Precision QCD Tests at HERA - The Standard Model of Particle Physics - HERA Machine and Experiments - Precision QCD Tests at HERA Summary Robert Klanner Hamburg Precision QCD Tests at HERA

Ch.1: Standard Model – Building Blocks In the Standard Model of Particle Physics, which summarizes 50 years of experimen- tal and theoretical research: Elementary building blocks of known matter: mass/energy distribution in universe 5% m t e leptons (weak IA) all elementary particles of the SM have been experimentally observed! ne nm nt missing element of the SM: generation of mass (of elementary particles): Higgs mechanism quarks (+strong IA) up charm top down strange bottom mass Quarks und Leptonen come in 3 families - masses vary by 106 (1012) Robert Klanner Hamburg Precision QCD Tests at HERA

Standard Model: Forces In SM forces mediated by the exchange of bosons, which couple to “charges” The form of the interactions is derived from the symmetry of “local gauge invariance” (e.g. em: arbitrary rotation in U(1) space) In Nature we know 4 fundamental forces: boson: photon with spin 1, U(1), electrom. charge bosons: 8 gluons with spin 1, SU(3), colour charge unified GSW bosons: W+ W- Z0 with spin 1, SU(2), weak charge bosons: graviton with spin 2, mass, not part of SM ! SM is a beautiful theory – one of the greatest achievements of 20th century physics, but many open questions: many “arbitrary“ parameters, relation quarks – leptons, unification of forces, gravity, … limit of a more general theory Robert Klanner Hamburg Precision QCD Tests at HERA

Standard Model: QED Why do we believe in “correctness” of SM? precise predictions directly testing the struc- ture of the theory, which have been verified experimentally to high accuracy Quantum-Electro-Dynamics: - thanks to smallness of e.m. coupling a(E~0) =1/137 035 989 … and the ingenuity of our theoretical colleagues perturbative calculations to high accuracy ½(g-2)e = (1 159 652 185.9±3.8) 10-12 meas. ½(g-2)e = (1 159 652 201.2±27.1) 10-12 theo. ½(g-2)m = (1 165 920.80±.58) 10-9 meas. (meas.-theory) (1.19±0.73) 10-9 (Dm (theoretical) dominated by had. contributions!) Lamb shift, a(m), and many more Robert Klanner Hamburg Precision QCD Tests at HERA

Standard Model: Electro-Weak Sector Precision data from LEP,SLC,FNAL, etc test higher order e.w. predictions of SM Status: Winter 2005 demonstration of e.w. unification at HERA rate distance [m] Open Question: Why does SM work so well ?! Robert Klanner Hamburg Precision QCD Tests at HERA

Predictive Power of SM (EW) Quantum fluctuations (Heisenberg: DE*Dt > h/2p) allow access to higher masses and energies: e+ e- l,q,W+ l,q,W- virtual heavy particle influences reaction-rates and -properties e.g. corrections of higher order in the electro-weak force:  Mass of Top-Quarks was predicted by precision measurements within SM Robert Klanner Hamburg Precision QCD Tests at HERA

Gravity – Strong Force – Summary Ch. 1 Gravity not part of SM - F(gravity)/F(em) ~ 10-43 (major puzzle !)  so far not relevant for experimental particle physics - Newton’s law verified only down to ~ 0.1 mm  possible deviations from 1/r2  extra dimensions to accommodate difference in strength of gravity compared to the other interactions (at low energy) ? Precision tests of the strong force  ch.3 Summary chapter 1: Standard Model of Particle Physics is an impressive intellectual achievement: a theory which makes precise and testable predictions so far all experimental results agree with predictions (sometimes to an incredible accuracy) but limitations + incomplete  SM is only limiting case of a broader theory Robert Klanner Hamburg Precision QCD Tests at HERA

Chapter 2: HERA and its Experiments The world’s only electron/positron - proton storage ring 27.5 GeV polarised electrons (positrons) 920 GeV protons ⇨ 320 GeV in cms Four experiments H1, ZEUS, HERMES and {HERAb} (≈ 1000 scientists) data taking: 1992 until mid 2007 when HERA data taking ends Robert Klanner Hamburg Precision QCD Tests at HERA

HERA machine 2 HERA I (1992-2000): 110 pb-1 e+ and 15 pb-1 e- data for H1 and ZEUS + polarised e- on pol./unpol. gas target for HERMES + pN data for HERAb HERAII ( 2007): polarised e+/e--p data for H1/ZEUS + data for HERMES upgrade in 2000/01, 2002/03 severe BG problems, now solved and (aging) HERA runs well Lmax~ 4 1031cm-2s-1 ;Luminosity aims: ~0.7 fb-1 until end of data taking in mid 2007 Robert Klanner Hamburg Precision QCD Tests at HERA

HERA Collider Detectors - 1 - detectors conceived in 1985 to 1988 - first data in 1992 - HERA first collider with short (96 ns) time between bunches  trigger/event pipe-lined - 1-1.5% Lumi accuracy - compared to LEP/D0/CDF: precision hadron calorimetry DE(100GeV) ~ 3.5-5% calibration at 1% level (essential for precision physics at HERA) - HERAb with 20 MHz inter- action rate: major progress in trigger + radiation tolerance H1 Detector Robert Klanner Hamburg Precision QCD Tests at HERA

HERA Collider Detectors 2 A (fairly typical) NC ep  e+q(jet)+X event (Q2=3500GeV2, x=0.05) events clean  precise reconstruction of kinematics (directly seen underlying Feynman graph) e e e p p rest q q  jet Robert Klanner Hamburg Precision QCD Tests at HERA

Chapter 4: Tests of QCD at HERA HERA: precision microscope shining (e.m. and weak) light onto the proton resolution Dx~1/Q can be tuned at HERA down to 10-18m (1/1000 rp) Q2 Dx GeV2 fm ~0.5 1/3 ~ 2 1/10 > 5 <1/10 >105 <1/1000 charge distr. quarks scaling scaling violation sub-struct.? p momentum fraction of parton (QPM) resolution power can be tuned ⊕ for Q2  0 g: has a hadronic component (e.g. g  r)  transition from point-like g/Z-hadron to hadron-hadron scattering Robert Klanner Hamburg Precision QCD Tests at HERA

Tests of QCD: Structure of photon vs Q2 Is the picture of the “photon structure” vs resolution – 1/Q2 correct?  2 jet production vs Q2 ~ yes “direct” xg > 0.8 “resolved” xg < 0.8 description not perfect qualitatively o.k!  with increased Q2 – exchanged g getting point-like Robert Klanner Hamburg Precision QCD Tests at HERA

Tests of QCD: Properties of Exchanged Partons Is the picture of the “exchange of virtual quarks and gluons” correct?  2 jet production vs Q2 yes “direct” xg > 0.8 “resolved” xg < 0.8 angular distribution of jets in jet-jet cm system is sensitive to the spin of the exchanged particle: Spin 1 (gluons): (like Rutherford) Spin ½ (quarks): g g q q Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: The running coupling constant aS 1973 Breakthrough in development of QCD: asymptotic freedom  strong coupling weak at small distances (high energies – scale m)  perturbative calculations possible for precise predictions m dependence of aS controlled by b-function: < 0 aS(m) expressed via parameter L[GeV]: Robert Klanner Hamburg Precision QCD Tests at HERA

Precision Tests of QCD: What are the Problems 1.) aS is small only at small distances (high Q2)  only*) domain for precision tests using perturbative expansion in aS, e.g. calculate Ai from Feynman graphs  divergences have to be regulated in some scheme  Ai depend explicitly on scale m (infinite sum does not) if wrong scale m’ is chosen  terms ln(m’/m) appear choice not obvious (if higher order terms small  confidence that o.k.) (NB there are also problems with two scales m1,m2  terms ln(m1/m2)) 2.) b function changes when m passes quark mass M some arbitrariness how to treat effect 3.) no free quarks  non perturbative effects “everywhere” – handled via models (pdfs, Monte Carlo)  use reactions where effects not so important (e.g “total cross sections”) *) Lattice Gauge Theory is start to produce precise results Robert Klanner Hamburg Precision QCD Tests at HERA

Measurement of aS – Why?  test QCD Besides masses, aS [L] only free parameter of QCD Why precise measurements in many different ways? all strong interaction cross- sections depend on aS, if QCD correct  all measure- ments should agree  test QCD if disagree problem with QCD ??? (more probably large distance effects) unification of forces: precision at today’s energies is required for pre- cise extrapolation to unification scale and the physics on the way to there Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: aS from DIS Structure Functions Q2 evolution of structure functions q, g: splitting functions P have been calculated up to 2nd order – for unpol. 3rd order soon - theoretically “clean” method, - HERA alone: correlation gluon - aS (resolved by fit SF + jets) - uncertainty on sea quarks: , - terms at large x, - terms at small x, - photon structure at low Q2. improvements (experimental + theoretical) are under way  later (H1: 2000, ZEUS: 2002) Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: aS from Jet Production Diagrams contributing to jet production: Example-1: H1 DIS in Breitframe: deep inelastic scattering: photoproduction: - theoretically less clean than DIS - but measurement of m dependence running of aS in agreement with QCD prediction observed in single experiment Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: aS from 2-Jet to 3- Jet Ratio Example-2: ZEUS ratio of 3-jet to 2-jet production: : - uncertainty of parton distribution functions cancel (in some approximation) running of aS in agreement with QCD prediction observed in single experiment Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: aS from Jet Sub-structure Example-3: ZEUS from jet structure: small experimental error theoretical error ??? integrated jet shape: fraction jet transverse energy within cone of radius r in η, φ plane ψ(r=0.5) vs ET(jet) aS(ET) ψ(r) comparison to theory running of aS in agreement with QCD prediction observed in single experiment Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: aS Summary measurements compatible combine results for each expt. many different aS measurements give consistent results “running of aS as predicted by QCD  major success QCD Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Proton Structure (1) - HERA ! Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Proton Structure (2) dr ∝ 1/Q2 major success of perturbative QCD Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Proton Structure (3) (use low Q2 fixed target data to constrain high x pdfs) HERA has provided a precision determination of proton structure  essential input for SM and BSM study at present and future accelerators Robert Klanner Hamburg Precision QCD Tests at HERA

Proton Structure and Higgs Cross section at LHC Impact on precision of parton functions on Higgs signal (+background) at LHC Spread of existing pdf gives already up to 10% uncertainty  improve ! Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Proton Structure (4) Use all (>100pb-1) HERAI data (neutral and charged current reaction): e p data only (no nuclear data !) Q2/GeV2 HERA has provided a precision determination of proton structure  essential input for SM and BSM study at present and future accelerators Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Jets in the Final State QCD: parton functions universal  the same parton function describes different reactions e.g. jet production, heavy quark production, single photons, …. Events with two jets: - dominant graph (LO) “photon-gluon fusion” (direct coupling to gluon – in DIS only derivative ∝ (gluon density in p) - in two jet events momentum of gluon can be reconstructed Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Jets in the Final State Combined fit of proton structure function and s(jet)  data well described ⊕ improved precision at high x ⊕ no correlation between aS and gluon ⊕ data from a single experiment simultaneous description  major success for QCD Robert Klanner Hamburg Precision QCD Tests at HERA

Test of QCD: Heavy Flavour in the Final State Production of heavy flavour particles: high quark mass provides large scale m scc/stot=F2cc/F2 first results become available for b-quarks NLO QCD predicts scharm correctly Robert Klanner Hamburg Precision QCD Tests at HERA

HERMES: Spin of Nucleon NLO QCD (MS) analysis/fit of spin data: Assumptions: - Flavour symmetric spin dependent sea - uv and dv constrained by F and D (SU(3) symmetry) low-x extrapolation questionable !  results for Q02 = 4 GeV2: uv  0.73 .....0.86 (0.10) dv  -0.40...-0.46 (0.10) qs  -0.04 ...-0.09   0.14 ...0.20 G  0.68 ...1.26 information from high pT had. pairs (HER-MES, COMPASS) and charm (COMPASS) Data described by NLO QCD fit (aS(MZ) = 0.1182) Robert Klanner Hamburg Precision QCD Tests at HERA

QCD: Diffraction in Deep Inelastic Scattering HERA 1992: ~ 10% of deep inelastic events have no particle flow between proton and jet (rapidity gap) - (same effect also seen in W-exchange) Surprise: - why does p remain intact - confinement? - are there colour neutral objects in p? - can process be described by QCD?  HERA microscope the ideal instru- ment for study define and measure diffractive structure function: rap. gap to proton Robert Klanner Hamburg Precision QCD Tests at HERA

QCD: Diffraction in Deep Inelastic Scattering systematic measurements using different methods: - rapidity gap, - fit to particle flow, - measurement of proton. after hard work results of measurements in good agreement Robert Klanner Hamburg Precision QCD Tests at HERA

QCD: Diffractive Structure Function comparison diffractive ⇔ proton structure function: H1 diff. SF: positive  gluon dominance; data well described by NLO QCD Robert Klanner Hamburg Precision QCD Tests at HERA

QCD: Diffractive Final States using QCD jet and heavy flavour production in diffraction predicted: charm structure function D* cross sections good description by NLO QCD high Q2 diffraction: well described by QCD – relation to basic QCD however unclear Robert Klanner Hamburg Precision QCD Tests at HERA

Summary The Standard Model of Particle Physics beautifully summarizes the present experimental results and knowledge of Particle Physics. QCD, the theory of the strong force, is the least tested part of the SM. Tests of QCD (and not of models) is so far (essentially) limited to the small distance predictions (perturbative) – but non-perturbative effects are present everywhere and have to be carefully understood. HERA has put the tests of QCD to a new level of breadth and precision (scaling of structure functions, final states in photo-production and deep inelastic scattering, aS) – sometimes reaching the 2% level. So far QCD has very well passed the tests + lots has been learned on QCD These results, interesting in themselves, are also important for understan- ding the much more complex situation at the LHC. Robert Klanner Hamburg Precision QCD Tests at HERA