Copenhagen, Apr QCD Phenomenology at Hadron Colliders Peter Skands CERN TH / Fermilab

Peter Skands QCD Phenomenology at Hadron Colliders - 2 May 2008Overview ►Introduction Calculating Collider Observables ►The LHC from the Ultraviolet to the Infrared Bremsstrahlung Hard jets Towards extremely high precision: a new proposal The structure of the Underlying Event What “structure” ? What to do about it? Hadronization and All That Stringy uncertainties QCD and Dark Matter: an example Disclaimer: discussion of hadron collisions in full, gory detail not possible in 1 hour  focus on central concepts and current uncertainties

Peter Skands QCD Phenomenology at Hadron Colliders - 3 ►Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory Example: Q uantum C hromo D ynamics Reality is more complicated High transverse- momentum interaction

Peter Skands QCD Phenomenology at Hadron Colliders - 4 Event Generators ►Generator philosophy: Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events 1.Parton Showers 2.Hadronisation 3.The Underlying Event 1.Soft/Collinear Logarithms 2.Power Corrections 3.All of the above (+ more?) roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for fully exclusive events is asking for quite a lot …

Peter Skands QCD Phenomenology at Hadron Colliders - 5 Non-perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio,... Soft Jets and Jet Structure Soft/collinear radiation (brems), underlying event (multiple perturbative 2  2 interactions + … ?), semi-hard brems jets, … Resonance Masses… Hard Jet Tail High-p T jets at large angles & Widths s Inclusive Exclusive Hadron Decays Collider Energy Scales + Un-Physical Scales: Q F, Q R : Factorization(s) & Renormalization(s) Q E : Evolution(s)

Peter Skands QCD Phenomenology at Hadron Colliders - 6 T he B ottom L ine The S matrix is expressible as a series in g i, g i n /Q m, g i n /x m, g i n /m m, g i n /f π m, … To do precision physics: Solve more of QCD Combine approximations which work in different regions: matching Control it Establish comprehensive understanding of uncertainties Improve and extend systematically Non-perturbative effects don’t care whether we know how to calculate them FODGLAP BFKL HQET χPT

Peter Skands QCD Phenomenology at Hadron Colliders - 7 Problem 1: bremsstrahlung corrections are singular for soft/collinear configurations  spoils fixed-order truncation e + e -  3 jetsBremsstrahlung

Peter Skands QCD Phenomenology at Hadron Colliders - 8 ►Supersymmetric particles: pair production + up to two explicit extra QCD bremsstrahlung jets Each emission  factor of the strong coupling  naively factor 0.1 per jet For this example, we take MSUSY ~ 600 GeV Collider Energy = 14 TeV Conclusion: 100 GeV can be “soft” at the LHC Matrix Element (fixed order) expansion breaks completely down at 50 GeV With decay jets of order 50 GeV, this is important to understand and control Bremsstrahlung Example: LHC FIXED ORDER pQCD inclusive X + 1 “jet” inclusive X + 2 “jets” LHC - sps1a - m~600 GeVPlehn, Rainwater, Skands PLB645(2007)217 (Computed with SUSY-MadGraph)

Peter Skands QCD Phenomenology at Hadron Colliders - 9 Beyond Fixed Order 1 ►dσ X = … ►dσ X+1 ~ dσ X g 2 2 s ab /(s a1 s 1b ) ds a1 ds 1b ►dσ X+2 ~ dσ X+1 g 2 2 s ab /(s a2 s 2b ) ds a2 ds 2b ►dσ X+3 ~ dσ X+2 g 2 2 s ab /(s a3 s 3b ) ds a3 ds 3b ►But it’s not a parton shower, not yet an “evolution” What’s the total cross section we would calculate from this? σ X;tot = int( dσ X ) + int( dσ X+1 ) + int( dσ X+2 ) +... Probability not conserved, events “multiply” with nasty singularities! Just an approximation of a sum of trees. But wait, what happened to the virtual corrections? KLN? dσXdσX α s ab s ai s ib dσ X+1 dσ X+2 This is an approximation of inifinite- order tree-level cross sections “DLA”

Peter Skands QCD Phenomenology at Hadron Colliders - 10 Beyond Fixed Order 2 ►dσ X = … ►dσ X+1 ~ dσ X g 2 2 s ab /(s a1 s 1b ) ds a1 ds 1b ►dσ X+2 ~ dσ X+1 g 2 2 s ab /(s a2 s 2b ) ds a2 ds 2b ►dσ X+3 ~ dσ X+2 g 2 2 s ab /(s a3 s 3b ) ds a3 ds 3b + Unitarisation: σ tot = int( dσ X )  σ X;PS = σ X - σ X+1 - σ X+2 - … ►Interpretation: the structure evolves! (example: X = 2-jets) Take a jet algorithm, with resolution measure “Q”, apply it to your events At a very crude resolution, you find that everything is 2-jets At finer resolutions  some 2-jets migrate  3-jets = σ X+1 (Q) = σ X;incl – σ X;excl (Q) Later, some 3-jets migrate further, etc  σ X+n (Q) = σ X;incl – ∑σ X+m<n;excl (Q) This evolution takes place between two scales, Q in and Q fin = Q F;ME and Q had ►σ X;PS = int( dσ X ) - int( dσ X+1 ) - int( dσ X+2 ) +... = int( dσ X ) EXP[ - int(α 2 s ab /(s a1 s 1b ) ds a1 ds 1b ) ] dσXdσX α s ab s ai s ib dσ X+1 dσ X+2 Given a jet definition, an event has either 0, 1, 2, or … jets “DLA”

Peter Skands QCD Phenomenology at Hadron Colliders - 11 Perturbative Evolution ►Evolution Operator, S (as a function of “time” t=1/Q ) Defined in terms of Δ(t 1,t 2 ) – The integrated probability the system does not change state between t 1 and t 2 (Sudakov) Pure Shower (all orders) w X : |M X | 2 S : Evolution operator {p} : momenta “X + nothing” “X+something” A: splitting function S unitary  total (inclusive) σ unchanged, only shapes are predicted (i.e., also σ after shape-dependent cuts)

Peter Skands QCD Phenomenology at Hadron Colliders - 12 Constructing Parton Showers ►The final answer will depend on: The choice of evolution “time” The splitting functions (finite terms not fixed) The phase space map ( dΦ n+1 /dΦ n ) The renormalization scheme (argument of α s ) The infrared cutoff contour (hadronization cutoff) ►They are all “unphysical”, in the same sense as Q Factorizaton, etc. At strict “Leading Log”, any choice is equally good However, 20 years of parton showers have taught us: many NLL effects can be (approximately) absorbed by judicious choices Effectively, precision is much better than strict LL, but still not formally NLL E.g., (E,p) cons., “angular ordering”, using p T as scale in α s, with Λ MS  Λ MC, …  Clever choices good for process-independent things, but what about the process-dependent bits?  showers + matching to matrix elements

Peter Skands QCD Phenomenology at Hadron Colliders - 13 Some Holy Grails ►Matching to first order matrix elements + parton showers ~ done 1 st order : (X+1) tree-level PYTHIA, HERWIG; + X 1-loop : POWHEG Multi-leg : (X+1,2,…) tree-level CKKW, MLM, … (but still no nontrivial loop information) ►Simultaneous 1-loop and multi-leg matching : not yet done 1 st order : X 1-Loop + (X+ 1,2,…) tree-level + (X + ∞) leading-log 2 nd order : (X+1) 1-Loop + (X + 1,2,…) tree-level + (X + ∞) leading-log ►Showers that systematically resum subleading singularities : not yet done Leading-Log  Next-to-Leading-Log  … ? Leading-Colour  Next-to-Leading Colour ? Unpolarized  Polarized ? (Herwig) ►Solving any of these would be highly desirable Solve all of them ? X 2-Loop + (X+1,…?) 1-loop + (X + 1,2,…) tree-level + (X + ∞) NLL + string-fragmentation + reliable uncertainty bands

Peter Skands QCD Phenomenology at Hadron Colliders - 14 Parton Showers ►The final answer depends on: The choice of evolution “time” The splitting functions (finite/subleading terms not fixed) The phase space map ( dΦ n+1 /dΦ n ) The renormalization scheme (argument of α s ) The infrared cutoff contour (hadronization cutoff) ►Step 1, Quantify uncertainty: vary all of these (within reasonable limits) ►Step 2, Systematically improve: Understand the importance of each and how it is canceled by Matching to fixed order matrix elements, at LO, NLO, NNLO, … Higher logarithms, subleading color, etc, are included ►Step 3, Write a generator: Make the above explicit (while still tractable) in a Markov Chain context  matched parton shower MC algorithm

Peter Skands QCD Phenomenology at Hadron Colliders - 15 Gustafson, PLB175(1986)453; Lönnblad (ARIADNE), CPC71(1992)15. Azimov, Dokshitzer, Khoze, Troyan, PLB165B(1985)147 Kosower PRD57(1998)5410; Campbell,Cullen,Glover EPJC9(1999)245 VINCIA ►Based on Dipole-Antennae Shower off color-connected pairs of partons Plug-in to PYTHIA 8 (C++) ►So far: 3 different shower evolution variables: pT-ordering (= ARIADNE ~ PYTHIA 8) Dipole-mass-ordering (~ but not = PYTHIA 6, SHERPA) Thrust-ordering (3-parton Thrust) For each: an infinite family of antenna functions Laurent series in branching invariants with arbitrary finite terms Shower cutoff contour: independent of evolution variable  IR factorization “universal” Several different choices for α s (evolution scale, p T, mother antenna mass, 2-loop, …) Phase space mappings: 2 different choices implemented Antenna-like (A RIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler Dipoles (=Antennae, not CS) – a dual description of QCD a b r VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Giele, Kosower, PS : hep-ph/ Les Houches 2007

Peter Skands QCD Phenomenology at Hadron Colliders - 16 Dipole-Antenna Functions ►Starting point: “GGG” antenna functions, e.g., gg  ggg: ►Generalize to arbitrary double Laurent series:  Can make shower systematically “softer” or “harder” Will see later how this variation is explicitly canceled by matching  quantification of uncertainty  quantification of improvement by matching y ar = s ar / s i s i = invariant mass of i’th dipole-antenna Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056 Singular parts fixed, finite terms arbitrary Frederix, Giele, Kosower, PS : Les Houches NLM, arxiv:

Peter Skands QCD Phenomenology at Hadron Colliders - 17 Tree-level matching to X+1 1.Expand parton shower to 1 st order (real radiation term) 2.Matrix Element (Tree-level X+1 ; above t had )  Matching Term (= correction events to be added)  variations in finite terms (or dead regions) in A i canceled (at this order) (If A too hard, correction can become negative  negative weights) Inverse phase space map ~ clustering Giele, Kosower, PS : hep-ph/

Peter Skands QCD Phenomenology at Hadron Colliders - 18 Matching by Reweighted Showers ►Go back to original shower definition ►Possible to modify S to expand to the “correct” matrix elements ? Pure Shower (all orders) w X : |M X | 2 S : Evolution operator {p} : momenta Sjöstrand, Bengtsson : Nucl.Phys.B289(1987)810; Phys.Lett.B185(1987)435 Norrbin, Sjöstrand : Nucl.Phys.B603(2001)297 1 st order: yes Generate an over- estimating (trial) branching Reweight it by vetoing it with the probability But 2 nd and beyond difficult due to lack of clean PS expansion  w>0 as long as |M| 2 > 0

Peter Skands QCD Phenomenology at Hadron Colliders - 19 Towards an NNLO + NLL MC ►Basic idea: extend reweigthing to 2 nd order 2  3 tree-level antennae  enough to reach NLO 2  3 one-loop + 2  4 tree-level antennae  NNLO ►And exponentiate it Exponentiating 2  3 (dipole-antenna showers)  (N)LL Complete NNLO captures the singularity structure up to (N)NLL So a shower incorporating all these pieces exactly should be able to Reach NLL resummation, with a good approximation to NNLL; + exact matching up to NNLO should be possible Start small, do it for Z decay first (if you can’t do Z, you can’t do anything)

Peter Skands QCD Phenomenology at Hadron Colliders  4 Matching by reweighting ►Starting point: LL shower w/ large coupling and large finite terms to generate “trial” branchings (“sufficiently” large to over-estimate the full ME). Accept branching [i] with a probability ►Each point in Z  4 phase space then receives a contribution Also need to take into account ordering  cancellation of dependence 1 st order matching term (à la Sjöstrand-Bengtsson) 2 nd order matching term (with 1 st order subtracted) (If you think this looks deceptively easy, you are right)

Peter Skands QCD Phenomenology at Hadron Colliders - 21 Tree-level 2   4 in Action ►The unknown finite terms are a major source of uncertainty DGLAP has some, GGG have others, ARIADNE has yet others, etc… They are arbitrary (and in general process-dependent) α s (M Z )=0.137, μ R =p T, p Thad = 0.5 GeV Varying finite terms only with First example of a parton shower including second-order corrections

Peter Skands QCD Phenomenology at Hadron Colliders - 22 LEP Comparisons Planning public release this summer, then on to hadrons

Peter Skands QCD Phenomenology at Hadron Colliders - 23 The Structure of the Underlying Event

Peter Skands QCD Phenomenology at Hadron Colliders - 24 ► Domain of fixed order and parton shower calculations: hard partonic scattering, and bremsstrahlung associated with it. ► But hadrons are not elementary ► + QCD diverges at low p T ►  multiple perturbative parton-parton collisions should occur  pairwise balancing minijets (‘lumpiness’) in the underlying event ► Normally omitted in explicit perturbative expansion ► + Remnants from the incoming beams ► + additional (non-perturbative / collective) phenomena? Bose-Einstein Correlations Non-perturbative gluon exchanges / colour reconnections ? String-string interactions / collective multi-string effects ? Interactions with “background” vacuum / with remnants / with active medium? e.g. 4  4, 3  3, 3  2 Additional Sources of Particle Production

Peter Skands QCD Phenomenology at Hadron Colliders - 25 Classic Example: Number of tracks 540 GeV, single pp, charged multiplicity in minimum-bias events Simple physics models ~ Poisson Can ‘tune’ to get average right, but much too small fluctuations  inadequate physics model More Physics: Multiple interactions + impact-parameter dependence Moral: 1)It is not possible to ‘tune’ anything better than the underlying physics model allows 2)Failure of a physically motivated model usually points to more physics

Peter Skands QCD Phenomenology at Hadron Colliders - 26 The ‘New’ Model Sjöstrand, Skands : JHEP03(2004)053, EPJC39(2005)129 multiparton PDFs derived from sum rules Beam remnants Fermi motion / primordial k T Fixed order matrix elements parton shower (matched to further matrix elements) perturbative “intertwining”? ►Parton Showers resum divergent emission cross sections ►Multiple interactions “resum” divergent interaction cross sections  A “complete” model for hadron collisions Also note new Herwig++ model March 2008: Bahr, Gieseke, Seymour; arXiv:

Peter Skands QCD Phenomenology at Hadron Colliders - 27 Hadronization and All That Simulation from D. B. Leinweber, hep-lat/ Anti-Triplet Triplet pbar beam remnant p beam remnant bbar from tbar decay b from t decay qbar from W q from W hadronization ? q from W

Peter Skands QCD Phenomenology at Hadron Colliders - 28 Underlying Event and Colour ►Not much was known about the colour correlations, so some “theoretically sensible” default values were chosen Rick Field (CDF) noted that the default model produced too soft charged- particle spectra. The same is seen at RHIC: For ‘Tune A’ etc, Rick noted that increased when he increased the colour correlation parameters But needed ~ 100% correlation. So far not explained Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations What is their origin? Why are they needed? M. Heinz, nucl-ex/ ; nucl-ex/

Peter Skands QCD Phenomenology at Hadron Colliders - 29 ►Searched for at LEP Major source of W mass uncertainty Most aggressive scenarios excluded But effect still largely uncertain P reconnect ~ 10% ►Prompted by CDF data and Rick Field’s studies to reconsider. What do we know? Non-trivial initial QCD vacuum A lot more colour flowing around, not least in the UE String-string interactions? String coalescence? Collective hadronization effects? More prominent in hadron-hadron collisions? What (else) is RHIC, Tevatron telling us? Implications for precision measurements:Top mass? LHC? Normal WW Reconnected WW OPAL, Phys.Lett.B453(1999)153 & OPAL, hep-ex Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more … Colour Reconnection (example) Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Color Reconnections Existing models only for WW  a new toy model for all final states: colour annealing Attempts to minimize total area of strings in space-time Improves description of minimum-bias collisions Skands, Wicke EPJC52(2007)133 ; Preliminary finding Delta(mtop) ~ 0.5 GeV Now being studied by Tevatron top mass groups

Peter Skands QCD Phenomenology at Hadron Colliders - 30 WIMP (QCD and Dark Matter: an example) ►Imagine the galaxy is filled with dark matter zipping around at a few hundred km/s Look for elastic interactions with nuclei  CDMS phonon detectors coupled to arrays of cryogenic (0.02 K) germanium and silicon crystals ►In MSSM, dominated by heavy Higgs exchange  Relation between CDMS Dark Matter search and Tevatron MSSM Higgs search  Need to know strange and gluon content of proton under elastic scattering: factor 2 uncertainty in our study Less important for discovery / exclusion, but would be significant for subsequent precision studies Carena, Hooper, Skands PRL97 (2006) LEP excl CDMS 2006 exclCDMS 2007 proj What does this have to do with colliders and QCD ?

Peter Skands QCD Phenomenology at Hadron Colliders - 31Conclusions ►QCD Phenomenology is in a state of impressive activity Increasing move from educated guesses to precision science Better matrix element calculators+integrators (+ more user-friendly) Improved parton showers and improved matching to matrix elements Improved models for underlying events / minimum bias Upgrades of hadronization and decays Clearly motivated by dominance of LHC in the next decade(s) of HEP ►Early LHC Physics: theory At 14 TeV, everything is interesting Even if not a dinner Chez Maxim, rediscovering the Standard Model is much more than bread and butter. Real possibilities for real surprises It is both essential, and I hope possible, to ensure timely discussions on “non-classified” data, such as min-bias, dijets, Drell-Yan, etc  allow rapid improvements in QCD modeling (beyond simple retunes) after startup

Peter Skands QCD Phenomenology at Hadron Colliders - 32 A Problem ►The best of both worlds? We want: A description which accurately predicts hard additional jets + jet structure and the effects of multiple soft emissions  an “inclusive” sample on which we could evaluate any observable, whether it is sensitive or not to extra hard jets, or to soft radiation

Peter Skands QCD Phenomenology at Hadron Colliders - 33 A Problem ►How to do it? Compute emission rates by parton showering (PS)? Misses relevant terms for hard jets, rates only correct for strongly ordered emissions p T1 >> p T2 >> p T3... Unknown contributions from higher logarithmic orders, subleading colors, … Compute emission rates with matrix elements (ME)? Misses relevant terms for soft/collinear emissions, rates only correct for well-separated individual partons Quickly becomes intractable beyond one loop and a handfull of legs Unknown contributions from higher fixed orders

Peter Skands QCD Phenomenology at Hadron Colliders - 34 A (Stupid) Solution ►Combine different starting multiplicites  inclusive sample? ►In practice – Combine 1.[X] ME + showering 2.[X + 1 jet] ME + showering 3.… ►Doesn’t work [X] + shower is inclusive [X+1] + shower is also inclusive X inclusive X+1 inclusive X+2 inclusive ≠ X exclusive X+1 exclusive X+2 inclusive Run generator for X (+ shower) Run generator for X+1 (+ shower) Run generator for … (+ shower) Combine everything into one sample What you get What you want Overlapping “bins”One sample

Peter Skands QCD Phenomenology at Hadron Colliders - 35 Double Counting ►  Double Counting: [X] ME + showering produces some X + jet configurations The result is X + jet in the shower approximation If we now add the complete [X + jet] ME as well the total rate of X+jet is now approximate + exact ~ double !! some configurations are generated twice. And the total inclusive cross section is also not well defined Is it the “LO” cross section? Is it the “LO” cross section plus the integral over [X + jet] ? What about “complete orders” and KLN ? ►When going to X, X+j, X+2j, X+3j, etc, this problem gets worse 