# Presentation: 577534

## Effective Lagrangians and Physics Beyond the Standard Model

- S. Dawson
- TASI06
- Lecture 5

## SM Higgs Boson

- Theory is perturbatively consistent only within chimney

## Theory is perturbatively unitary

- At all energies if:
- For infinitely massive (or no) Higgs at energies
-    less than:

- Mh < 800  GeV

- Ec 1.7 TeV

## The theory works

## Effective Field Theory

- Effective Lagrangian
- Oi contain light fields
- All information about heavy degrees of freedom in ci
- Categorize operators by their dimensions, di
- Operators with di>4 suppressed by powers of E/

- Operating assumption is that >> MZ

## Counting Dimensions

- Fermions: dim=3/2
- Gauge bosons/scalars: dim=1
- : dim=1
- SM Lagrangian is dimension 4
- Only 1 SU(2) x U(1) invariant dimension 5 operator:
- L5=(L)(L )/(Lv)(Lv)/m
- 1015 GeV

## Many Possible Dimension-6 Operators

- Philosophy:  We don’t know what the physics at high energy scales is
- We assume it respects the SU(2) x U(1) symmetry

## Little Hierarchy Problem

- Much possible new physics is excluded at the TeV scale
- Look at possible dimension 6 operators
- Many more operators than shown here
- Limits depend on what symmetry is violated

- Schmaltz, hep-ph/0502182

- New Physics typically  must be at scale  > 5 TeV

- Experimental limits

- New operators

## No Higgs?

- Remember, Higgs is used to unitarize the SM
- Unitarity violated at 1.7 TeV without a Higgs
- This sets the scale for something new
- Construct the Standard Model without a Higgs
- Higgs is only piece we haven’t seen experimentally

## Standard Model Revisited

- Scalar sector described by SU(2) doublet
- Scalar potential invariant under global SU(2)L x SU(2)R symmetry:
- Global symmetry broken by

## Higgsless Standard Model

- Construct most general effective Lagrangian with 2 derivatives describing Goldstone bosons with global SU(2)L x SU(2)R  symmetry
- This construction is expansion in powers of E2/2

- Assume  = 0

## Higgsless Standard Model, #2

- Gauge theory:

- Unitary gauge is =1

- This is SM with massive gauge bosons

- D=-igW/2+ig’B3/2

- At O(E2/2) gauge couplings are identical to those of the SM

## Higgsless Standard Model, #3

- Add O(E4/4) operators
- Contributions from O(E2/2)  operators generate infinities (SM is not renormalizable without Higgs)
- These infinities absorbed into definitions of O(E4/4)  operators
- Can do this at every order in the energy expansion
- Coefficients are unknown but limited by precision measurements
- A particular model of high scale physics will predict these coefficients
- The O(E4/4) terms will change 3 and 4 gauge boson interactions

## WW scattering at LHC

- Four gauge boson interactions are sensitive to unitarity violating physics (Vector boson fusion)
- Look for W+W-, ZZ, Z, W pair production in vector boson fusion
- Consistent expansion in powers of E2/2

- V=W,Z,

## WW Scattering without a Higgs

- Add terms of O(E4/4) to effective L
- This Lagrangian violates unitarity
- n derivative vertex En/n-4
- This is counting experiment (no resonance)
- Example: Search for anomalous WW vertex through gauge boson fusion

- Hard!

- Eboli et al, hep-ph/0310141

- LHC

- Normalized to show difference in shape of signal and background

## Contruct Models without Higgs

- Problems with unitarity
- Something must come in to conserve unitarity if theory is to remain perturbative
- Extra dimension “Higgsless” models have tower of Kaluza Klein particles
- These look like heavy copies of the W, Z, and photon

## Models without Higgs have difficulties with Unitarity

- Without Higgs*, W*-boson scattering grows with energy
-                    *A*~*G**F**E**2*
- Violates unitarity at 1.7 TeV
- SM Higgs has just the right couplings to restore unitarity
- Extra D models have  infinite tower of Kaluza-Klein states
- Need cancellations both in E2 and E4 contributions to amplitudes
- Arrange couplings to make this happen

***Look for heavy***
*** ******gauge bosons***

## Higgsless phenomenology

- Tower of KK vector bosons
- Can be produced at LHC, *e*+*e**–*
- Tension between:
- Unitarity wants light KK
- precision EW wants heavy KK

***J=0 partial wave for WW scattering***

***Heavier ************ heavier KK gauge bosons***

- Davoudiasl, Hewett, Lillie, Rizzo, hep-ph/0312193

## Experimental Signatures of Higgsless Models

- Look for massive W, Z,  like particles in vector boson fusion
- Need small couplings to fermions to avoid precision EW constraints
- Narrow resonances in WZ channel

- Birkedal, Matchev, Perelstein, hep-ph/0412278

- LHC

- Different resonance structure from SM!

## Gauge Boson Pair Production 

- W+W-, W, etc, production sensitive to new physics
- Expect effects which grow with energy
- At(...)(s/v2)+O(1)
- As-(...)(s/v2)+O(1)
- TOT O(1)
- Interesting angular correlations: eg, W,  has radiation zero at LO

- Remember e+e- W+W-

- Non-SM 3 gauge boson couplings spoil unitarity cancellation

## Consider Non-SM W+W-V Couplings

- Most general gauge and Lorentz invariant couplings with C and P separately conserved
- Where V=Z,
- V higher order in derivative expansion (often ignored)
- SM: =Z=g1Z=g1=1, V=0
- EM gauge invariance requiresg1=0
- Often assume SU(2)c and neglect higher dimension operators
- g1Z= Z  + tan2W
- V= 

***A model of BSM will specify these anomalous couplings***

## What size effects can we hope to see?

- NLO corrections to W+W- known
- Can hope to see small BSM effects
- At the Tevatron:
- With Non-SM couplings:

- Theory

## But don’t precision measurements require a light Higgs?

- Higgs mass limits from precision measurements assume SM
- Suppose the SM is effective low energy theory valid to scale 
- Include all operators allowed by SU(3) x SU(2) x U(1) gauge symmetry (and assume a light Higgs)
- Include effects of new operators in fits

## Higgs can be heavy with new physics

- Mh  450-500 GeV allowed with large isospin violation, T

- Chivukula, Holbling, hep-ph/0110214

***Constructing actual models with this feature is hard***

## Much Activity in EW Scale Model Building

- Remove Higgs completely
- Dynamical symmetry breaking
- Higgsless models in extra D
- Lower cut-off scale
- Large extra dimensions
- Force cancellations of quadratic contributions to Higgs mass
- SUSY
- Little Higgs
- Make Higgs component of gauge field in extra D

***Symmetries maintain cancellations at higher order!***

***Strong limits from ***
***precision ***
***measurements***

- Much more satisying to have a model than just an effective theory!

## Little Higgs Models

- New particles at scale f ~  cancel SM quadratic divergences
- Cancellation from same spin particles
- Need symmetry to enforce cancellation

- Heavy WH,ZH,AH cancel gauge loops
- Scalar triplet cancels Higgs loop
- Vector-like charge 2/3 quark cancels top loop

- Arkani-Hamed, Cohen, Katz, Nelson, hep-ph/0206021

## More on little Higgs

- Broken to subgroup H (SO(5))  at scale 4f
-  Higgs is Goldstone Boson of broken symmetry
- Effective theory below symmetry breaking scale
-  Gauged subgroups of G ([SU(2)xU(1)]2) contain SM
-   Higgs gets mass at 2 loops (naturally light)
- Freedom to arrange couplings of 1st 2 generations of fermions (their quadratic divergences small)

- Heavy W’s, Z’s, ’s
- Heavy top
- Extended Higgs sector

**Notes:**
Littlest higgs has 14 gbs

## Little Higgs & Precision EW

- Mixing of heavy-light gauge bosons leads to problems with precision measurements
- Many models
- Triplets cause problems with 
-       parameter unless VEV small
- Typically,

- Chen& Dawson, hep-ph/0311032

## New Phenomenology in Little Higgs Models

- Drell-Yan production of ZH
- EW precision limits prefer  cot .2 (Heavy-light gauge mixing parameter)
- BRs very different from SM
- MZH2MZ2f2/v2
- Look for heavy tops
- Look for non-SM 3 gauge boson vertices

- Scale down by  cot2 .04

-      Han,Logan,McElrath, Wang,  hep-ph/0301040

**Notes:**
Tevatron limit on ZH interesting

## Higgs production & decay in Little Higgs Models

- Rate  could be reduced by 25%
- Have to see new particles
-  ZH, WH, H

- LHC

- Han, Logan, McElrath, Wang, hep-ph/0302188

- ggh

***Growing realization that EWSB isn’t just Higgs discovery, but requires finding spectrum of new particles!***

- This is theoretically allowed region

## Possibilities at the LHC

- We find a light Higgs with SM couplings and nothing else
- How to answer our questions?
- We find a light Higgs, but it doesn’t look SM like
- Most models (SUSY, Little Higgs, etc) have other new particles
- We don’t find a Higgs (or any other new particles)
- How can we reconcile precision measurements?
- This is the hardest case

## Science Timeline

- Tevatron

- LHC

- LHC Upgrade

- LC

- 2004

- 2007

- 2012

- 2015?

***This is the decade of the hadron colliders!***