# Presentation: 369139

## Standard Model Higgs

- at the LHC

- Peter Z. Skands
- Fermilab Theoretical Physics Department
- (Significant parts taken from TASI & PASI lectures by:
- M. Carena (Fermilab), S. Dawson (BNL), D. Rainwater (U Rochester) )

## The Role of Particle Physics

- To discover what the Universe is made of and how it works.
- Particle Accelerators reproduce in a controlled lab environment forms of matter and energy last seen in the early universe.
- Elementary particles are the ultimate constituents of matter
- Five basic forces act between these elementary matter particles:
- GRAVITATION (couples to energy)
- ELECTROMAGNETISM (couples to electromagnetic charge)
- THE STRONG FORCE (couples to colour charge)
- THE WEAK FORCE (couples to weak isospin)
- + “MASS” = rest energy (where does it come from?)

- Gauge
- Forces

- Relativity

- ?

- Standard Model Higgs at the LHC

- Peter Skands

## What we Know

- The photon and gluon appear to be massless
- The W and Z bosons are very heavy
- MW = 80.404 GeV ± 0.030 GeV
- MZ = 91.1875 GeV ± 0.0021 GeV
- There are 6 quarks (actually 36)
- Mt = 171.4 ± 2.1 GeV (CDF+DØ July 2006)
- Expected  ± 1.5 GeV at end of Run II
- Mt >> other fermion masses
- There appear to be 3 neutrinos                                with small but non-zero masses
- The pattern of fermions appears to replicate itself 3 times

- Dec 8 2006:
- DØ Reported
- 3.4σ Evidence
- for single top

- Standard Model Higgs at the LHC

- Peter Skands

## The Higgs Mechanism

- Spontaneous Symmetry Breaking

## Why is the photon massless?

- U(1) gauge theory with spin-1 photon *A**μ** **  *
- Local gauge invariance
- Could we put in a mass term for *A*?
- Not gauge invariant!
- So charge conservation ↔ γ massless

- ?

- Standard Model Higgs at the LHC

- Peter Skands

## U(1) gauge theory with spin-1 Aμ and charged scalar φ 

V(φ) = Most general renormalizable potential allowed by U(1) invariance
 L is still invariant under U(1) rotations 

*V(**φ**) = *Most general renormalizable potential allowed by U(1) invariance
-  L is still invariant under U(1) rotations

- Adding a charged scalar

- Standard Model Higgs at the LHC

- Peter Skands

## Two solutions

- μ2 > 0:
- QED with mγ=0 and mφ=μ
- Unique minimum at φ=0

- μ2 < 0:
- Minimum energy state at
- Vacuum breaks U(1) symm.

- U(1) gauge theory with spin-1 *A**μ** *and charged scalar *φ** *

- Standard Model Higgs at the LHC

- Peter Skands

## A closer look at μ2 < 0:

- μ2 < 0: Minimum energy state at
- Write complex φ in (Mod,Arg) notation
- v = constant offset  minimum-energy (vacuum) state
- h = modulus d.o.f.  Higgs field, with mass mh = -2μ2 > 0
- χ = argument d.o.f.  massless Goldstone boson

- mγ=ev

- Standard Model Higgs at the LHC

- Peter Skands

## What happens to the Goldstone boson?

- What happens to the χ field?
- After gauge transformation (unitary gauge)
*L* becomes
- χ disappears, enslaved to longitudinal part of *A* (“eaten”)
- Physical degrees of freedom:
- before SSB: massless A (2 d.o.f) + complex scalar φ (2 d.o.f.)
- after SSB: massive A (3 d.o.f.) + real Higgs scalar (1 d.o.f.)

- Standard Model Higgs at the LHC

- Peter Skands

## Abelian Higgs Mechanism

- _Spontaneous breaking_ of a gauge symmetry by the non-zero VEV of a charged scalar field
- The Goldstone degree of freedom of the scalar is “enslaved (eaten)” to serve as the longitudinal component of the gauge field
- On this background, the gauge field propagator appears to be massive
- In QED, this is what happens in a superconductor
- For the weak force it happens in free space.

- Standard Model Higgs at the LHC

- Peter Skands

## SM Higgs Mechanism

- SU(2)WxU(1)Y gauge symmetry.
- Add a scalar doublet with Y=1
- For μ2<0 there is a minimum at:
- (direction not fixed)
- One massive Higgs scalar
- And 3 Goldstone bosons:
- (same for charged components)

- Standard Model Higgs at the LHC

- Peter Skands

## SM Mass Spectrum

- When replacing H by its vev: HVV  masses:
- LHiggs = ...
- This mass matrix has one zero eigenvalue and 3 others: g2, g2, and g2+g’2
- + Fermions acquire mass due to Yukawa (Hff) couplings

- Standard Model Higgs at the LHC

- Peter Skands

## Current Status

- Brief Summary

## WLWL scattering

Pertubative scattering P > 1for s ~ 1 TeV2 
Need something (e.g. Higgs) to unitarize theory
If SM Higgs, then mH < 800 GeV

- Pertubative scattering P > 1for s ~ 1 TeV2
- Need *something* (e.g. Higgs) to unitarize theory
- If SM Higgs, then mH < 800 GeV

- Unitarity

- Standard Model Higgs at the LHC

- Peter Skands

## Perturbativity and Stability

- The Higgs quartic coupling determines the Higgs mass:
- Running due to self-coupling and top quark loops:

*from M. Carena, TASI 2006*

- Standard Model Higgs at the LHC

- Peter Skands

##  Theoretical Constraints

- Self-coupling can become non-perturbative  ∞  upper bound
- Radiative corrections  deeper minima at large values of φ  lower bound

*from M. Carena, TASI 2006*

- Standard Model Higgs at the LHC

- Peter Skands

## Precision Tests of the Standard Model

- The Standard Model has been tested to very high precision (one part in a thousand) at experiments around the world:
- Although the Higgs has not been seen and its mass is unknown, via quantum corrections it enters electroweak observables (masses, decay rates, ...)
- All electroweak parameters have at most logarithmic dependence on mh, however, a preferred value of mh can still be determined

**Fermilab, SLAC, CERN, ...**

- Standard Model Higgs at the LHC

- Peter Skands

## The Blue Band Plot

- Standard Model Higgs at the LHC

- Peter Skands

## LEP and Tevatron

- Precise measurements of W and top masses can rule out SM above TeV ...
- Tevatron shooting for top mass at or below ±1.5 GeV uncertainty

- Standard Model Higgs at the LHC

- Peter Skands

## Before LHC

- Run II search ultimately depends on combination of many weak channels, impaired by low lumi, but still interesting window remains

- Standard Model Higgs at the LHC

- Peter Skands

## Higgs at the LHC

- Discovery and Measurement Strategies

## Higgs at Hadron Colliders

- Much progress recently in computing NLO (and even NNLO) QCD corrections, see:
- http://maltoni.home.cern.ch/maltoni/TeV4LHC/SM.html

- Standard Model Higgs at the LHC

- Peter Skands

## SM Higgs Decay Modes

- Uncertainties due to uncertainties in αs, mt, mb, and mc
- At low mh, mostly bb, ττ, but also cc and gg can be important.
- At large mh, HVV
- hgg, hγγ, hZγ generated at one loop, but due to heavy particles in loop  relevant contributions

- Standard Model Higgs at the LHC

- Peter Skands

## Choosing a Channel

- What channel works best at a hadron collider isn’t so obvious ...
- Tevatron uses multiple channels:
*If H****bb dominant then (light Higgs):*
*If H****WW/ZZ dominant then (heavy Higgs):*
- Requiring leptons in the final state help reject QCD but not ttbar
- Jet-jet mass resolution ± 15 GeV seriously impairs search for a narrow resonance

- Standard Model Higgs at the LHC

- Peter Skands

## Signal Cross Sections

- While ggH rises ~ QCD-like, the VH channels become relatively quite small

_**LHC**_

_**Tevatron**_

- Standard Model Higgs at the LHC

- Peter Skands

## Backgrounds

- Standard Model Higgs at the LHC

- Peter Skands

## Higgs at the LHC

- The story of *ttH*
*H**** **γγ** *and *H**** **ττ*
- Weak Boson Fusion
- Heavy Higgs, *H**** VV*

- Standard Model Higgs at the LHC

- Peter Skands

## Light Higgs: ttH at LHC

- Idea: ttH coupling is large and ttH final state should be easy to distinguish  Little Background?
- However, original studies did not treat QCD carefully, especially* ttbb* and* **ttjj *were underestimated

- Standard Model Higgs at the LHC

- Peter Skands

## Light Higgs: ttH current outlook

- Now ttH looks marginal at best
- S/B now about 1/6 for mh = 120 GeV
- Shape only differs very slightly  any shape uncertainty will make 5σ impossible, even if L∞

- Standard Model Higgs at the LHC

- Peter Skands

## Heavy Higgs: ttH

- ttH, HWW is viable!
- Complicated final states: WWWWbb  multileptons
- Best channels: same-sign dilepton, trilepton
- LOTS of nasty never-before-calculated bkgs:
- tt Z /γ* (jj) , ttWjj, ttWW, tttt
- lots of diagrams, large QCD uncertainties
- If HWW coupling known  only direct Yt measurement

- Standard Model Higgs at the LHC

- Peter Skands

## Heavy Higgs: ttH @ ATLAS

- Works over large mh range

- Standard Model Higgs at the LHC

- Peter Skands

## Light Higgs: ggHphotons

- Idea: rare decay might win because bkg is also EW, not QCD.
- BR(Hphotons) ~ 0.2% for light 110<mh<140 GeV
- Might not be discovery but gets mass to 1%
- Requires very good jet (fake photon) rejection – jγ , jj bkgs non-trivial – detector sim estimates still range over factor 2

- Standard Model Higgs at the LHC

- Peter Skands

## Light Higgs: What about Hττ?

- Problem: taus not observed directly
- Problem: lots of missing energy, how to reconstruct mass?
- Important: taus must not be back-to-back
- Limited usefulness for ggHττ

- Standard Model Higgs at the LHC

- Peter Skands

## Weak Boson Fusion

- Use the LHC as a W/Z collider:
- Quarks get scattered forward in detector, and no QCD current over central rapidity region:

- Standard Model Higgs at the LHC

- Peter Skands

## WBF: Hττ

- WBF  H  ττ  one or two leptons:

**Backgrounds:**

- Standard Model Higgs at the LHC

- Peter Skands

## WBF: Hττ @ LHC

- ATLAS and CMS say: it works very well!
- For  ~  110 < mh < 150 GeV   (100 fb-1)

- Standard Model Higgs at the LHC

- Peter Skands

## WBF: HWW

- For WW recall angular correlation
- At threshold, W’s at rest  mll = mνν, construct transverse mass
- Works well even away from threshold
- Detector effects smear things out ...

- Standard Model Higgs at the LHC

- Peter Skands

## WBF: HWW @ LHC

- ATLAS and CMS say: Jacobian peak still there!
- May even work down to mh = 120 GeV (but serious backgrounds  more study needed, e.g. ttj at NLO)

**m****h**** = 140 GeV**

**m****h**** = 160 GeV**

- Standard Model Higgs at the LHC

- Peter Skands

## WBF: Remaining Issues

- So WBF turns out to be great, but how well do we understand it?
- Minijet Veto (QCD radiation, underlying event) currently at primitive stage, but can be tested on data, e.g. WBF Zjj
- tt + jets (off-shell effects, normalization and shape changes at NLO)
- “Contamination” from gluon fusion + jets. Partially understood
- + real experimental issues: tagging, calibrations, underlying event, ...

- Standard Model Higgs at the LHC

- Peter Skands

## The Combination Machine

- mh < 120 GeV:
- 200 – 700 GeV:
- Inclusive HZZ4l
- > 800 GeV:
- WBF HWW lνjj
- WBF HZZllνν

**NO ESCAPE ROUTE FOR**
**SM HIGGS AT LHC!**

- Standard Model Higgs at the LHC

- Peter Skands

## Putting it together

- Standard Model Higgs at the LHC

- Peter Skands

## The LHC Potential

- ATLAS+CMS total sensitivity combining all channels  5σ discovery possible for all masses with 5fb-1 (?)
- For mh ~ 120 GeV, combination of many different channels necessary, hence requires a good understanding of the detectors
- Note: mh ~ 120 GeV is simultaneously most sensitive region for Tevatron

**Mass resolution for 300 fb-1:**
- 0.1 to 1% from HZZ4l or Hγγ

- Standard Model Higgs at the LHC

- Peter Skands