Experimental Issues in pQCD

Thomas J. LeCompte

High Energy Physics DivisionArgonne National Laboratory

2

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

3

Tale The First: The CDF High ET Jet Excess

4

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

5

The CDF Detector:More Than You Need To Know

Silicon Vertex Detector being installed

CDF rolling into the collision hall

(uphill both ways)

6

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

7

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

0 1 2 3 4 5 6 7 8 9

Degrees

1E-10

1E-8

1E-6

0.0001

0.01

1

100

Sca

tte

ring

(a

rbitr

ary

un

its)

DataThomson Model

Geiger-Marsden Results

8

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.

9

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…

GeV1800s

10

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

11

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.

12

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 FunctionsHard Scatter Calculation

Cross-Section Calculation

Measurement

Oversimplified view

Comparison between theory and experiment occurs here.

13

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 FunctionsHard Scatter Calculation

Cross-Section Calculation

Measurement

Less-Oversimplified view

14

Experiments to Measure PDF’s

Outline

– Deeply Inelastic Scattering

– Drell-Yan Lepton Pairs

– Direct Photons

15

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

)()(3

1)()(

3

222

xdxdxuxu

16

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.

17

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

18

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)

)(xq

)(xq

l+

l-

19

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. XNp

20

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.

21

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

qg

Direct photon “Compton” process.

22

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

23

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.

24

Direct Photon Data

FNAL E-706

background

background

Potential signal

Direct Photon Signal

25

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?

26

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

27

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

28

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

29

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

30

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.”

Bel

ief

this

is n

ew p

hysi

cs

Graduate student doing analysisPostdoc

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.

31

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

32

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)

33

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.

34

Tale The Second: Direct Photon Backgrounds

35

Direct Photons and Backgrounds

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

Again, data from E-706

36

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- …

37

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”.

38

Tale The Third: The Bottom Quark Cross-Section

39

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

40

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.

41

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.

42

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.

43

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

44

Commentary on measuring the top 10% of something

Just how important could the other 90%

be anyway?

45

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.

46

The Breakthrough

In Run II, CDF measured the entire B cross-section, down to pT = 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!

b 1.49.34.04.29

47

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

48

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

Fro

m M

. M

angano

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

49

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

50

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.