QCD Jet Measurements –Inclusive Jets –Rapidity Dependence –CMS Energy Dependence –Dijet Spectra QCD with Gauge Bosons –Production Cross Sections –Differential Cross Sections –W/Z and Jets Diffractive Physics –Rapidity Gaps –Roman Pots

Jet Variables Jet 2: E T 2,  2,  2 Jet 1: E T 1,  1,  1  = 0

Jet Production 2R 1.3R

Inclusive Jets- D0

Inclusive Jets- CDF

Inclusive Jet Cross Section |  | < 0.5 PRL82, 2451 (1999) 0.1 < |  | < 0.7 Preliminary Data and theory agreement prob 47-90% NLO QCD describes the data well

PRL82, 2451 (1999) Inclusive Jet Cross Section at 1.8TeV D0 and CDF data in good agreement. NLO QCD describes the data well. Preliminary

Rapidity Dependence of the Inclusive Jet Cross Section = 1.8 TeV, |  | < 1.5 l 0.0 <   0.5 H 0.5    1.0 s 1.0    1.5 DØ Preliminary  d 2  dE T d  (fb/GeV) l 0.5    1.0 l 0.0    0.5 l 1.0    1.5 E T (GeV) ( Data - Theory ) / Theory Data and NLO QCD in good agreement Extend measurement to |  | = 3 Refine error analysis New DØ Preliminary E T (GeV)

Ratio of Scale Invariant Cross Sections  d (630)/  d (1800) vs x T  d = (E T 3 /2  ) (d 2  /dE T d  X T  E T / (  s / 2 ) Preliminary Taking different renormalizations scales in theory for 630 vs 1800 GeV produces good quantitative agreement between D0 data and NLO QCD

Measurement of  S 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  S (E T )  S (E T ) is evolved to  S (M Z ) using 2-loop renormalization group equation Systematic uncertainties (~8%) from understanding of calorimeter response Measured value consistent with world average of  S (M Z )=0.119  New measurement of  S by a single experiment & from a single observable over a wide range of Q 2.

1      dMd   d   d 3  dM d    d   N events L  M     =  Dijet Mass Cross Section NLO QCD in good agreement with data

Inclusive Dijet Differential Cross Section Beam line Trigger Jet 0.1<|  |<0.7 Probe Jet E T >10 GeV 0.1<|  |<0.7, 0.7<|  |<1.4, 1.4<|  |<2.1, 2.1<|  |< Distributions are sensitive to PDFs - CTEQ4HJ shows better agreement with data at high E T

Inclusive Dijet Differential Cross Section     Beam line Consider 4  ranges: 0.0<|  |<0.5, 0.5<|  |<1.0, 1.0<|  |<1.5, 1.5<|  |<2.0 Divide data into two samples Measure E T of both jets  Total of 8 x-sections |  |   |  |   |  |   |  |   D0 data agree with NLO QCD with CTEQ family PDFs within the systematic uncertainty.    

Subjet Multiplicity in Quark & Gluon Jets Jet E T Motivation: Separate q jets from g jets (top, Higgs, W+Jets events) Test SU(3) dynamics (QCD color factors) Ü Measure the subjet multiplicity in quark and gluon jets Contributions of different initial states to the cross section for fixed Jet E T vary with  s   compare jets at same (E T,  )  produced at different  s & assume relative q/g content is known.  1800GeV  630GeV gg qg qq Method: Select quark enriched & gluon enriched jet sample and compare jet properties Ý challenge is not to bias the samples. New

Subjet Multiplicity in Quark & Gluon Jets Method: Subjet Multiplicity M = f g M g + (1-f g )M q (g jet fractions f g obtained from theory) f 630 = 33% f 1800 = 59% Assuming that the subjet multiplicity is independent of  s (verified with MC) M q = f 1800 M f 630 M 1800 f f 630 (1-f 630 )M (1- f 1800 )M 630 M g = Use k T algorithm; unravel jets until all subjets are separated by y cut =.001 Measure number of subjets for events with jets with 55<E T <100 GeV Dominant uncertainties come from g jet fraction and choice of jetE T MC Prediction =1.86  0.08(stat) Quark JetsGluon Jets Preliminary New

QCD with Vector Bosons

W&Z Production at the Tevatron p q q p W(Z) l  ( l ) O(  s 0 ) Production dominated by qq annihilation (~60% valence-sea, ~20% sea-sea) Due to very large pp  jj production, need to use leptonic decays (BR ~ 11% (W), ~3% (Z) per mode) W g q q’ O(  s ) Modifications due to QCD corrections: Boson produced with transverse momentum ( ~ 10 GeV ) Boson + jet events possible ( W + 1 jet ~ 7%, E T jet > 25 GeV ) Inclusive cross sections larger (K factor ~ 18%) Boson decay angular distribution modified Distinctive event signatures Low backgrounds Large Q 2 (Q 2 ~ Mass 2 ~ 6500 GeV 2 ) Well understood Electroweak Vertex Benefits of studying QCD with W&Z Bosons: q q’ W g

Production of W/Z Bosons  Cross section measurements test O(  2 ) QCD predictions for W/Z production  (pp  W + X) B(W  )  (pp  Z + X) B(Z  )  S=1.8 TeV  W B(W  e )  Z B(Z  ee) R= R=10.54  0.24  S=630 GeV DØ:  W  e = 658  67 pb (DØ) (CDF) R=10.36  0.18 Preliminary

Introduction to W, Z P T Theory Small P T region (  QCD < P T < 10 GeV): Resum large logs Ellis, Martinelli, Petronzio (83); Arnold & Reno (89); Arnold, Ellis, Reno (89); Gonsalves, Pawlowski, Wai (89) Altarelli, Ellis, Greco, Martinelli (84); Collins, Soper, Sterman (85) b-space: Parisi-Petronzio (79); Davies-Stirling (84); Collins-Soper-Sterman (85); Davies, Webber, Stirling (85); Arnold- Reno-Ellis (89); AK: Arnold-Kaufann (91); LY: Ladinsky-Yuan (94) qt-space: Dokshitser-Diaknov-Troian (80); Ellis-Stirling (81); Altarelli-Ellis-Greco- Martinelli (84); Gonsalves-Pawlowksl-Wai (89); ERV: Ellis-Ross-Veseli (97); Ellis- Veseli (98) Large PT region (P T  30 GeV): Use pQCD, O(  s 2 ) calculations exist Very low P T region (P T ~  QCD ): Non-perturbative parameters extracted from data

Boson+ Jet Theory

Arnold-Kauffman Nucl. Phys. B349, 381 (91). O(  s 2 ), b-space, MRSA’ (after detector simulation) Preliminary    dof=7/19 (p T (W)<120 GeV/c)    dof=10/21 (p T (W)<200GeV/c) Resolution effects dominate at low P T High P T dominated by statistics & backgrounds D0 W P T measurement Preliminary

D0 Z P T measurement  2 /dof = 17/16  2 /dof = 83/16 Ladinsky, Yuan, PRD 50, 4239 (94), O(  s 2 ), b-space. Arnold, Kauffman, NP B349, 381 (91), O(  s 2 ), b-space. Preliminary Arnold, Reno, Nucl. Phys. B319, 37. O(  s 2 ), MRSA’, pQCD calculation Data resolution allows to discriminate between different models for VB production.

CDF P T measurements Ellis, Ross, Veseli, NP B503, 309 (97). O(  s ), qt space, after detector simulation. ResBos: Balas, Yuan, PRD 56, 5558 (1997), O(  s 2 ), b-space VBP: Ellis, Veseli, NP B511,649 (1998), O(  s ), qt-space Preliminary

W+ Jet Production LO ss ss A test of NLO

Sensitive to PDF’s, higher orders Depends on R, E T min due to jet definition Calculations of A, B from NLO DYRAD (Giele, Glover, Kosower) W+ Jet Production

W + Jets: CDF

W/Z + Jets: CDF

W+ Jet Ratio

W + Jets: CDF

Rapidity Gaps D0 and CDF study hadronic events with peculiar structure - a rapidity gap due to color-singlet exchange (pomeron). What is the Pomeron? (gap)   p hard single diffraction (gap)   p hard double pomeron (gap) p   hard color singlet (gap) p p p p p p } Probe the pomeron structure CDF and D0 made the first studies of these topologies. } pomeron

Rapidity Gaps Typical event Hard single diffraction Hard double pomeron Hard color singlet

Hard Color-singlet Exchange Dijet Production Count tracks and EM Calorimeter Towers in |  | < 1.0 for events with two jets. jet    Fraction rises with parton x Consistent with soft color rearrangement model preferring initial quark states Inconsistent with BFKL two-gluon or massive photon/U(1) gauge boson models Phys. Lett. B (1998), hep-ex / (E T > 30 GeV,  s = 1800 GeV) Measured fraction of dijet events arising from color-singlet exchange is.94 .04(stat) .12(syst)% Too large to be explained by EW boson exchange  indication of strong-interaction process.

Double Gaps at 1800 GeV |Jet  | 15 GeV D0 Preliminary Demand gap on one side, measure multiplicity on opposite side Gap Region 2.5<|  |<5.2

Double Gaps at 630 GeV |Jet  | 12 GeV D0 Preliminary Demand gap on one side, measure multiplicity on opposite side Gap Region 2.5<|  |<5.2

Demand gap on one side, measure multiplicity on opposite side Demand gap on one side, measure multiplicity on opposite side Ý Observe an excess of double gap events Plot E T distribution of the leading two jets for three data samples: Inclusive Two Jet sample with |  Jet |<1.0, One forward gap & Double Gap events Plot E T distribution of the leading two jets for three data samples: Inclusive Two Jet sample with |  Jet |<1.0, One forward gap & Double Gap events   E T spectra of double-gap events is harder than expected if Pomeron carries  5% of the proton’s momentum  s = 630GeV  s = 1800GeV DØ Preliminary Double Gaps at 1800 & 630 GeV

Kinematic Characteristics of Diffractive Dijets Absolute normalization Stat errors only Diffractive Dijet spectrum is steeper Diffractive Dijet system recoils against pot track Diffractive events are cleaner (fewer 3rd jets)

Diffractive Dijet Production Use roman-pot triggered data from Run 1C at 1800&630GeV Select events with two jets and roman pot hits Measure production rates and kinematic characteristics of difractive dijet events

Diffractive to Non-Diffractive Ratio vs Rate of diffractive to non-diffractive events decreases with increasing