# Presentation: 557624

## Physics Analysis 

**Physics Analysis **

**John Womersley**** **
**CERN-Fermilab Hadron Collider Physics Summer School August 9-18, 2006 **

## Outline

**Some basics**
**Simulation tools**
**Case studies to illuminate some issues**
**Top at the Tevatron**
**Single top at the Tevatron**
**Including a digression on multivariate techniques**
**Top at UA1**
**Analysis “after discovery”**
**Systematic errors**
**Conclusions**

## Basics

**Hadron Colliders – especially those that allow access to a new energy regime – are machines for discovery**
**In the case of the TeV scale, this is reinforced by the fact that the known SM forces and particles violate unitarity at around 1 TeV: ****there must be something new (if only a SM Higgs)**
**Discovery means producing convincing evidence of something new**
**In most of our models this means the production of new particles **
**(though this need not be the only way) **
**Goals of analysis in this case: produce this evidence**
**Separation of a signal from the backgrounds   **
**Show that the probability of this signal arising from known sources is small   **
**Demonstrate that the backgrounds are understood**
**Statistics and systematics **

**Much more from Louis Lyons tomorrow**

**Today**

## Access to the data: typical setup

**Access to the data: typical setup**

**Raw data**
****** ****Centrally managed reconstruction – batch-like, only once if possible**
**Reconstructed data**
****** ****skimming – copying subsets of data**
**Skim dataset**
****** ****compress, possibly after re-reconstruction**
**Analysis dataset(s)**
**This is what you work on**
**Should be**
**	****small enough for rapid turnaround**
**	****large enough to enable background estimation**
**	****have clear parentage (so luminosity, trigger efficiency well defined)**
**	****use standard definitions of objects unless a very good reason not to**

## Simulation

**In order to convince the world that you have produced something new, or to set limits on a proposed model, you need to understand**
**What the standard model processes we already know about would look like in your detector**
**How your detector would respond to the proposed model ****(and thus that non-observance of a signal is significant)**

## Simulating hadron-hadron collisions

**Complicated by**
**parton distributions — a hadron collider is really a broad-band quark and gluon collider**
**both the initial and final states can be colored and can radiate gluons**
**underlying event from proton remnants**

**fragmentation**

**parton**
**distribution**

**parton**
**distribution**

**Jet**

**Underlying**
**event**

**Photon, W, Z etc.**

**Hard scattering**

**ISR**

**FSR**

## Simulation tools

**A “Monte Carlo” is a Fortran or C++ program that generates events**
**Events vary from one to the next (random numbers) — expect to reproduce both the average behavior and fluctuations of real data**
_**Event Generators**_** may be**
**parton level:**
**Parton Distribution functions**
**Hard interaction matrix element**
**and may also handle:**
**Initial state radiation**
**Final state radiation**
**Underlying event**
**Hadronization and decays**
**Separate programs for **_**Detector Simulation**_
**GEANT is by far the most commonly used**

## Things to remember – 1 

**Event generators**
**May or may not generate additional jets through parton showering**
**May or may not treat spins properly (should you care?)**
**May or may not get the cross section right**
**NLO much better than LO – but sometimes no choice**
**Be careful over things like**
**You can’t necessarily just add (for example) a W+1 jet simulation and W+2 jets and W+3 jets to model a W + n jet signal.  Likely to be double counting.**
**You can’t necessarily just run a W+1 jet simulation and generate the extra jets through parton showering either...**
**   **

## Things to remember – 2 

**Detector simulation**
**Your detector simulation is only as good as the geometrical modeling of the detector**
**Are all the cables and support structures in place?**
**Example of D****Ø silicon detector**
**While EM showers can be modeled very well (limited by the above) hadronic shower simulation is acknowledged to be an imperfect art**
**Short time structure in current detectors adds another dimension**
**Nuclear de-excitations, drift of charge in argon can be slower than bunch crossing time**
**In general**
**You can probably get the average behavior right**
**Don’t blindly trust tails of distributions or rare processes**
**random numbers may not populate them fully**
**modelling not verified at this level**
- e.g. I would be wary of an MC estimate of the probability for a jet to be reconstructed as a photon – a 10-3 or 10-4 probability

## Example: b-tagging

**To correctly simulate the b-tagging efficiency of the detector requires proper modelling of**
**Alignment of the silicon tracking detector**
**Processes of charge deposition**
**The nature and amount of material in the tracking volume**
**Can use e****+****e****-**** conversions**
**Pattern recognition **
**Track-finding efficiencies**
**Better to determine efficiencies from data**
**calibration data must be collected at appropriate E****T**** and ****η**** **

**In the end: “Monte Carlo scale factors”**

## Simulation: bottom line

**Don’t think of your simulations so much as predictive tools but as multidimensional parameterisations of your knowledge of the detector and SM processes**
**Like any parameterisation, you have no real right to use it without having verified that it works in the region of phase space that you care about **

**Trust but verify**

## Case Study 1 Top at the Tevatron

**Case Study 1 ****Top at the Tevatron**

## How can we extract a signal for top?

**Properties of top are predicted by theory, in this case the SM, except for its mass ****	****	****	****	****            ****(just like the Higgs ********)**
**but even before discovery we had a good idea of the top mass, from limits set by earlier negative searches and from EW fits ****	****	****	****	****	****            ****(just like the Higgs ********)**
**Production cross section **
**Colored particle – expect relatively high cross section **
**Pair production turns out to be the dominant mode ********qq ******** ********tt **
**QCD, color octet, spin 1⁄2: ******** 5 – 10 pb in********pp**
**Decay mode**
**In SM, weak decay **
**CKM matrix elements constrained by unitarity**
**~100% to t ******** Wb ******** known decay modes of W**
**Massive object ******** high p****T**** decay products**

## tt final states

**Standard Model: t ******** Wb dominates**

**21%**

**15%**

**15%**

**1%**

**3%**

**1%**

**44%**

**tau+X**

**mu+jets**

**e+jets**

**e+e**

**e+mu**

**mu+mu**

**all  hadronic**

**   ****30% ****	****e/******** + jets**
**     ****5% ****	****ee/e********/******

## Lepton signatures

**	**
**	****Cross sections for high p****T**** jets**** **
**	**
**	****Cross sections for high p****T**** leptons**
**	****10****2**** - 10****3**** times more high p****T**** jets than high p****T**** leptons**

-         Jets 	> 30 GeV
- 	> 50 GeV

- 1.4 x 105

- 1.4 x 106

## Final state signatures

**The best bet seems to focus on the following two modes:**
**“****Lepton + jets”**
**One W decays leptonically**
**High p****T**** lepton, two b-jets and two light quark jets + missing E****T**
**Good balance between signal and background**
**“****Dilepton”**
**Both W’s decay leptonically**
**Two high p****T**** leptons, two b-jets + missing E****T**
**Only 1/6 of the signal rate but much lower backgrounds**

## How to catch a Top quark

**How to catch a Top quark**

## So...

**This kind of signature requires an excellent understanding of the whole detector**
**Triggering, tracking, b-tags, electrons, muons, jets, missing E****T**
**Performance must be understood and modelled**
**and of the likely backgrounds**

## Lepton + jets

**Require isolated lepton + ME****T ****+ jets**
**Dominant backgrounds will then be W+jets processes**
**There are 4 quarks in the********tt ****partonic final state. Require 4 jets?**
**	**
**# partons ******** # jets!**
**Get more jets from**
**gluon radiation from initial or final state**
**Get fewer jets from **
**Overlaps (merged by reconstruction) **
**Inefficiencies or cracks in the detector**
**Jets falling outside acceptance in ******
**Jets falling below p****T**** cut**

## How to catch a Top quark

**How to catch a Top quark**

## How many b-tags?

**Since typical b tagging efficiency ~ 0.5, ****then for a final state with two b jets**
**Prob(2 tags) ~ 0.25**
**Prob(******** 1 tag) ~ 0.75**
**Best number to ask for depends on signal:background and nature of background **
**is it dominated by real b’s or not? **
**If the signal has two real b jets, and so does the main background, then there is little to gain from asking for a second b-tag**
**In the top sample, requiring ******** 1 tag is good**
**But want to look at ******** 0 and ******** 2 tags as well, to check that all behaves as we expect given the signal and background composition we estimate**

## Lepton + jets signals 

**Lepton + jets signals **

**N****jets**** = 1, 2**
**Control region (little signal)**
**Verify background modelling:**
**tagging efficiencies from data**
**b:c:light q ratio from MC**

**N****jets**** = 3, 4**
**Signal region **

**Analysis with 2 tags**

**Combine results (including correlations) to get best estimate of cross section**

## Dileptons

**Note non-negligible contribution from fake (misreconstructed) leptons**
**Recall that # jets/# leptons ~ 10****3**
**So unless Prob(jet ******** reconstucted lepton) << 10****-3 ****,**** ****cannot be ignored**
**Fake muons from calorimeter punchthrough**
**Fake electrons from jet ******** leading ********0**** + track overlap **

**Signal selection**

## Feeling lucky, punk?

**Then we’ll look for top ******** all jets**

## Top  jets

**Six jets final state with two b-jets**
**Decay of massive objects: tend to be central, spherical, acoplanar events  **
**Only leading order QCD calculation for ********pp ******** 6 jets: use data for bkg**
**Impressive to see a signal but not (yet) in itself a discovery mode **

- “medium” selection on topological variables

- “tight” selection on topological variables

- tighten cuts

## Case Study 2Single Top at the Tevatron

**Case Study 2****Single Top at the Tevatron**

## Single Top production

**Probes the electroweak properties of top and measures CKM matrix element |V****tb****|**
**Good place to look for new physics connected with top**
**Desirable to separate s and t-channel production modes:**
**The s-channel mode is sensitive to ****charged resonances****.**
**The t-channel mode is more sensitive to ****FCNCs and new interactions****.**
**Expected cross section is about 1 pb (s-channel) and 2 pb (t-channel)**

## Backgrounds

**Final state is Wbb ******** lepton + ME****T**** + two b-jets**
**Signal to background much worse than for********tt**
**Basic reason: ****	****tt is a “W+4 jet” signal****	****single top is a “W+2 jet” signal**

**Factor ~ 25 higher cross section**

## 1998...

**hep-ph/9807340**
**Signal: background ~ 1**
**“****5******** signal in 500 pb****-1”**

## 2005...

**Real life ****signal:background ~ 0.1 ****in this example**
**What happened?**
**Reality is not a parton level simulation – lose signal**
**Real b-tagging (lower efficiency at lower p****T****)**
**Real jet resolutions (jets not partons) and missing E****T ****resolution**
**Life’s a bitch.  And it’s almost always worse than your TDR.**

## Never fear – help is at hand

## Neural Networks

**“****Artificial” (i.e. software) Neural Network**
**Algorithm is stored as weights in the links**
**Network is trained with samples of “signal” and “background(s)”**
**Samples repeatedly presented to the network**
**Outcome compared with desired**
**Link strengths adjusted **

- (optional)

- Input variables

- Output variable
- 0 to 1
- (discriminant)

## What you get out (example)

Advantages
Develops non-linear selection criteria on combinations of variables
A way to discriminate between S & B when you have many, correlated variables none of which individually show a clear separation
Disadvantages
Often seen as something of a black box
Only as good as your “training” samples
reliance on simulations?

**What you get out (example)**
**Advantages**
**Develops non-linear selection criteria on combinations of variables**
**A way to discriminate between S & B when you have many, correlated variables none of which individually show a clear separation**
**Disadvantages**
**Often seen as something of a black box**
**Only as good as your “training” samples**
**reliance on simulations?**

**For single top, gave a factor of 2 better sensitivity than the cut-based analysis**

- Signal-like

- Background-like

## Other multivariate techniques

**Likelihood Discriminants**
**Less of a “black box”**
**For single top, analysis using 4 likelihood discriminants has comparable sensitivity to NN analysis**

- Signal-like

- Background-like

## Decision trees
Rather new in high energy physics – miniBooNE is using 
Some attractive features (again, “not a black box”)

“boosted” and “bagged” decision trees

Many more: Support vector machines, Bayesian NN, genetic algorithms,...
http://www.pa.msu.edu/people/linnemann/stat_resources.html

**Rather new in high energy physics – miniBooNE is using **
**Some attractive features (again, “not a black box”)**
**“****boosted” and “bagged” decision trees**
**Many more: Support vector machines, Bayesian NN, genetic algorithms,...**
**http://www.pa.msu.edu/people/linnemann/stat_resources.html**

**Split data recursively until a ****stopping criterion is reached****(e.g. purity, too few events)**
**All events end up in either a**
**“****signal” or a “background” leaf**

## Not yet able to see SM rate, but starting to disfavor some models

A few inverse femtobarns for discovery

**A few inverse femtobarns for discovery**

**Back to single top **

**NN analysis**

## Case Study 3Top at UA1

**Case Study 3****Top at UA1**

## Nature, July 1984

## Top at UA1

**Associated Production of an isolated, large transverse momentum lepton (electron or muon) and two jets at the CERN********pp Collider**G. Arnison et al., Phys. Lett. 147B, 493 (1984)
**Looking for**** ********pp ******** W****	****    ****|******** b t**** ****	****             ****|******** bl******
**Signature is isolated lepton****plus ME****T**** and two jets **
**Mass (jl********) should peak at m****t**
**Mass (jjl********) should peak at m****W**

- l

## What they found

**6 events observed**
**0.5 expected**
**JW (a young, naïve student):**
**“****This looks pretty convincing!”**
**My advisor (older and wiser):**
**“****Not necessarily...”**

## Slide 41

## The moral

**If the kinematic cuts tend to make events lie in the region where you expect the signal, you are really doing a “counting experiment” which depends on absolute knowledge of backgrounds**
**UA1 claim was later retracted after analysis of more data and better understanding of the backgrounds (J/********, Y, bb and cc)**
**In fairness, the knowledge of heavy flavor cross sections and the calculational toolkit available at that time were much less complete **
**Final limits from UA2 (UA1): m****t ****> 69 (60) GeV**

- x

- =

- efficiency

- background

- peak

## After Discovery...

**After Discovery...**

## Once a new state has been discovered...

Want to
Verify production mechanism (cross section, kinematic distributions)
Verify decay modes
Measure mass
Measure quantum numbers (spin, charge...)

**Want to**
**Verify production mechanism (cross section, kinematic distributions)**
**Verify decay modes**
**Measure mass**
**Measure quantum numbers (spin, charge...)**

## All channels consistent with each other and with QCD
Ongoing effort to combine measurements within and among experiments.

**Ongoing effort to combine measurements within and among experiments.**

**Top Cross section measurements**

## New particles decaying to top?

**One signal might be structure in the********tt invariant mass distribution from (e.g.) X ********tt **
**Consistent with QCD**

**Feb 2006 Update**
**682 pb****-1**

## Mass measurements

**Straightforward for a clean final state with all particles reconstructed:**
**Harder if there is missing energy involved, multi-step decay chain(s), jets (jet energy calibration becomes an issue) and combinatorics (which jet comes from which particle)**
**Often the case at LHC, especially for supersymmetry**
**Again, top is an example**

**Mass(B****c****) = 6275.2 +/- 4.3 +/- 2.3 MeV/c****2**

## Extracting the top mass

**Two basic techniques**
**“****Template method”: **
**extract a quantity from each event, e.g. a reconstructed top mass**
**find the best fit for the distribution of this quantity to “templates”**
**“****Matrix element” (or “dynamic likelihood”) method**
**Calculate a likelihood distribution from each event as a function of hypothesised top mass, including SM kinematics, and multiply these distributions to get the overall likelihood**
**The “ideogram method” is a simplified version of this technique**

## Jet energy scale

**The jet energy scale is the dominant uncertainty in many measurements of the top quark.**
**CDF and D****Ø**** use different approaches to determine the jet energy scale and uncertainty:**
**CDF: ****Scale mainly from single particle response (testbeam) + jet fragmentation model ****Cross-checked with photon/Z-jet p****T**** balance**
**~3% uncertainty, further improvements in progress. **
**D****Ø****: ****Scale mainly from photon-jet p****T**** balance. ****Cross-checked with closure tests in photon/Z+jet events**
**Run II calibration uncertainty ~ 2%**

## Top mass

**Both experiments are now simultaneously calibrating the jet energy scale in situ using the W ******** jj decay within top events**

**Combined fit to **
**top mass **
**and ****shift in overall jet scale ****from nominal value**

**But ...**
**no information on E****T**** or ******** dependence, or on b-jet scale**
**(these become systematic errors)**

**CDF **** lepton + jets****template method **

## Top mass status Summer 2006

**Most precise measurements come from lepton + jets**
**Use of W ******** jets calibration is an important improvement**

- http://tevewwg.fnal.gov

## How does top decay?

**How does top decay?**

**In the SM, top decays almost exclusively to a W and a ****b-quark, but in principle it could decay to other down-type quarks too**
**Can test by measuring **
**	****R = B(t ******** b)/B(t ******** q)**
**Compare number of double ****b-tagged to single b-tagged events **
**	****All consistent with R = 1 (SM)****i.e. 100% top ******** b **

- DØ Run II Preliminary

- Lepton+jets (~230 pb-1)

- Lepton+jets and dilepton (~160 pb-1)

- PRL 95 102002

- hep-ex/0603002

## Top  charged Higgs

**If M****H******** ****<m****t ******** m****b**** then t ********  H****+****b competes with t ********  W****+****b **
**Sizeable B(t******** H****+****b) expected at**
**low tan********: ****H******** ********cs, Wbb dominate**
**high tan******** : H******** ******** ******** dominates**
**different effect on cross section measurements in various channels. **
**CDF used ********tt**** measurements in dileptons, lepton+jets and lepton+tau channels**
**allowed for losses to t******** H****+****b decays**
**Simultaneous fit to all channels assuming same ********tt**

**But still room for substantial ****B(****t ******** H****+****b) – as high as 50%?**** **

- PRL 96, 042003

## Top charge

**Using 21 double-tagged events, find 17 with convergent kinematic fit**
**Apply jet-charge algorithm to the b-tagged jets**
**Expect b (q = ********1/3) to fragment to a jet with leading negative hadrons, but********b (q = +1/3) to fragment to leading positive hadrons**
**Jet charge is a p****T**** weighted sum of track charges**
**Allows to separate hypothesis of ****top ******** W****+****b**** from ****Q ******** W****-****b**
**Data are consistent with q = ****±****2/3 ****and exclude q = ****±****4/3 (94%CL) **

## Spin in Top decays

**Spin in Top decays**

**Because its mass is so large, the top quark is expected to decay very rapidly (~ yoctoseconds) **
**No time to form a top meson**
**Top ******** Wb decay then preserves the spin information**
**reflected in decay angle and momentum of lepton in the W rest frame**
**We find the fraction of RH W’s ****to be (95% CL)**
**	****F****+**** = 0.08****±0.08±0.05**** (D****Ø) ****     < 0.09 (CDF) **
**	****CDF finds the fraction of longitudinal W’s to be**
**	****F****0**** = ****	****0.74 +0.22 –0.34 ****(lepton p****T ****and**** ****cos ********* combined)**
**	****In the SM, F****+**** ******** 0 and F****0**** ~ 0.7**

**All consistent with the SM**

- PRD 72, 011104 (2005)

**Left-handed**

**Right-handed**

**Longitudinal**

**cos ***********

## Blind Analysis

**Blind Analysis**

**Optimize cuts on side bands in mass**
**Open box – is there a signal?**
**In fact find no events**
**Set limits**
**Constrain SUSY models**

**Mass of muon pairs**

**Example: ****the rare decay of B****s**** and B****d**** ******** ******************** **
**In the Standard Model, cancellations lead to a very small decay probability**
**3 ******** 10****-9 ****and 10****-10**** **
**New particles (e.g. SUSY)  contribute additional ways for this to happen, increase probability**
**up to 10****-6**

**“****blind analysis”: hide the signal region**

## A few words on Systematic Errors

**Estimating systematic errors is not an exact science**
**Need to be honest – not over conservative, not over aggressive**
**Sometimes there’s a tendency to overestimate errrors to “cover our butts” for things we forgot**
**Remember, theorists are liable to add your systematic error in quadrature with the statistics, input it into a ********2**** fit and expect ********2****/DF ~1**
**assumes ****±1********sys**** is a 68% confidence interval**
**While we often tend to think of the systematic error as more like a 95% (or 100%) interval**
**e.g. “How far off could we be?”**
**Need to be clear what we did and how we estimated the numbers we quote**

## Example: top mass

**CDF note 8375**
**Be prepared for a significant amount of work!**
**	****Each line in this table is essentially a re-analysis of the top mass**

- Possible Variation with ET or (change by ±1)
- How different from light quarks?
- PYTHIA vs. HERWIG
- Vary parameters in generator
- Change by ±1 in estimated efficiency
- Change backgrounds by estimated undertainties and vary model of W+jets
- Divide sample
- Shift lepton pT by ±1%
- Room for MC not to model properly

## Conclusions

**The only way to learn physics analysis is by doing it.**
**To your great good fortune, you (as students and postdocs) have the opportunity to carry out cutting edge analysis at forefront facilities – as a routine part of your careers.**
**Seize this opportunity and enjoy it!   **

## Questions, comments...

**Questions, comments...**