Quantum Chromodynamics (QCD) Andrew Brandt UT-Arlington/DØ Experiment Quarknet June 6, 2001

Structure of Matter Matter Molecule Atom Nucleus Baryon Quark (Hadron) u cm 10-9m 10-10m 10-14m 10-15m <10-19m Chemistry protons, neutrons, mesons, etc. p,W,L... top, bottom, charm, strange, up, down Atomic Physics Nuclear Physics Electron Mass (Lepton) Give scale and relationship to the domain that high energy physicists work in. Introduce the fundamental bits of matter loosely so that audience can point back to bulk matter. Domain. proton ~ 1 GeV/c2 <10-18m High Energy Physics

Forces Forces work by the exchange of Boson’s Electromagnetic: Photon Exchange Weak Nuclear Force: Causes Nuclear Decays neutron proton W- boson e- photon  p+ electron n

Forces: Strong Nuclear or Color Strong Nuclear Force: Quantum Chromodynamics Gluon Exchange, also holds the nucleus together. All quarks carry a color charge Gluons carry two color charges Different from other Forces: Gluons can interact with other gluons. Quarks and gluons are free at small distances (asymptotic freedom), but not at large distances (confinement)  cannot observe bare color Always observe quarks in multiplets: Baryons qqq (Proton neutron) and Mesons (quark antiquark pair ) Proton: uud Also contains gluons and quark-antiquark pairs in a sea. Neutron: udd Pion: ud

Proton Antiproton Collisions A word about units: HEP uses “natural units” 900 GeV Protons 900 GeV Antiprotons The mass of a proton is then given by Collide protons and antiprotons each with 900 GeV of kinetic energy.

Life at Fermilab

Particle Colliders as Microscopes QM: large momenta = small distances How we see different-sized objects:

Rutherford Scattering The actual result was very different. “It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back at you” Implied the existence of the nucleus. We perform a similar experiment at Fermilab to look for fundamental structure

Proton Structure Proton contains three valance quarks: uud Also contains sea of virtual quark anti-quark pairs. All held together by gluons Quarks and gluons are called partons. Proton with momentum P. Individual parton carries momentum xP d u s uv uv u s u d dv u

Parton-Parton Scattering Described by QCD. Scattered Parton Anti-Proton 900 GeV Proton 900 GeV Scattered Parton

Perturbative QCD and Jet Production s ~ a2s (LO) ^ Observable jet of particles in detector q Parton distribution (PDF) q (x1) jet g q (x2) q jet Fragmentation into hadrons p Hard scatter (pQCD) s ~ a3s (NLO) ^ Includes radiative corrections and gluon emission - much of current QCD is a study of this additional radiation p

Jets Jets are formed by the scattered partons. QCD requires that colourless objects are produced (hadrons) e.g..: , K, , etc. At DØ a jet is defined to be the energy deposited in a cone of radius:

Measured Event Variables In a Two Jet event the following is measured: Jet 1: ET1, h1, 1   ET = Energy x sin  Jet 2: ET2, h2, 2 h = 0

The DØ Detector x y z  

Charged Particle Tracks Detection EM hadronic B Ä Interaction Point Scintillating Fiber Silicon Tracking Calorimeter (dense) Wire Chambers Absorber Material electron photon jet muon neutrino -- or any non-interacting particle missing transverse momentum Charged Particle Tracks Energy Muon Tracks We know x,y starting momenta is zero, but along the z axis it is not, so many of our measurements are in the xy plane, or transverse The Run 2 detector. Schematically how it works. SVX and the like.

Inclusive Jet Cross Section as a Test of the Standard Model (pQCD) Single Inclusive Jets:

Jet Production and Reconstruction Time “parton jet” “particle jet” “calorimeter jet” hadrons  CH FH EM Highest ET dijet event at DØ RECO [Slide 1] Very briefly mention RECO version used. Mention that these are fixed-cone jets of R=0.7 found by iterative algorithm, Et is the scalar Et sum of the towers. List corrections we apply (basically) to RECO. No more is needed for AIDA restoration or Ht-revertexing at this point, but following three slides will be about eta bias -- so just briefly prepare listeners for this! Fixed cone-size jets Add up towers Iterative algorithm Jet quantities:

“Typical DØ Dijet Event” ET,1 = 475 GeV, h1 = -0.69, x1=0.66 ET,2 = 472 GeV, h2 = 0.69, x2=0.66 MJJ = 1.18 TeV Q2 = ET,1×ET,2=2.2x105 GeV2

High Energy Art

The DØ Central Inclusive Jet Cross Section DØ Run 1B PDF, substructure, … ? d2/dET d ET How well do we know proton structure (PDF)? Is NLO ( ) QCD “sufficient”? Are quarks composite? 0.0    0.5 JETRAD Phys. Rev. Lett. 82, 2451 (1999)

Data Selection and Corrections Unfold effects of finite jet energy resolutions from very steeply falling inclusive jet cross sections E0 DØ “observed” “true” “smearing” “unsmearing” or “unfolding” ET (GeV) Smearing Correction 0.86 0.90 0.94 0.98 50 100 150 200 250 300 350 400 450 500

Data Selection and Corrections Cut on central p-pbar vertex position Eliminate events with large missing ET Apply jet quality cuts Jet energy scale correction: “calorimeter”  “particle” jet “parton jet” “particle jet” “calorimeter jet” hadrons  CH FH EM E = (EObs-Offset)*Det.Uniformity RH * Out of Cone Showering RECO [Slide 1] Very briefly mention RECO version used. Mention that these are fixed-cone jets of R=0.7 found by iterative algorithm, Et is the scalar Et sum of the towers. List corrections we apply (basically) to RECO. No more is needed for AIDA restoration or Ht-revertexing at this point, but following three slides will be about eta bias -- so just briefly prepare listeners for this!

Uncertainties in Cross Section Calculations |h|<0.5 Inclusive Jet CS s=1800GeV NLO pQCD predictions (s3): - Ellis, et al., Phys. Rev. D, 64, (1990) EKS - Aversa, et al., Phys. Rev. Lett., 65, (1990) - Giele, et al., Phys. Rev. Lett., 73, (1994) JETRAD Choices (hep-ph/9801285, EPJ C5, 687, 1998): - Renormalization Scale (~10%) - PDFs (~20% with ET dependence) - Clustering Alg. (~5% with ET dependence) 2R 1.3R DØ uses: JETRAD, , Rsep= 1.3. PDF's dominate uncertainties  Jets offer valuable constraints! But sensitivity is reduced in ratios, angular distributions...

Jets in PDFs CTEQ5 Q (GeV) 1/ x Tevatron jet data serves as stronger 101 x-Q region spanned by experimental data in modern fits Tevatron jets in blue Q (GeV) 101 CTEQ5 100 100 101 102 103 104 1/ x Tevatron jet data serves as stronger constraint in medium x region for CTEQ. MRST uses does not use these data.

Inclusive Jets- CDF

Inclusive Jet Cross Section at 1.8TeV Preliminary PRL82, 2451 (1999) This plot shows the Data-Theory/Theory plot for CDF and D0 results together. The D0 x-sec has been remeasured to match CDFs pseudorapidity range of 0.1 to 0.7. CDF is now presenting their systematic uncertainties for the final Run I measurement for the first time. They are plotted down here together with the uncertainties from D0. Roughly 10% for D0, 15% for CDF in the lowest Et bins; 22% for D0 and 27% for CDF at 400GeV. Overall nice agreement between the two experiments and with NLOQCD. D0 and CDF data in good agreement. NLO QCD describes the data well.

Rapidity Dependence of the Inclusive Jet Cross Section ET (GeV) d2 dET d (fb/GeV) 0.0    0.5 0.5    1.0 1.0    1.5 1.5    2.0 2.0    3.0 DØ Preliminary Run 1B Nominal cross sections & statistical errors only

Are Quarks composite particles? Compositeness Atom Nucleus Nucleon Quark Continuing Search for fundamental building block Atom  Nucleus  Nucleons  Quarks Three quark and lepton generations suggests that quark and leptons are composites. Question Are Quarks composite particles? Search for compositeness in Proton Anti-proton collisions

Search for Compositeness Define the preons interaction scale as  Existence of substructure at energies below  indicated by presence of four-fermion contact interactions. Strength of interactions related to Proton Quark Preons? t’Hooft: interactions at high energy leads to massless composite fermions via unbroken chiral symmetries of the preons and confinement by their strong precolour interactions. The presence of three quark and lepton generations suggests that they could be composite particles Composed of “preons” M cos

Predictions If quarks are made up of smaller particles then expect more events at high mass, and at smaller scattering angles Prediction for composite quarks Number of Events Number of Events Prediction for fundamental quarks cos * M

Dijet Production To search for compositeness we need a good prediction for Standard Model dijet production  NLO QCD. NLO event generator JETRAD (Giele, Glover, Kosower Nucl. Phys. B403, 633) Need to choose pdf Choose Renormalization and Factorization scales (set equal) Rsep: maximum separation allowed between two partons to form a jet (mimic exp. algorithm) Rsep=1.3R (Snowmass: Rsep=2.0R) Factorization Scale: Arbitrary parameter that separates the long and short distance physics. A parton with PT < mu will be absorbed into the hadron structure. Renormalization Scale: scale introduced to remove divergences, as perturbation series reaches infinity dependence drops to zero. 1.3R 2R

Dijet Cross Section Phys. Rev. Lett. 82, 2457 (1999)

Cross Section Ratio Submitted to PRL: hep-ex/9807014 Calculate Ratio of Cross Sections. Two different angular regions Submitted to PRL: hep-ex/9807014 Model with LL coupling

Quark-Quark Compositeness Limits Limit on size of preons is fempto-meters

Conclusions No evidence for Compositeness found at the Tevatron Standard Model (QCD) in excellent agreement with the data Quark-Quark Compositeness  > 2 to 3 TeV depending on models

Numerous other QCD studies to probe scattering dynamics W/Z PT,W/Z+Jets + +... W, Z q(x) Jets in High E Limit  Photons Color Flow Diffraction etc...

Measurement of aS from Inclusive Jet Production NLO x-section can be parametrized as Measured by CDF Obtained from JETRAD Fitting the NLO prediction to the data determines aS(ET) aS(ET) is evolved to aS(MZ) using 2-loop renormalization group equation Systematic uncertainties (~8%) from understanding of calorimeter response Measured value consistent with world average of aS(MZ)=0.119±0.004 CDF measures the value of the strong coupling constant from the inclusive jet cross section over a large range of transverse energies. The NLO x-sec can be parametrized as a function of the strong coupling constant and two parameters, A and B, that depend on the Jet transverse energy. CDF measures the x-section, the parameters A and B can be obtained from JETRAD. For simplicity the renormalization and factorization scale are set to Et/2. Fitting the NLO prediction to the measured x-sec determines alpha_s as a function of transverse energy. The result is shown in this plot in blue compared to the expected running of alpha_s with Et. The measured alpha_s can then be evolved to the value of alpha_s at the Z mass using a 2 loop renormalization group equation. The result is shown in this plot in red. The measured value for alpha_s at the Z mass obtained when using the CTEQ4M parton distribution is 0.1129+-0.0001 (stat). The systematic uncertainty comes mostly from the understanding of the calorimeter response and is below 10%. This result extended the measurement of alpha_s to a very high Q2 range and clearly shows the running of alpha_s. The result is consistent with the world average for alpha_s at the Z mass of 0.119. New measurement of aS by a single experiment & from a single observable over a wide range of Q2.

Conclusions Standard Model (QCD) in excellent agreement with the data No evidence for Compositeness of quarks found at the Tevatron Studies continue improving theory, detectors, and using better microscopes