# Presentation: 196435

## Factorization of Jet Energy Corrections

**Jet Energy Scale Task Force**
**Monica Vazquez Acosta, Anwar Bhatti, Rick Cavanaugh, Jorgen D’Hondt’, Guenther Dissertori, Daniel Elvira, Robert Harris, Bob Hirosky, Olga Kodolova, Nikos Varelas &  Marek Zielinski**
**Jet Calibration Workshop**
**April 26, 2007**

## Overview

- CMS would benefit from a factorized multi-level jet correction.
- Total jet energy correction is decomposed into (semi) independent factors applied in a fixed sequence
- Offset: removal of pile-up and residual electronic noise.
- Relative (): variations in jet response with  relative to control region.
- Absolute (pT): correction to particle level versus jet pT in control region.
- Flavor: correction to particle level for different types of jet (b, tau, etc.)
- Underlying Event:  luminosity independent spectator energy in jet removed.
- Parton: correction to parton level.
- More details on each factor, and other possible factors, later in the talk.
- Each factor can be separately determined, refined and understood.
- 1st MC truth (now), then data driven with MC data (next 1⁄2 year), then data driven with real data (2008).
- Factorizing the correction allows for collaborative work and continuity.
- Monolithic corrections are either kept or replaced: we lose prior work.
- All the current CMS corrections are MC truth based monolithic corrections.

- Robert Harris, Fermilab

## Priority, Scope and Evolution

- Factorization facilitates prioritization, evolving corrections & scope
- Addressing problems one-by-one, factorization allows us to
- Use more people to solve the jet energy correction problem quicker.
- Address the most essential corrections first (prioritization)
- Flattening  response of the jets, requested by Online Selection for HLT !
- Correction of calorimeter based jets to the particle level.
- Providing reliable corrections for significant pile-up as the luminosity ramps up.
- Provide a framework to include less pressing but needed corrections
- Flavor corrections and model dependent correction to the parton level.
- Factors can then evolve independently on different time scales
- Relative correction vs.  may be redone every year as needed.
- Absolute correction vs. pT could change as new techniques emerge.
- Scope can gradually expand to include sophisticated jet definitions
- Corrections for “jet plus track” algorithm, or full particle flow.
- May not change the Offset, Underlying Event or Parton level correction.

- Robert Harris, Fermilab

## Factorization Essentials

- Factor out the hard problem and move it away from the easier problems
- Allows simultaneous work on both the hard and easy problems.
- Allows re-use of stable solutions without too much coupling.
- Prevents ambiguities in solving the hard problem from affecting the solution to the easy problem.
- The hard problem:
- Absolute jet correction as a function of PT in a control region in .
- We want to know the error of this independent of the other corrections
- The easier problems (not necessarily that easy):
- Jet correction as a function of  relative to the control region.
- Determination of the pile-up energy in a jet cone.
- Control Region in is usually a single “uniform” calorimeter: the barrel.
- Barrel covers all PT and has earliest functioning detectors.

- Robert Harris, Fermilab

## Level 1: Offset Correction (see workshop talk from Olga Kodolova)

- Subtract offsets from pile-up and electronic noise.
- Pile-up (multiple pp interactions)
- Includes luminosity dependent energy in jet (pile-up not underlying event)
-  Allows subsequent corrections to be independent of luminosity
- Reason we think it is important to apply this correction first at CMS.
- Correction determined from data or MC
- Random cone method estimating energy in data or MC
- Enegy density in phi slices at fixed  values.
- Actual change in jets methods: pure MC or data/MC mixing
- Average correction in beginning of run, event-by-event based on vertices later ?
- Electronic noise
- Noise above the cell and tower thresholds
- Although we want to keep this _small_ it may be significant.
- Correction determined from data
- Noise in pedestal runs and special runs without zero suppression.

- Robert Harris, Fermilab

## Level 2: Relative Correction versus (see workshop talk from Anwar Bhatti)

- Flattens the jet response versus 
- Corrects energy of each jet back to the response in the barrel (control region).
- Correction has small pT dependence.
- Applied to jets corrected for offsets (level 1)

- Gives a “barrel equivalent” jet response.
- Allows difficult pT dependent correction to be common for all jets.
- Correction well understood with many data driven methods.
- Lots of calib data : pT balance or MPF in dijets or  / Z + jets.
- Important correction for uniform trigger response.
- Needs to be a smooth function of both  and pT.
- Binned or discontinuous corrections will produce spurious signals.

**1**

**Before**

**After**

**1**

**3**

**2**

**Jet  ******

**4**

**Relative**
**Response**

- Robert Harris, Fermilab

## Options for Relative Correction versus (see workshop talk from Daniel Elvira)

- The relative correction could be further factorized
- Jet Response vs.  = Calorimeter Correction (MPF) * Showering Correction
- Calorimeter correction for eta variation of calorimeter response
- Showering correction for calorimeter showering outside jet cone.
- D0 method
- The relative correction was factorized
- MPF was used to find the calorimeter correction versus .
- A _few percent_ additional showering correction was applied in the forward regions.
- CDF method
- The relative correction was not factorized any more
- Dijet pt balance was used to find a jet correction versus 
- This included the showering correction.
- The total relative correction should be the same in both cases.

- Robert Harris, Fermilab

## Level 3: Absolute Correction vs. pT (see workshop talks from Cammin, Bhatti, Van Mulders)

- Flattens the absolute jet response of calorimeter vs. pT
- Corrects energy of jet back to the particle level.
- For the barrel (control region):  independent.
- Applied to Level 2 jets: luminosity independent.

**1**

**Before**

**After**

**10**

**1000**

**100**

**Jet  p****T  ****(GeV)**

**Absolute**
**Response**

- Last correction needed for particle level jets
- Corrects to "observable" and predictable quantity:
- The total pT of colorless particles in jet algorithm (jet cone).
- Hardest part of correction with largest systematic uncertainty.
- Determined first with MC tuned on Test Beam, later tuned on in-situ data.
- Data driven calibration or MC tuning samples:
- Isolated charged tracks,  / Z + jets, t mass & W mass.
- Must be smooth function of pT, or we will get  spurious signals.

- Robert Harris, Fermilab

## Level 4: Jet Flavor Correction

- Corrects for jet “flavor” dependence
- Applied to jets corrected at level 3.
- Level 3 correction was for QCD mixture of quarks and gluons
- Other input objects will give different jet corrections.
- For example b-jets (see workshop talk by Sasha Nikitenko).
- Also, tau jets, gluons, light quarks, charm, etc.
-  Correction is _optional_.
- Many analyses cannot identify jet flavors, or want special corrections.
- Correction desired for specialized analysis (top, h  bb, h  , etc.)
- CMS needs a standard way to include this additional correction.
- However, physics analysis groups must determine this correction.
- The default value of the correction is 1, for QCD mixture.

- Robert Harris, Fermilab

## Level 5: Underlying Event Correction(see workshop talk by Olga Kodolova)

- Subtract underlying event  energy
- Energy in jet from spectator parton interactions
- Luminosity independent energy
- Applied to Level 3 corrected jets.
-  Correction determined from measurements in data/MC
- Similar to pile-up correction but with low lumi events/MC
- Theory interest: Dedicated studies in QCD group have already begun.
- Correction is _optional_ for many analyses
- Underlying event is now a well established part of MC
- Does not necessarily need to be corrected away
- Unlike early Tevatron days.
- Many parton level calculations do not have underlying event.
- This correction is useful for comparing against those.
- Need to know how big this is, regardless of whether we correct for it

- Robert Harris, Fermilab

## Level 6: Parton Correction

- Correct jets to the parton level
- Also corrects for changes in jet response between parton types
- Applied to Level 4 corrected jets.
- Replace energy lost “outside” the algorithm (cone).
- Correction is optional
- Many calculations (NLO and NNLO) simulate out-of-cone effects by clustering partons
- Correction is model dependent and often undesired for QCD tests
- Correction is widely used and should be part of standard software.
- Correction is desirable for getting parton energy scale for resonances.
- Searches for new physics, top and higgs mass measurements, etc.
- This correction requires a parton type choice
- Mixture of quarks and gluons from QCD jets should be supported
- Recommend it as the "default" parton type for QCD jet analysis.
- Single specific parton types could also be supported, with PAG assistance:
- Gluon, light quark, charm, bottom, or even top quark at high pT.

- Robert Harris, Fermilab

## Uses of different levels of corrected Jets

- Level 1: Jets corrected for offsets from pile-up and electronic noise.
- Level 2: Jets corrected for  response & offsets
- Trigger: flatten the  response at L1 and HLT w/o introducing other uncertainties into the trigger ?
- Level 3: Jets corrected  to the particle level.
- Most important level of correction for analysis.  The level we must reach with priority.
- Level 4: (Optional) Flavor jets corrected to the particle level.
- Specialized jets at particle level for top and higgs measurements.
- Level 5: (Optional) Jets corrected to particle level with underlying event removed.
- Comparisons with perturbative QCD NLO calculations.
- Level 6: (Optional) Jets corrected to the parton level.
- Model dependent searches for new physics, top and higgs mass measurements, etc.
- Additional Corrections:
- As we learn, we will want to include other levels to improve jet & MET resolution
- e.g., correcting vs. **EM fraction** improves resolution (shown by Esen & Landsberg, April 19)
- Analysis dependent jet corrections (unsmearing, etc.) are beyond our scope.

- Robert Harris, Fermilab

## Conclusions

- We have proposed a factorized multi-level jet correction.
- Derived from prior HEP experience applied to the CMS environment.
- We are at an early stage and more levels may need to be added.
- Approach facilitates completion and evolution corrections.
- Allows simultaneous collaborative work on (semi) independent factors.
- Allows some factors to be stable, while other factors evolve with study.
- We recommend that CMS adopt this factorized approach.
- Software to apply corrections should be designed for multiple levels.
- Initial values of factors could be found now from MC truth.
- Correction can evolve to data-driven factors as methods are understood

- Robert Harris, Fermilab