1. Higgsless Theories, Electroweak Constraints, and Heavy Fermions Carl Schmidt Michigan State University July 18, 2005 SUSY 2005 Based on hep-ph/0312324, Roshan Foadi, Shri Gopalakrishna, and CS hep-ph/0409266, Roshan Foadi, Shri Gopalakrishna, and CS hep-ph/0507xxx, Roshan Foadi and CS

2. Introduction Motivation: New physics must restore the unitarity apparently lost by breaking electroweak symmetry (ex. W L W L  W L W L ) Options: Restore through scalar channel -> Higgs, SUSY,.... or Restore through vector channel -> Technicolour, Higgsless,... Question: Is the second option viable? (Until Higgs is discovered, must consider it) Higgsless models in extra-dimension/theory space offer a new framework to address this question. [Csaki, Grojean, Murayama, Pilo, Terning/ others...]

3. Outline 1)Introduction 2)SU(2) 5-dim Theory Space Model* 3)Problems with fermions (and solutions) A.Electroweak S-parameter B.FCNC C.Top quark mass 4)Unitarity and limits on parameter space 5)Conclusions *view as both effective theory and toy model

4. SU(2) 5-dim Theory-Space Model Gauge sector: with boundary conditions: W ± (  R) = 0 * for others 5D SU(2)gauge theory with explicit breaking to U(1) on boundary. Results in: *Move  -function in by amount   Impose ∂ 5 W=0 on boundary. Take  0. gg’

5. Delayed Unitarity Violation in W L + W L -  W L + W L - m W’ = 500 GeV N = 0 to 100

6. Adding Fermions (1) Simplest choice: Brane fermions with Note:  L  lives at y=0 but also couples to W 3 at y=  R. -Okay in theory space. It just couples to both W N+1 and B. Fermions massless.

7. Confronting EW constraints (1) The real problem: By extracting couplings of W and Z to fermions, we find T ≈ 0 but U ≈ 0 (at tree level) Limits on the S parameter from EW data require Too large to cure unitarity problem. (Important: Limits from direct production of W 1 ’ or Z 1 ’ are weaker, because coupling of heavy gauge bosons to light states are suppressed by a factor proportional to.) ~

8. Details Couplings: Parametrize with S,T,U with model 1 fermions: comparing gives:

9. Adding Fermions (2) Try Bulk fermions with Brane kinetic terms with *Technical point to define  -functions: 1)Move  -function in by amount  2)Impose ∂ 5  L =0 at y=0, ∂ 5  R =0 at y  R  3)Take  0. Bulk mass

10. Adding Fermions (2) Try Bulk fermions with Brane kinetic terms with  (y)  for all y couples to W 3 (  R). -Still okay in theory space. 2)Mass of lightest fermions: Different t R to fit each fermion mass. Heavy fermions have m n ≈ (n+1/2)/R (or larger for bulk mass M >0) Bulk mass

11. Confronting EW constraints (2) Now must extract couplings of W and Z to light fermion eigenstate. We find T ≈ 0 U ≈ 0 and if we chose (for bulk mass M = 0) then also S ≈ 0  Although it requires tuning, we now have a Higgsless model with all S,T,U zero (at tree level). [Cacciapaglia, Csaki, Grojean Terning] [Foadi,Gopalakrishna,CS]

12. Details Recall in model 1: : In model 2, couplings obtained from convolution of fermion wave functions (  with W and Z wave functions (f and g): : Identical suppression factor for and can precisely cancel gauge contribution to S.

13. Fermion mixing Now with three families: In general, M and t L -2 are 3x3 matrices ==> FCNC! Impose U(3) flavor symmetry on Bulk and Left-Brane. The K u and K d matrices diagonalized by separate U(3) transformations. Result: with V is the CKM matrix! t L and M universal t R determines fermion mass

14. Top Quark Mass Problem: Not possible to obtain m t =175 GeV for reasonable R. Lightest fermion mass for t L fixed to cancel S, for, and various t R.

15. Top Quark Mass Solution: Separate Gauge Radius R g and Fermion Radius R f Scales R f =R/ , while R g = R Natural in theory space models: - gauge & Yukawa couplings unrelated All fermion masses proportional to 1/R f Can obtain top mass

16. Limits on Parameter space If we set M = 0, the model is determined by 2 parameters: 1/R g ~ m W1 ~ m Z1 and 1/R f ~ 2m f1 (t L fixed to cancel S, various t R ’s used to obtain fermion masses) Upper limit (crude) on 1/R g from unitarity in W L + W L -  W L + W L - scattering Lower limit on 1/R g (~500 GeV) from limits on production of W 1

17. Limits on Parameter space Similarly, Upper limit on 1/R f from unitarity in tt  W L + W L - scattering [Schwinn] Only occurs in same-helicity channel Only linear growth in energy, which cancels exactly due to b n tower of states Amplitude may still become too large if 1/R f ~2m b1 too large Minimally, lower limit on 1/R f (~2.5 TeV) needed to give top quark mass. SM Higgsless

18. Limits on Parameter space Upper limits require a 0 <1/2 for s 1/2 <10 TeV From W L + W L -  W L + W L - From tt  W L + W L - From top mass From W’ limits

19. Limits on Parameter space Lower limit on 1/R f is actually stronger. Right-handed tbW coupling To make this coupling smaller (while allow top mass): -decrease t tR and increase 1/R f Limits from b->s  give Gives 1/R f > 3.8 TeV for 1/R g = 550 GeV Perhaps even stronger constraints from right-handed ttZ coupling, but phenomenological analysis more subtle [Larios, Perez, Yuan]

20. Conclusions We’ve presented a toy Higgsless model, which appears viable as an effective theory up ~10 TeV –S-parameter canceled by delocalization of light fermions into bulk –Global SU(3) flavor in bulk and left-brane suppresses FCNC and leads to CKM matrix –Top quark mass allowed by separating R f from R g Parameter space given by R f and R g (for M =0) –Approximate upper bounds from unitarity –Approximate lower bounds from experiment Limits from W’ search Limits on right-handed tbW coupling