Search for Fundamental

Structure

Some Interesting New Data

Pekka K. Sinervo University of Toronto

1. Some History - A “How-To” Guide

2. Sharpening the Probe

3. New Results on Quark-Quark Scattering 4. Summary and Conclusions

West Coast Colloquium October 1996

Some History

Lord Rutherford performed seminal scattering studies

• Looked at α scattering off gold (1911)

• Consistent with Coulomb scattering off point particle ⇒ Uncovered the nucleus

Hofstadter and colleagues extended this work

• Studied 1 GeV e− scattering off nuclei (1953)

• Found that nucleus had extended charge distribution ⇒ shape of the nucleus

Taylor and colleagues probed more finely

• Used ∼ 18 GeV e− scattering off proton (1968)

• Found that nucleons were extended objects ⇒ discovered quarks!

Clear what the next step should be....

About Rutherford Scattering

Rutherford developed classical theory of scattering

• Charged particle Z1e scattering off nucleus Ze

• Define q⃗ = p⃗ − p′, so that q = 2p sin \frac{θ}{2}

• Differential cross section is

(\frac{dσ}{dΩ} )R = \frac{4m2 (Z1Ze2)2}{q4}

• Correct classical and QM result ⇒ Rutherford Scattering

Extended to spin-1/2 particles incident on spin-0 target

• Obtain Mott Scattering

(\frac{dσ}{dΩ} )Mott = (\frac{dσ}{dΩ} )R × (\frac{E2}{m2c4}) (\frac{1 − [q/2p]2}{1 + q2/(2Mp)} )

What Happens for Extended Targets?

When scattering particle is extended in space

• Introduce “form factor” f(q2)

f(q2) = ∫ ρ(R⃗)eiq⃗·R⃗d3 R⃗

• Fourier transform of “charge” density ρ

⇒ (\frac{dσ}{dΩ} ) = (\frac{dσ}{dΩ} )Mott |f(q2)|2

Study of Nuclear Structure

These studies were motivated by poor understanding of strong force

• Protons and neutrons are nuclear constituents

• Structure of nucleus was not understood

• Dynamics not well understood

Nuclear “charge distribution” obtained from f(q^{2})

Tells us that nucleus is ∼ 2 − 4 fm in “size”

Proton Structure

Deep inelastic e^{−}p scattering reveals proton structure

• study inelastic part of cross section

e−p → e−Xhadrons

– suppress “coherent” and resonant nuclear scattering – Begin to see scattering off of constituents

– Hitting partons with smaller x (x is momentum fraction)

• epitomised by “structure functions” Fi(x, q2)

(\frac{d2σ}{dq2dx}) ∼ \frac{4πα2}{q4} [(1 − y)\frac{F2(x, q2)}{x} + ...]

Deep Inelastic Scattering Results

SLAC DIS studies revealed clear internal structure

• Evident as hadronic energy W increases (decreases x)

Detailed studies of structure functions F_{1} and F_{2} show

• Charge 1/3 and 2/3 particles

• Spin 1/2 particles

• Presence of anti-particles (the “sea”)

Structure of Quarks

Why would we think that quarks have substructure?

• Now 6(!) known flavours

• No reason 10−12 cm should be fundamental distance scale • We don’t believe that Standard Model is last word

To uncover structure, have to increase energy scale

• DIS limited by e− energies and EWK nature of probe

• Need high-energy hadronic probe

– closest thing to q − q scattering is hadron-hadron scattering

– Highest energies possible are at Fermilab Tevatron

Complications are that quarks are bound in proton

• Only have part of total energy available (x)

• Need to know distribution of quarks as function of x

Parton Distribution Functions

Fraction of momentum carried by parton given by pdf’s

• Example is EHLQ (Set I) at q2 = 5 GeV2

• Derived from deep inelastic scattering

• Note large non-valence quark contribution – Largest uncertainty comes from gluon contribution

QCD predicts these PDF’s to evolve with q^{2}

• Get “softer” as centre-of-mass energy ŝ increases

• Best measurements come from neutrino and DIS

• Raison d’etres for several experiments

Quark–Antiquark Scattering

Standard Model describes qq̄ scattering using QCD

• Gluons interacting via strong scale αs

• Can make perturbative QCD calculations of scattering

• Next-to-leading order (NLO) calculations are the state of the art....

These predict the kinematics of pp̄ → qq̄

• The transverse energy distributions of jets

• The correlations in polar angle (or η ≡ − ln tan \frac{θ}{2})

• Do have some model-dependence – The parton distribution functions

– The renormalisation scale μ

– The truncation of the perturbation expansion 11

The Fermilab Collider Experiments

CDF and D0 / designed to study p p interactions

• Collisions with √s = 1.8 TeV created by Tevatron Collider

• Sophisticated general-purpose detectors operated by big collaborations

Main detector features:

• Hermetic Calorimetry

– D0 / has state-of-the-art Ur/Li Ar calorimeter ∗ detection of e±, γ and jets

– CDF has more traditional Pb and Fe calorimeter ∗ Scintillator readout for central region |η| < 1.1

∗ Gas proportional chamber readout for plug/forward – Coverage over |η| < ∼ 4.2

– Good hermiticity for E̸T measurement

– Provides electron ID and jet detection

Resolutions  D0 /  CDF
EM  0.15√E ⊕ 0.004E  0.13√E ⊕ 0.02E
π±, K±  0.50√E  0.80√E
E̸T x,y  1.08 + 0.019 ∑ ET

Run I Dataset

D0 / and CDF experiments ran from 1992-96

• Collected 20 pb−1 in 1992-93 (Run Ia)

• Collected 85 pb−1 in 1994-96 (Run Ib)

• Maximum L of ∼ 2.7 × 1031 cm−2s−1

The most sensitive dataset to date

• Have data on collisions up to √ŝ ∼ 1 TeV

• Can study q2 and energy dependence with high statistics • sensitive to distance scales of ∼ 10−17 cm

Focus is on dijet data

• Two high-energy jets recoiling against each other

• Easy sample to trigger on and select – Require at least one “cluster” with ET > 100 GeV

Reconstructing Jets

The final state quarks fragment into jets

• Results in a “squirt” of 20-40 particles

• Measure energy flow into calorimeter

• Define jet as a cluster of energy in η − ϕ cone of radius 0.7 • Correct for

– calorimeter response

– particles falling outside cone – acceptance

Select those events with 2 → 2 topology

• Require to be azimuthally back-to-back

• Remove events with third jet

Forms data sample used to search for substructure

Inclusive Jet Spectrum

E_{T} distribution of jets very steeply-falling

• Deconvolute detector response from spectrum

• Results in “true” ET distribution

• Can compare directly with QCD predictions that assume point scattering

High Energy Data

The high E_{T} tail does show an excess

• Best seen when comparing relative difference

One sees a fairly significant discrepancy

• Probability ∼ 1% that it arises from QCD

Tests for Compositeness

To test for compositenss, have to employ model

• Classic approach is to add 4-fermion interaction

L ∼ \frac{g2}{4π} \frac{1}{Λ} (q̄lγμql)2

• Characterised by an energy scale Λ

• Interpret it as the scale associated with the quark constituents

Effect is to enhance high jet E_{T} cross section

• Previous limits has been Λ > 1.4 TeV

Compositeness Result

We can add a 4-fermion interaction to LO QCD

• Best fit with Λ ∼ 1.6 TeV

• Rather large uncertainties

• Very model dependent

What About the D0 / Experiment?

D0 / has performed similar analysis

• somewhat less data

• larger systematic uncertainties

Their result is equivocal

• They see no need to add a compositeness term • They also are consistent with CDF data

A Possible Resolution?

Use jet polar angle (θ^{∗}) distribution

• Prefer to use the angle χ = \frac{1+cos θ∗}{1−cos θ∗}

• Rutherford scattering has flat χ distribution

CDF Angular Distributions

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Reactions

Knee-jerk reactions fall into three categories

1. We don’t know what we are doing

• American (sic!) physicists do not understand intricacies of QCD

• CDF physicists do not understand how to calibrate detector

2. There is actually some physics here • Quarks do have a size (and structure)

• We don’t understand structure of proton

3. Just a statistical fluctuation

The first assertion is hard to disprove

• However, we have cross-checked the data extensively

• Reasonably confident that understand systematics

What About the Theory?

Could QCD predictions be wrong?

1. Most suspicion turns to parton distributions • Much “churning” of PDF data taking place • Can manufacture a set that fit “better”

• Still unclear....

2. Perturbative Calculation?

• Have compared several different calculations • General agreement in results

• Doesn’t appear to be likely source

Focused attention on the calculations and assumptions

To Summarise....

We see an excess of high E_{T} jets

• consistent with a new contact interaction

• But D0 / data is equivocal

Angular distribution is QCD-like

• Not isotropic as expected in naive compositeness models

Theorists are going wild...

• Trying to figure out what could be wrong

Conclusions

Have we discovered something smaller than a quark?

• Certainly not!

• But have seen something we don’t fully understand

Clearly need more thought and study

• Continuing to receive theoretical input

• More data will be available starting in 1999 – Run II will start in April 1999

– CDF and D0 / undergoing major upgrades – Expect to get ×20 more data

So the search will continue....