QCD Phenomenology at Hadron Colliders

1. Copenhagen, Apr 28 2008 QCD Phenomenology at Hadron Colliders Peter Skands CERN TH / Fermilab

2. Overview May 2008 • 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 QCD Phenomenology at Hadron Colliders - 2

3. QuantumChromoDynamics • Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory • Example: High transverse-momentum interaction Reality is more complicated QCD Phenomenology at Hadron Colliders - 3

4. Event Generators • Generator philosophy: • Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events • Parton Showers • Hadronisation • The Underlying Event • Soft/Collinear Logarithms • Power Corrections • 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 … QCD Phenomenology at Hadron Colliders - 4

5. Collider Energy Scales Hadron Decays 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, … Exclusive & Widths Resonance Masses… Hard Jet Tail High-pT jets at large angles Inclusive s • + Un-Physical Scales: • QF , QR : Factorization(s) & Renormalization(s) • QE : Evolution(s) QCD Phenomenology at Hadron Colliders - 5

6. TheBottomLine HQET FO DGLAP • The S matrix is expressible as a series in gi, gin/Qm, gin/xm, gin/mm, gin/fπm, … • 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 BFKL χPT QCD Phenomenology at Hadron Colliders - 6

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

8. Bremsstrahlung Example: SUSY @ LHC LHC - sps1a - m~600 GeV Plehn, Rainwater, Skands PLB645(2007)217 FIXED ORDER pQCD inclusiveX + 1 “jet” inclusiveX + 2 “jets” • 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 (Computed with SUSY-MadGraph) QCD Phenomenology at Hadron Colliders - 8

9. Beyond Fixed Order 1 dσX+2 “DLA” α sab saisib • dσX = … • dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b • dσX+2 ~ dσX+1 g2 2 sab/(sa2s2b) dsa2ds2b • dσX+3 ~ dσX+2 g2 2 sab/(sa3s3b) dsa3ds3b dσX dσX+1 dσX+2 This is an approximation of inifinite-order tree-level cross sections • But it’s not a parton shower, not yet an “evolution” • What’s the total cross section we would calculate from this? • σX;tot = int(dσX) + int(dσX+1) + int(dσX+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? QCD Phenomenology at Hadron Colliders - 9

10. Beyond Fixed Order 2 dσX+2 “DLA” α sab saisib • dσX = … • dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b • dσX+2 ~ dσX+1 g2 2 sab/(sa2s2b) dsa2ds2b • dσX+3 ~ dσX+2 g22 sab/(sa3s3b) dsa3ds3b +Unitarisation:σtot = int(dσX)  σX;PS= σX - σX+1 - σX+2- … dσX dσX+1 dσX+2 Given a jet definition, an event has either 0, 1, 2, or … jets • 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 =σX+1(Q) = σX;incl– σX;excl(Q) • Later, some 3-jets migrate further, etc  σX+n(Q) = σX;incl– ∑σX+m<n;excl(Q) • This evolution takes place between two scales, Qin and Qfin = QF;ME and Qhad • σX;PS = int(dσX) - int(dσX+1) - int(dσX+2) + ... = int(dσX) EXP[ - int(α 2sab /(sa1s1b) dsa1 ds1b ) ] QCD Phenomenology at Hadron Colliders - 10

11. Perturbative Evolution “X + nothing” “X+something” wX : |MX|2 S : Evolution operator {p} : momenta Pure Shower (all orders) • Evolution Operator, S (as a function of “time” t=1/Q) • Defined in terms of Δ(t1,t2) – The integrated probability the system does not change state between t1 and t2(Sudakov) A: splitting function • S unitary  total (inclusive)σ unchanged, • only shapes are predicted (i.e., also σ after shape-dependent cuts) QCD Phenomenology at Hadron Colliders - 11

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 ( dΦn+1/dΦn ) • The renormalization scheme (argument of αs) • The infrared cutoff contour (hadronization cutoff) • They are all “unphysical”, in the same sense as QFactorizaton, 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 pT as scale in αs, with ΛMSΛMC, …  Clever choices good for process-independent things, but what about the process-dependent bits?  showers + matching to matrix elements QCD Phenomenology at Hadron Colliders - 12

13. Some Holy Grails • Matching to first order matrix elements + parton showers ~ done • 1st order : (X+1)tree-level PYTHIA, HERWIG; + X1-loop : MC@NLO, 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 • 1st order : X1-Loop + (X+ 1,2,…)tree-level + (X + ∞)leading-log • 2nd 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 ? • X2-Loop + (X+1,…?)1-loop + (X + 1,2,…)tree-level + (X + ∞)NLL + string-fragmentation • + reliable uncertainty bands QCD Phenomenology at Hadron Colliders - 13

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 ( dΦn+1/dΦn ) • The renormalization scheme (argument of αs) • 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 QCD Phenomenology at Hadron Colliders - 14

15. 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 αs (evolution scale, pT, mother antenna mass, 2-loop, …) Phase space mappings: 2 different choices implemented Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler VINCIA VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE 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 Dipoles (=Antennae, not CS) – a dual description of QCD a Giele, Kosower, PS : hep-ph/0707.3652 + Les Houches 2007 r b QCD Phenomenology at Hadron Colliders - 15

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 Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056 yar = sar / si si = invariant mass of i’th dipole-antenna Frederix, Giele, Kosower, PS : Les Houches NLM, arxiv:0803.0494 Singular parts fixed, finite terms arbitrary QCD Phenomenology at Hadron Colliders - 16

17. Tree-level matching to X+1 • Expand parton shower to 1st order (real radiation term) • Matrix Element (Tree-level X+1 ; above thad)  Matching Term (= correction events to be added) •  variations in finite terms (or dead regions) in Aicanceled (at this order) • (If A too hard, correction can become negative  negative weights) Inverse phase space map ~ clustering Giele, Kosower, PS : hep-ph/0707.3652 QCD Phenomenology at Hadron Colliders - 17

18. Matching by Reweighted Showers wX : |MX|2 S : Evolution operator {p} : momenta • Go back to original shower definition • Possible to modify S to expand to the “correct” matrix elements ? Pure Shower (all orders) 1st order: yes Generate an over-estimating (trial) branching Reweight it by vetoing it with the probability Sjöstrand, Bengtsson : Nucl.Phys.B289(1987)810; Phys.Lett.B185(1987)435 Norrbin, Sjöstrand : Nucl.Phys.B603(2001)297 w>0 as long as |M|2 > 0 But2nd and beyond difficult due to lack of clean PS expansion QCD Phenomenology at Hadron Colliders - 18

19. Towards an NNLO + NLL MC • Basic idea: extend reweigthing to 2nd 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) QCD Phenomenology at Hadron Colliders - 19

20. 24 Matching by reweighting (If you think this looks deceptively easy, you are right) • 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 1st order matching term (à la Sjöstrand-Bengtsson) 2nd order matching term (with 1st order subtracted) QCD Phenomenology at Hadron Colliders - 20

21. Tree-level 23 + 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) Varying finite terms only with αs(MZ)=0.137, μR=pT, pThad = 0.5 GeV First example of a parton shower including second-order corrections QCD Phenomenology at Hadron Colliders - 21

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

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

24. Additional Sources of Particle Production • 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 pT •  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 QCD Phenomenology at Hadron Colliders - 24

25. Classic Example: Number of tracks More Physics: Multiple interactions + impact-parameter dependence UA5 @ 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 • Moral: • It is not possible to ‘tune’ anything better than the underlying physics model allows • Failure of a physically motivated model usually points to more physics QCD Phenomenology at Hadron Colliders - 25

26. The ‘New’ Model • Parton Showers resum divergent emission cross sections • Multiple interactions “resum” divergent interaction cross sections Fixed order matrix elements parton shower (matched to further matrix elements) Sjöstrand, Skands : JHEP03(2004)053, EPJC39(2005)129 multiparton PDFs derived from sum rules  A “complete” model for hadron collisions perturbative “intertwining”? Beam remnants Fermi motion / primordial kT Also note new Herwig++ model March 2008: Bahr, Gieseke, Seymour; arXiv:0803.3633 QCD Phenomenology at Hadron Colliders - 26

27. Hadronization and All That hadronization bbar from tbar decay pbar beam remnant p beam remnant qbar from W q from W q from W b from t decay ? Triplet Anti-Triplet Simulation from D. B. Leinweber, hep-lat/0004025 QCD Phenomenology at Hadron Colliders - 27

28. 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 <pT> 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? Underlying Event and Colour M. Heinz, nucl-ex/0606020; nucl-ex/0607033 QCD Phenomenology at Hadron Colliders - 28

29. Color Reconnections W W Normal W W Reconnected Colour Reconnection (example) Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more … OPAL, Phys.Lett.B453(1999)153 & OPAL, hep-ex0508062 • Searched for at LEP • Major source of W mass uncertainty • Most aggressive scenarios excluded • But effect still largely uncertain Preconnect ~ 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? • 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 QCD Phenomenology at Hadron Colliders - 29

30. 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 (QCD and Dark Matter: an example) Carena, Hooper, Skands PRL97 (2006) 051801 CDMS 2006 excl CDMS 2007 proj WIMP LEP excl What does this have to do with colliders and QCD ? QCD Phenomenology at Hadron Colliders - 30

31. Conclusions • 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 QCD Phenomenology at Hadron Colliders - 31

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 QCD Phenomenology at Hadron Colliders - 32

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 pT1 >> pT2 >> pT3 ... • 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 QCD Phenomenology at Hadron Colliders - 33

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

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]MEas 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  QCD Phenomenology at Hadron Colliders - 35