David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Experimental Tests of QCD at Colliders: Part 1 David Milstead Stockholm University ITEP 2006 Winter School, Moscow.

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow What do we mean by ”testing QCD” ? Quantum Chromodynamics is established as the theory of the strong force  S is the least constrained coupling constant of the fundamental forces. Difficulty calculating beyond NNLO. To test pQCD -> measurements devised to suppress higher orders To develop pQCD -> measurements devised to enhance higher orders

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow High precision is vital!

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Themes of part 1 Precision tests of perturbative QCD using ’clean’ jet, event shapes and structure functions. The capabilities of different collision environments Extraction of  s and parton densities. Important theoretical and experimental errors to consider! What have we done and what more can we do ? Are tests limited by experiment/theory/both ? Part 2 – particle production + non-perturbative QCD

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow lepton- h Pdf (h,   ISR FSR h-h pdf (h) ISR FSR Collision environments and experiments  scattering e+e- annihilation Pdf  ISR  FSR q q

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Understanding Particle Collisions Jets, particle production, energy flow, correlations (1) Partonic structure into nucleon pdf (3) ME-based pQCD (2) Higher orders via parton showering, leading log resummation Hadronisation – String, cluster, power corrections, LPHD { } QCD factorisation to separate out long and short distance interactions Eg. DIS

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Proton structure and pdfs Deep-Inelastic Scattering – Reminder! Q 2 /GeV 2 x HERA

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Collinear factorisation and parton densities Factorise long and short range interactions and neglect virtuality of interacting parton. DGLAP equations describe evolution of quark and gluon densities with  F Below a factorization scale  F emissions are absorbed into a universal parton density/distribution function (pdf)

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow F 2 from HERA-1 Range in x: Q 2 : GeV 2 Directly sensitive to sum of all quarks and anti-quarks Indirectly sensitive to gluons through scaling violations NLO DGLAP fit pQCD describes the data well over 4 orders of magnitude in Q 2

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Determination of  s NLO QCD fits to structure function data provide most precise determination from DIS data. Large theoretical error outsanding.

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow The work of HERA in determining proton structure

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Nucleon Structure with BFKL LO BFKL fit hep-ph/ H.Navelet et al. Difficult to disentangle BFKL/DLGAP/CCFM from F 2

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow DGLAP-model underestimates hard emissions in gluon ’ladder’. CCFM model describes data well + heavy quarks in ep,pp But, large uncertainties!

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Structure Functions at the LHC x Expand phase space First measurements to include Drell-Yan, multi-jet, prompt photons to determine pdfs. Problem… How do we know SUSY/UED/? Backgrounds. Require precision from pre-discovery colliders – High x gluon may inhibit discoveries Low x evolution must be well modelled

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow T. Carli, (proc. DIS 2004)

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Lessons for using pdfs Is DGLAP appropriate at low x ? Is your measurement likely to be sensitive to effects from non-ordered emissions ? How do you decide on a pdf uncertainty ? Compare several ? But then one compares only central values. CTEQ prescription (J.Pumplin et al., JHEP0207). Pdfs can be derived at LO, NLO, NNLO. Order of pdf should be matched to scale of matrix element in fixed order program which is used (coming soon).

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Disentangling perturbative QCD from the hadronic final state. Fixed order perturbative QCD calculations for jet cross-sections, leading particles, event shapes, charged particle scaling violations. Into the Hadronic Final State…

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow An incomplete list of QCD Models for the hadronic Final State Leading order multi-purpose event generators -QCD Matrix Element + parton showering+ hadronisation model (string, cluster – lecture 2): PYTHIA, HERWIG, ARIADNE (CDM), PHOJET…. Next-to-leading order models calculating specific 2-4 jet processes. Can be combined with resummed logarithms - JETRAD, JETVIP, MEPJET….. See

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow QCD uncertainties- Renormalisation These are lectures about data not QCD calculations… To test QCD we must understand QCD uncertainties. Renormalisation scale Contribution to cross- section from loops. Divergent as Regularise cross-section with introduction of cut-off – new scale  R P Observable R should be independent of choice of scale – renormalisation group equation

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Renormalisation Scale Uncertainty pQCD calculations contain an assumption for the value of the renormalisation scale – it is arbitrary but related to a hard scale in the event (eg b-mass, jet pt, Q 2 ) -Variation of this scale is often the largest theoretical uncertainty. - Scale uncertainty reduces with higher orders A question to ask anyone who shows a QCD calculation is ”what is the scale and what is the scale uncertainty?”

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Scale uncertainty and k-factors Choices of renormalisation scale K-factors for inclusive jet production in DIS Variation in value of scale (0.5  to 2  ) (customary) { { K-factors

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow NLO – LO cross-section Scale Dependence Scale uncertainity reflects contribution of higher orders. Reduced scale uncertainty for NLO Dijets in DIS with kt-algorithm 

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Jets and Partons Differences between e+e- and hh S. Chekanov, ”jet algorithms A mini-review”, (hep-ph/ )

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Gluino pair production at the LHC Quantification of discovery of any particle with colour requires pQCD calculations scale uncertainty

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Jet Physics ’Reconstruct’ pQCD process with a jet of hadrons -  s Jet clustering algorithms used to measure cross-sections. Requirements: (1)Infrared and collinear stability -jet cross-section must not change if the original parton radiates a soft parton or splits into 2 collinear partons. (2)Close correlation with parton direction (3) Small hadronisation corrections (3) Small renormalisation scale uncertainty (4) Suppression of contributions from beam remnants. e+ e- q Hadronisation jet

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Reduce experimental (energy scale) error by studying angular properties

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow 4-Jet Rate from ALEPH-LEP Based on NLO+ resummed NLL  s =

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Jets at HERA Ratio of 3-2 jets – cancel theoretical uncertainties

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow 2005 The evolution of the strong coupling constant with time!

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Event Shape Variables Thrust  Thrust: longitudinal momentum sum  Broadening: transverse momentum sum  Measured with n set to the thrust axis, and photon axis  Jet Mass and C parameter: correlations of pairs of particles Infra-red safe and excellent probe of pQCD – use current region of Breit-frame in ep. n for T T axis

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow e + e - & ep : Breit Frame DIS event Lab Frame Breit Frame  Breit Frame definition:  “Brick wall frame” incoming quark scatters off photon and returns along same axis.  Current region of Breit Frame is analogous to e + e -.  Scale Q in DIS equivalent to sqrt(s) in e+e- PTPT PLPL e+e- event

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow E Event Shapes at LEP Consistent  s from 6 different variables Running sqrt(s) variables

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Power corrections: an analytical approach  Power correction is used to calculate hadronization corrections for any infrared safe event shape variable, F  Mean event shape variables are sum of perturbative and non- perturbative (power correction) parts  The power correction depends on two parameters, α 0 and α s “non-perturbative universal parameter” Used to determine the hadronization corrections -(Dokshitzer, Webber Phys. Lett. B 352(1995)451)

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Power corrections in e+e- and DIS Consistent picture over full space range. Many experients single experiment e+e- ep

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Simultaneous extraction of  s of  0 Reasonably good agreement over many different variables

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Summary Precision tests of perturbative QCD using ’clean’ jet signals and structure functions. No sign of failure of pQCD or new physics The capabilities of different collision environments Complementary precision work at e+e-,hh,lh Extraction of  s and parton densities. Both extracted to high precision – high x pdf uncertainties - low x evolution in question Important theoretical and experimental errors to consider! Renormalisation scale uncertainties and energy scale uncertainties are some present limitations What have we done and what more can we do ? Higher orders needed. Optimal calibration. New variables Are tests limited by experiment/theory/both ? Both

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Collision environments and experiments e+e- annihilation Pdf  ISR  FSR lepton- h Pdf (h,   ISR FSR h-h pdf (h) ISR FSR  scattering Pdf(  ISR  FSR

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Photon Structure at LEP

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow SM or BSM ? Precision limited by experimental and theoretical errors Optimal to determine pdfs at HERA and then test at the Tevatron.