# Presentation: 085806

## Experimental Issues in pQCD

*Thomas J. LeCompte*
- High Energy Physics DivisionArgonne National Laboratory

## Outline

- Tale #1: The High ET CDF Jet Excess
- Tale #2: Backgrounds in Direct Photons
- Tale #3: The Bottom Quark Cross-section

- A collection of stories of mystery and mayhem, intended to be “cautionary tales”.

- I talk too fast.  So stop me when I say something confusing.
- I will overlook more than I will cover.
- My background is in HEP.  I may be coming at things with a different perspective than other people.
- Don’t try this at home!

- Important Warnings:

- “I yam what I yam” – Popeye the Sailor

## Tale The First: The CDF High ET Jet Excess

## Jets

- A “blast” of particles, all going in roughly the same direction.

- Calorimeter View

- Same Events, Tracking View

- 2 jets

- 2 jets

- 3 jets

- 5 jets

- 2

- 2

- 3

- 5

## The CDF Detector:More Than You Need To Know

- Silicon Vertex Detector being installed

- CDF rolling into the collision hall

- (uphill both ways)

## The “Rutherford Experiment” of Geiger and Marsden

-  particle scatters from source, off the gold atom target, and is detected by a detector that can be swept over a range of angles(n.b.) a particles were the most energetic probes available at the time

- The electric field the  experiences gets weaker and weaker as the  enters the Thomson atom, but gets stronger and stronger as enters the Rutherford atom and nears the nucleus

## Results of the Experiment

- At angles as low as 3o, the data show a million times as many scatters as predicted by the Thomson model
- Textbooks often point out that the data disagreed with theory, but they seldom state how bad the disagreement was
- There is an excess of events with a large angle scatter
- This is a universal signature for substructure
- It means your probe has penetrated deep into the target and bounced off something hard and heavy
- An excess of large angle scatters is the same as an excess of large transverse momentum scatters
- We usually prefer to think about momentum instead of angles, but it’s really the same thing

## More On Jets

- Where do they come from?
- The force between two colored objects (e.g. quarks) is independent of distance
- Therefore the potential energy grows linearly with distance
- When it gets big enough, it pops a quark-antiquark pair out of the vacuum
- These quarks and antiquarks ultimately end up as a collection of hadrons
*Process is called “fragmentation” or “hadronization”*

- g

- g

- g

- g

- One (of several) processes that produce jets in collisions.

## CDF Jet Cross-Section

- The data seem to agree with Theory over an impressive 11 orders of magnitude
- But all is not as it seems...

## A Logarithmic Plot Hides a Multitude of Sins

***A Logarithmic Plot Hides a Multitude of Sins***

- Instead, plot on a linear scale:
- (data-theory)/(theory)
- This shows a strong deviation from theoretical predictions at high ET.
- This deviation appears to be consistent with quark substructure at a scale of ~1.5 x 10-19 m
- What’s going on?
- A good question
- What could be going wrong?
*A better question*

## Where Does The Prediction Come From?

- pQCD can “easily” predict the following rates:
- qq → qq
- qg → qg
- gg → gg
- etc.
- However, we don’t have a beam of quarks and gluons
- We have a beam of protons and antiprotons
- We need to know what the flux of quarks and gluons is for a given final state momentum.

## Anatomy of a pQCD Calculation

- PDF’s are usually expressed in terms of x (the fraction of the momentum of the proton carried by the parton) and Q2 (the PDF’s are functions of Q2).
- PDF’s are sometimes incorrectly called “structure functions”.  This is as wrong as “Deep Inelastic Scattering”.

- Parton Density Functions

- Hard Scatter Calculation

- Cross-Section Calculation

- Measurement

- Oversimplified view

- Comparison between theory and experiment occurs here.

## Anatomy of a pQCD Calculation II

- Connection between theory and experiment, as well as input and output, occurs pretty much everywhere
- This looks like circular reasoning, but it is not:
- The system is overconstrained – zillions of measurements
- This works because parton densities are **universal**. The same PDFs work for all processes.

- Parton Density Functions

- Hard Scatter Calculation

- Cross-Section Calculation

- Measurement

- Less-Oversimplified view

## Experiments to Measure PDF’s

- Outline
- Deeply Inelastic Scattering
- Drell-Yan Lepton Pairs
- Direct Photons

## Deeply Inelastic Scattering

- “It’s déjà vu all over again” – this is essentially the Rutherford Experiment
- This process is directly sensitive to the quarks in the nucleus
- A wide variety of probes are used:
- Electrons
- Muons
- Neutrinos
- The virtual photon can also be a W or a Z in some processes: probes different combinations of quark PDFs

- e-

- e-

- q

- q

- 

## A-Typical DIS Event

- Incoming electron beam (30 GeV)

- Scattered electron

- Incoming proton beam (820 GeV)

- Struck quark jet

- ZEUS Experiment, DESY

- Beam’s-Eye View

- Side View

- This event is a neutral current event at very large Q2.

## Deeply Inelastic Scattering III

- The ensemble of DIS measurements with different beams, targets and energies forms a coherent whole
- Some extremenly high quality data is now available:
- The Zeus and H1 experiments at HERA deserve a lot of credit for improving our understanding of proton structure

- 5 experiments

## Drell-Yan Lepton Pairs

- DIS measures the sum of quarks and antiquarks
- Sensitive to the magnitude of quark charge
- Insensitive to the sign
- This process measures a different combination:
- e.g. with a proton beam and proton target, you are looking at a valence quark in one proton and a sea antiquark in the other
- Allows one to easily separate the quark and antiquark PDFs

- Either electrons or muons can be used
- Muons are easier to trigger on and built high-rate experiments around
- Electrons can have better resolution (no multiple scattering from muon absorbers)

*l*+

*l*-

- 

## A Typical Fixed Target Drell-Yan Experiment

- Magnet

- Muon Shield

- DownstreamTracking

- Beam

- Target

- HadronAbsorber

- +

- -

- Muon Detector

- By looking only at the muons produced, this spectrometer can tolerate very high rates.

## Why You Might Want Better Resolution

- The dimuon experiment has many more events, but the peak at 3.1 is smeared out.
**No Nobel Prize**. (yet)

- The dielectron experiment has fewer events, but the peak at 3.1 is clearly visible.
**Go to Stockholm****.**

- Lederman et al.

- Ting et al.

## But What About the Gluons?

- DIS and Drell-Yan are sensitive to quarks
- Gluon sensitivity is indirect
- The fraction of momentum not carried by the quarks must be carried by the gluon.
- I guess.
- It would be useful to have a direct measurement of the gluon PDFs
- Even if it were less sensitive than the indirect measurements, it would lend confidence to the picture that is developing
- This process depends on the (known) quark distributions and the (unknown) gluon distribution

- q

- q

- g

- 

- Direct photon “Compton” process.

## Direct Photons

- In principle, simple: build a calorimeter (right) and measure the energy of photons detected in it
- In practice, tough
- You need to measure direct photons, not decay photons
- The background from 0 →  and 0 →  decays is fierce
*E-706 reports a factor ~30 over direct **s*
*If that weren’t bad enough, each background event gives you two photons*
- E-706’s final paper was published 12 years after they took data

- FNAL E-706

## Identifying Photons – Basics of Calorimeter Design

- A schematic of an electromagnetic shower

- A GEANT simulationof an electromagnetic shower

- Not too much or too little energy here.

- Not too wide here.

- Not too much energy here.

- You want exactly one photon – not 0 (a likely hadron) or 2 (likely 0)

- One photon  and not two nearby ones (again, a likely 0)

- Indicative of a hadronic shower: probably a neutron or KL.

## Direct Photon Data

- FNAL E-706

-  background

-  background

- Potential signal

- Direct Photon Signal

## Putting it Together: Global Fits

- Each class of experiment gets part of the story
- Like the tale of the blind men and the elephant
- No experiment measures the entirety of the proton
- The data from each experiment is entered into a global fit
- Two principal groups do this:
- Martin, Roberts and Stirling (MRS)
- CTEQ (Coordinated Theoretical-Experimental project on QCD)
- Other groups construct more specialized PDFs (e.g. including spin)
- There is an art to this as well as science
- Not all experiments agree – how do you average them together?

## Details of the Global Fits

- “Laws are like sausages.  It’s better not to see them being made.” – Otto von Bismark

- “The same goes for PDFs” – Anonymous

## Outcome of the Process

***Outcome of the Process***

- One fit from CTEQ and one from MRS is shown
- Despite differences in procedure, the conclusions are remarkably similar
- Lends confidence to the process
- The gluon distribution is enormous:
- The proton is mostly glue, not mostly quarks

- Want to know the uncertainties?  Use the Durham pdf plotter: http://durpdg.dur.ac.uk/hepdata/pdf3.html

## Nuclear Effects

- A proton in a nucleus is not the same as a free proton
- Proof: An  particle is smaller than a proton!
- There are number of modifications of PDFs inside nuclei
- Shadowing: a decrease in a parton’s density in a particular kinematic range
- Anti-shadowing: an increase in a parton’s density in a particular kinematic range
*If you have one, you *_*must*_* have the other.  (The total is a constant)*
- Cronin Effect: a broadening of kinematic distributions in nuclei relative to protons (usually manifests itself as a high-ET excess)
- Fermi motion
- What’s typically done is maximally confusing
- Nuclear effects are taken out as best they can before the global fit
- Then if you are interested in nuclei, you put them back in by hand

## And Now A Word From Our Sponsor

***And Now A Word From Our Sponsor***

- Many retirements in MRS and CTEQ expected over the next few years
- New data will be coming from the RHIC pp and LHC programs
- There exists an opportunity for theorists and experimenters willing to work on PDFs

## Back to the CDF Jet Excess

- “Until a realistic method for represening the theoretical uncertainties from  higher order QCD corrections and from the PDFs is found, **any claim** about the presence or absence **of new physics is indefensible**.”

- Belief this is new physics

- Graduate student doing analysis

- Postdoc

- Graduate student’s advisor

- Other faculty on experiment

- Spokesperson

- Average theorist

- Bigshot theorist

- From the PRL

- Why so coy?Because we already knew the answer.

## What Wasn’t In The Paper

- Two other papers were in preparation (published a few months later) at the time the Jet PRL was published
- #1. The angular distribution of jets
- #2. The jet cross-section at 630 GeV
- If it were really substructure
- The angular distribution would be different
- The excess would appear at the same ET if you changed beam energy
*Instead, we see that it tracks x, like you would expect if the problem was in PDFs*

## The Anticlimatic Climax

- New PDF’s were calculated that agreed about as well with previous data, but also agreed with CDF
- High x gluons increased
- The old PDFs had uncertainties, but none of the quoted uncertainties covered this particular difference
- The paper has 294 citations, many proposing new physics explanations

- (Old)

- (Old)

- (New)

## The Moral of Our Tale

- This is a tricky business – especially in understanding the uncertainties
- How do you know that the quoted uncertainties in a multivariate system cover all the possible errors?
- In a large collaboration, knowing who to talk to is vital in understanding what’s going on
- This is usually the grad student or postdoc who actually did the work
- Often there are other measurements in the pipeline that can help one interpret the data
- Some people will believe ***anything***.

## Tale The Second: Direct Photon Backgrounds

## Direct Photons and Backgrounds

- We’ve already discussed that the 0 and  background to direct photons is large.

- Again, data from E-706

## Early Background Subtractions

- Early measurements made the following argument:
- I know the total number of photon candidates
- I measure the 0 and  spectra
- I subtract the inferred number of photons from decays
- What’s left must be direct.
- The problem is, it’s not.

- If one looks in samples where one expects no direct photons and applies the same procedure, one does not get zero.
- In the trade, this is called the “Mystery Background”
- It’s a few % of the background
- But so is the signal

**What is it?**We don’t know for sure, but suspect it is the sum of many modes that contribute at a fraction of a percent:  → , ’ →  ,  → e+e- ...

## The Moral of This Tale

- Add up a large number of “negligible” backgrounds and the sum may not be so negligible.
- It’s always difficult to make a measurement of a small quantity (e.g. the direct photon cross-section) by subtracting two big quantities (the total and the background)
- It’s usually a better strategy to try and kill background than subtract it off.
- But be careful! These cuts (e.g. isolation) can make comparison with theory more treacherous.
- Theorists told us this would be easy.  They were wrong.

- Over beer some time, I would be happy to rant and rave about “the principle of minimum sensitivity”.

## Tale The Third: The Bottom Quark Cross-Section

## Why Bottom?

- The Goldilocks principle
- Charm is too light: m(c) is close to m(p), which is in turn set by non-perturbative QCD dynamics
- Top is too heavy: you don’t make many of them
- Bottom is *just right*.
- Several interesting processes (or categories of processes) contribute:

- Flavor Creation

- Flavor Excitation

- Gluon Splitting

## The First NLO Bottom Cross-Section

- P. Nason, S. Dawson and R.K. Ellis calculated the heavy flavor cross-section and found it to be in agreement with UA1 measurements at 630 GeV.
- See Nucl. Phys. B327, 49

- Note – this is an integrated cross-section, not a differential cross-section.

## Agreement?

- Note that the experimental error bars are approximately an order of magnitude
- Some points match better than others
- The last point is a factor of 15 off from the theory’s central value.

- Nonetheless, this was regarded by the community as good evidence of the agreement between theory and experiment.

## The First Tevatron Measurements

***The First Tevatron Measurements***

- At DPF92, CDF reported bottom quark cross-sections a factor of at least two greater than theory.
- This was at a center of mass energy of 1800 GeV.
- Note that the error bars are a factor of 3-5 smaller than the early UA1 measurement.
- Note also that the most discrepant point is a factor ~3 high, not 15.
- Nonetheless, this was viewed by the community as disagreement.

## Later Tevatron Measurements

- More recent CDF measurements show the same difficulty – the theory underpredicts the data by the same factor
- This problem wasn’t not going away
- Note that CDF (and UA1) measure only the high pT tail of the cross-section
- Most b’s are invisible

## Commentary on measuring the top 10% of something

- Just how important could the other 90% be anyway?

## CDF Runs at UA1’s Energy

- CDF ran for 9 days at 630 GeV
- The same data used to untangle the high ET jet excess
- CDF is still above theory
- Note that the theory, which used to go straight through the UA1 points, is now clipping the bottom.
- PDFs had improved since the original calculation

- Pointless aside: it was great fun to propose and run this nine day experiment within an experiment.

## The Breakthrough

- In Run II, CDF measured the entire B cross-section, down to *p**T* = 0.
- No extrapolation required
- This was done with ~30000 b → J/ X decays
- This barely worked – if the collision hall door were 6 inches bigger, it wouldn’t have!
- NLO QCD predicts 20-40 b

- Note: linear scale!

## Detailed comparison with theory

- Agreement with modern theory is substantially better
- No more factor of 2
- Experimental uncertainties are now ~3x smaller than theoretical uncertainties
- The high pT 10% or so of the b cross-section agrees with past measurements: a factor of 2-3 above theory
- The ***total*** cross-section agrees with theory
- Conclusion: the pT spectrum is stiffer (shifted to higher transverse momenta) than predicted

- Theory: Cacciari, Frixione, Mangano, Nason & Ridolfi hep-ph/0312132

## Theoretical Developments

- PDF’s have changed
- About a  20% effect
- Calculations now available to NLL
- About a 20% effect
**Fragmentation functions have changed**
**remember, pQCD predicts quark production, but experiments measure hadron production**
**Fragmentation cannot change the total cross section, but does change the spectrum**
**About a 20-50% effect**** **

- From M. Mangano

- All these pull in the same direction, so the agreement is now substantially better than in the past.

## The Moral Of This Final Tale

- People build particle detectors, not parton detectors
- Theory calculates the b *quark* production; we can only measure physical objects: bottom *hadrons*.
- pQCD got the b cross-section right.  It was the non-perturbative pieces that caused problems
- Going from b quarks to bottom hadrons
- To a lesser extent, PDF’s
- It’s important for experimenters to know what goes into “the theory”.  “The theory” is often not a simple thing.
- These problems were evident even in the very early data.  It was not widely recognized because of the perception “UA1 agrees with Theory”
- Despite large uncertainties
- Despite “theory” evolving in the direction of poorer agreement
- Despite mounting evidence from CDF and D0

## Final Comments

- The same rich phenomenology that makes pQCD interesting makes the experimental measurements “interesting.”
- There’s more to this than I covered – my apologies to people and topics I gave short shrift to.
- Special thanks to: the organizers, my CDF and ATLAS collaborators, the E-706 collaboration, Carlos Lourenco, the CTEQ collaboration, Tim Tait and Puneet Batra.

- All errors are strictly my own.