1. Looking for New Effects in Electroweak Precision Data J. de Blas In collaboration with F. del Águila & M. Pérez-Victoria XXXI Reunión Bienal de la Real Sociedad Española de Física Granada, 11 de Septiembre de 2007

2. Introduction SM is a great success Good agreement with experimental data. But: Theoretical Problems: Hierarchy problem. SM must be considered as an effective theory with a cutoff Λ<Λ Planck. Naturalness → Λ~1 TeV Discrepancies (≥ 2σ) with some measuments: A b FB, σ Had …: Maybe statistical fluctuations. Otherwise, one could use these small discrepancies to obtain some information about the theory at energies E> Λ.

3. Introduction We would like to parametrize the new physics in a model independent way → → Effective Lagrangians Precise measurements are necessary to constrain or exclude indirect new physics effects: → → Precision Electroweak Data We have developed a code that allows us to: Select different classes of new physics. Incorporate different sets of Data. Study specific models.

4. Outline Effective lagrangians: Heavy vectors Heavy fermions: Dirac, Majorana Electroweak Precision Data: Effects of new physics. Example: Bounds on heavy fermions Conclusions

5. Effective Lagrangians Beyond usual oblique analysis. Decoupling scenario, weak coupling. Heavy (~ Λ) states are integrated out L n involves only SM fields. L Eff valid for E<< Λ. We consider only operators up to dimension 6, classified in the basis of 1 (dim. 5) +81 (dim. 6) operators of W. Buchmüller & D. Wyler. Integration at tree-level ( only gives a subset of the above) → Big Effects After EWSB L 6 corrects the SM:  Nuc. Phys B268 (1986) 621-653)

6. Heavy Vectors Construct the most general lagrangian for a heavy vector coupled to the SM particles. Renormalizability+Lorentz&Gauge invariance leaves two possibilities:

7. Heavy Vectors: Operators VectorEffect 4-Fermion Vector-Fermion vertex,, Fermion masses, Vector Boson masses, Higgs Potential

8. Heavy vector-like Dirac Fermions Vector-like Quarks: F.del Águila et al. Easily generalized for vector-like Leptons:  JHEP 09 (2000) 011

9. Heavy Dirac Quarks: Operators EffectFermion Vector-Fermion vertex Fermion Masses

10. EffectFermion Vector-Fermion vertex Fermion Masses - Heavy Dirac Leptons: Operators

11. Heavy Majorana Fermions Renormalizability+Invariance & Majorana condition leaves only two types: Integration similar to Dirac’s case but gives also the only dimension five operator of the basis: Majorana mass for neutrinos Lepton number violation ∆L=2 →

12. EffectFermion Vector-Fermion vertex Fermion Masses Heavy Majorana Leptons: Operators

13. Electroweak Precision Data The program includes: Z-pole measurements: Low-Energy measurements: LEP II measurements: New physics effects linear in.

14. MWMW Z-poleLow-EnergyLEP II SM Inputs: G F, M Z W ± & Z 0 mass  W ± FF & Z 0 FF Vertex     Effects of new physics  4-Fermion

15. Example: Bounds on SM-like Heavy Fermions Bounds at 1-σ: Bound [x (M/1TeV)] <(0.31 0.32 ----- ) <(0.40 0.30 0.16) <(0.42 0.46 ----- ) <(0.17 0.70 0.30) <(0.05 0.15 0.10) <(0.06 0.25 0.11)

16. → Mixing with the SM b quark?→, v=246 GeV. Example: Bounds on SM-like Heavy Fermions Example: Heavy B quark singlet with mass M B =500 GeV. (D type) Read the bound on Y DQ3 and apply the formula. Mixing bB < 0.03

17. Conclusions The Effective Lagrangian parametrizes heavy physics at low energies in a model independent way. Constraints on masses and couplings of generic new particles. Specific Models can be easily analyzed. Electroweak Precision Tests are complementary to LHC searches.

18. Looking for New Effects in Electroweak Precision Data Backup slides

19. Effects of new physics II Best measurements: Z-pole and Low-Energy experiments. Z-pole is the main constraint over operators that modify vector-fermion vertex. Low-Energy and LEP II: 4-fermion operators becomes relevant. Heavy fermion corrections are mainly constrained by Z-pole. Heavy vector corrections constrained by all data. { →

20. Example II: Bounds over Exotic Heavy Fermions Bounds at 1-σ: Bound [x (M/1TeV)] <(0.15 0.24 ---- ) <(0.39 0.33 0.51) <(0.14 0.24 0.25) <(0.37 0.37 0.32) <(0.23 0.22 0.66) <(0.19 0.09 0.29) <(0.27 0.17 0.40) <(0.09 0.21 0.14)