Looking for New Effects in Electroweak Precision Data

J. de BlasIn collaboration with F. del Águila & M. Pérez-Victoria

XXXI Reunión Bienal de la Real Sociedad Española de Física

Granada, 11 de Septiembre de 2007

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<ΛPlanck.

Naturalness → Λ~1 TeV

Discrepancies (≥ 2σ) with some measuments: AbFB, σHad…:

Maybe statistical fluctuations.

Otherwise, one could use these small discrepancies to obtain some information about the theory at energies E> Λ.

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.

Outline

Effective lagrangians:

Heavy vectors

Heavy fermions: Dirac, Majorana

Electroweak Precision Data:

Effects of new physics.

Example: Bounds on heavy fermions

Conclusions

Effective Lagrangians

Beyond usual oblique analysis.

Decoupling scenario, weak coupling.

Heavy (~ Λ) states are integrated out

Ln involves only SM fields. LEff 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 L6 corrects the SM:

Nuc. Phys B268 (1986) 621-653)

Heavy Vectors

Construct the most general lagrangian for a heavy vector coupled to the SM particles.

Renormalizability+Lorentz&Gauge invariance leaves two possibilities:

Heavy Vectors: Operators

Vector Vector

EffectEffect

4-Fermion4-Fermion

Vector-Fermion Vector-Fermion vertexvertex

, ,Fermion Fermion massesmasses

,Vector Boson Vector Boson

massesmasses

,Higgs PotentialHiggs Potential

Heavy vector-like Dirac Fermions

Vector-like Quarks: F.del Águila et al.

Easily generalized for vector-like Leptons:

JHEP 09 (2000) 011

Heavy Dirac Quarks: Operators

EffectEffect

FermionFermion

Vector-Fermion vertexVector-Fermion vertex Fermion MassesFermion Masses

EffectEffect

FermionFermion

Vector-Fermion vertexVector-Fermion vertex Fermion MassesFermion Masses

-

Heavy Dirac Leptons: Operators

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→→

EffectEffect

FermionFermion

Vector-Fermion vertexVector-Fermion vertex Fermion MassesFermion Masses

Heavy Majorana Leptons: Operators

Electroweak Precision Data

The program includes:

Z-pole measurements:

Low-Energy measurements:

LEP II measurements:

New physics effects linear in . 2

2v

MW Z-pole Low-Energy LEP IISM Inputs:

GF, MZ

W ± & Z0

mass W ±

FF

&

Z0 FF

Vertex

Effects of new physics

4-F

erm

ion

Example: Bounds on SM-like Heavy Fermions

Bounds at 1-σ:

Bound [x (M/1TeV)]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)

Mixing with the SM b quark?→ → , v=246 GeV.

Example: Bounds on SM-like Heavy Fermions

B

DQM

vY

23

Example: Heavy B quark singlet with mass MB=500 GeV. (D type)

Read the bound on YDQ3 and apply the formula.

MixingbB < 0.03

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.

Looking for New Effects in Electroweak Precision Data

Backup slides

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.

→→

Example II: Bounds over Exotic Heavy Fermions

Bounds at 1-σ:Bound [x (M/1TeV)]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)