warped space;  models in flat space;  deconstructed models;  minimal 3 site models;  … Models in warped space have less freedom! I’ll use them as a guide to explore no-Higgs phenomenology.

6. We want to find significant signatures and correlate them with special features of this class of models, like:  unitarization of W L W L scattering;  the S parameter;  flavour;  top physics – custodial symmetry;  … Such signatures are generic for no-Higgs models! Allow to test various properties of the mechanism!

7. The model  AdS 5 space:  UV brane at z=R, IR brane at z=R’;  SU(2) L xSU(2) R xU(1) X in the bulk;  SU(2) R xU(1) X → U(1) Y on the UV brane;  SU(2) L xSU(2) R → SU(2) D on the IR brane. R R’ UV IR bulk SU(2) L xSU(2) R xU(1) X SU(2) L xU(1) Y SU(2) D xU(1) X Csaki, Grojean, Pilo, Terning, hep-ph/0310355

8. Spectrum The W mass is determined by the two mass scales in the problem: M W 2  M IR 2 /log(R’/R) M IR = 1/R’ The custodial SU(2) R ensures the correct M W to M Z mass ratio The KK masses are determined by the master equation: J 0 (M (k) R’) ~ 0 → M (1) ~ 2.4 M IR …. Generically, large corrections to the S parameter, like in Technicolor theories…

9. Light fermions  Light fermions are doublets of the SU(2)’s: ψ L = (u l, d l ) = (2, 1, 1/6) bulk mass c L ψ R = (u r, d r ) = (1, 2, 1/6) bulk mass c R  The bulk masses control the localization of the zero modes: UV for c L > ½, IR for c L < ½.  Masses generated on the IR brane  Splitting between up and down component from kinetic terms on the UV brane.

10.  Delocalizing the l.h. zero modes in the bulk (c L ~ 1/2) it is possible to minimize the EWPTs (S~0). hep-ph/0409126  The almost flat profile of the zero modes allows to decouple the KK gauge bosons from the light fermions: bounds from LEP and Tevatron relaxed! M (1) < 1TeV allowed!!  Therefore, additional corrections from KK states are small. Both representations choice and localization patterns are preferred by Precision tests and Unitarity! Only way to minimize S… fine tuning?

11. Flavour: a killer for flat fermions? Contributions of New Physics to FCNC’s are highly constrained: the SM contribution to such processes is already small! Typical scale suppressing FCNC’s is >10 3 TeV! We need to worry about:  Operators in the bulk (4-fermi operators) suppressed by a ~TeV,  Contribution of KK gauge bosons (masses ~ TeV). A flavour symmetry in the bulk may not be enough!

12. A flavour symmetry for the light generations. Let’s impose a SU(N f ) L xSU(N f ) R in the bulk broken to SU(N f ) D on the IR brane. Mixing arises from the kinetic terms on the UV brane for the right-handed quarks only! This ensures the absence of FCNCs at tree level and MVF in the charged sector! In this scenario, both effects from KK states and higher order operators are under control. Flavour with flat fermions is possible! See A.Weiler’s talk on Tuesday.

13. Numerical analysis: 1% 0.5% 0.1% Couplings to gauge KK states: g (1) L ~ 0 – 20% g sm, g (1) R ~ 30% g sm Deviations in the lh and rh couplings. M (1) ~ 700 GeV

14. Third generation: m top vs Zbb  In Higgsless models it is a challenge to have a heavy top and small corrections to the Zbb coupling (below 1%).  The top must be composite due to its heaviness: the b L is also composite.  The SU(2) R doublet ψ R contains a left-handed b’ that mixes with the b l via the top Yukawa.  If we extend the custodial symmetry to O(4) ~ SU(2) L xSU(2) R xP LR, we can use P LR to protect Zbb: need to use new representations that respect O(4). (Agashe, Contino, daRold, Pomarol) Cacciapaglia et al, hep-ph/0607146  Or, we can exile top and bottom to a different AdS throat (like, we have two independent CFT sectors – Cacciapaglia et al, hep- ph/0505001 and 0604218)

15. Top and Bottom: a brane on their own R’ t < R’ w Top and bottom decouple from the first KK states (localized on the IR w brane) The weak-throat is exactly like the model described before The top-throat is strongly coupled, but it does not affect EWPTs Light fermions Top- bottom Gauge bosons

16. The new custodian for the bottom. The top Yukawa (M1) does not involve the bottom! The dangerous mixing is absent. They will contain extra (heavy) degrees of freedom: Q(b L, b R ) = -1/3; Q(t L,t R,T L,T R ) = 2/3; Q(X L,X R ) = 5/3.

17.  Comparison between the new (continuous) and old (dashed) representations (neglecting m bottom )  A 4% deviation is still there due to the breaking of P LR on the UV brane.  Such contribution can be canceled tuning the bottom Yukawa.

18. Higgsless phenomenology: Higgsless models have some theoretical complications, but also nice phenomenological features:  Effectively, one free parameter: the mass of the KK states M (1). All the other parameters are fixed by matching the SM (M Z, G F, α, …) or constrained by precision tests.  Interesting mass range from perturbative unitarity: 600 GeV < M (1) < 1 TeV.  Perturbative and under control up to ~ 5-10 TeV. The model can be probed and excluded at the LHC! See next talk by G.Marandella!

19. Group portrait without the Lady: UV brane IR brane  Gauge bosons and light fermions are flat  Top, bL and KK resonances are localized near the IR brane → highly composite  right handed light fermions and bR are localized near the UV brane → elementary

20. Unitarity →  (600 GeV) < M (1) < 1 TeV  Couplings among GB’s S parameter →  flat fermions  V KK f f couplings  KK fermions deg. to V KK M top vs Z b b →  New states  large couplings to V KK  … or topless scenario! Flavour →  rh on the UV brane  V KK fr fr couplings

21. Indirect probes Couplings of the third generation:  Zb l b l = 1.004 g SM ;  Zb r b r = 0.993 g SM ;  Zt l t l = 0.461 g SM ;  Zt r t r = 1.908 g SM ;  Wb l t l = 0.862 g SM. Wbt measured in single top production at the LHC (and Tevatron) Ztt at ILC (poor sensitivity at the LHC) Deviations in the WWZ coupling: close to present bounds, new measurements at LHC (ILC) Log[R] cL 3% 2.5% 2% 1.5%

22. Conclusions and outlook EWSB via a strong sector is an interesting alternative to the (weakly coupled) Higgs mechanism. Extra dimensions provide efficient and constrained models. Rich phenomenology: many resonances can be discovered at the early LHC. Signatures can be traced back to a specific feature of the model: unitarity, S parameter, top. Limited parameter space: the early LHC can exclude this class of models! A more careful study of LHC signals is necessary.

23. Back-up slides

24. A gaugephobic Higgs  V IR fixes the normalization of v(z): we parametrize it as  In the limit V → V SM ~ 246 GeV, R’→ R, and we recover the 4D Standard Model.  M w = f(V, R’, R) = 80.4 GeV.  The theory has 3 free parameters: V, β, m h (we fix R = 10 -8 ). Cacciapaglia et al, hep-ph/0611358

25. HiggslessRS 4D Standard Model V β 246 GeV V >> TeV Flat profile Localized on the IR brane

26. Unitarity in W L -W L scattering  Expanding the scattering amplitude for large Energy: A (W L -W L ) ~ A (4) E 4 + A (2) E 2 + finite terms.  A (4) vanishes due to (5D) gauge invariance;  A (2) receives contributions both from the gauge KK modes and the Higgs: defines the “higgslessness” of the model.

27. Numerical results In RED, isocontours of 1/R’ (M KK ~ 2.4/R’) In BLUE, isocontours of ξ.

28. Higgs phenomenology  The heavier the particle, the more suppressed the coupling: m F = ∫dz ψ ∂ z ψ + y 5 ∫dz v(z) ψ ψ The larger m F, the larger the bulk contribution (distortion of the wave functions). While, the effective Yukawa coupling is prop to the overlap part. Couplings of the (light) Higgs to the SM fields relative to the SM one. (β = 2)

29. Benchmark point 1:  ~ 25% For a light Higgs, the only channel is tth (suppressed by a factor of ~4). h →γγ not observable. For heavy Higgs, WW and ZZ channels suppressed by a factor of ~4. In order to match the discovery potential of the SM, we need ~16 times more integrated luminosity. h →γγ is not useful anymore (sup. by a factor of ~20)