QCD at the Energy Frontier

Transcription

1 Frank Krauss Institute for Particle Physics Phenomenology Durham University WE Heraeus School on QCD Old Challenges and New Opportunities

2 what the talk is about lessons from the LHC the quest for precision anticipating the future summary

3 motivation & introduction

4 motivation QCD = well understood theory with subtle effects QCD radiation omnipresent at the LHC enters as signal (and background) in high-p analyses multi-jet signatures multijet merging & higher-order matching inner-jet structures e.g. from fat jets parton shower algorithms begs the question: can we improve our understanding? in addition: interesting physics in QCD alone (keep in mind: accuracy vs. precision) (think about multi-parton interactions, collective phenomena, etc.)

5 will need precision for ballistics of smoking guns

6 lessons from the LHC

7 lessons from the LHC jets are ubiquitous: QCD fills phase space if available: n-jet rates may scale beyond α n S if emissions well-separated: fixed order QCD works amazingly well however: subtle effects when emission logarithms become large QCD beyond fixed order! conceptual problems still open: mainly soft QCD hadronization, multiple parton interactions, the ridge

8 perturbation theory works!

9 factorization: calculating observables for the LHC master formula dσ pp X = ij 1 0 dx 1 dx 2 f i (x 1, µ F ) f j (x 2, µ F ) dφ X ˆσ ij X ({p X } ; µ F, µ R ) relating parton-level ˆσ with particle-level (observable) cross section σ (partons = quarks and gluons) based on factorization : parton distribution function f i (x, µ F ) process-independent if typical momentum scale Q µ F m proton (PDF = probability to find one parton of type i with energy fraction x at factorization scale µ F in proton)

10 overall agreement with data

11 soft QCD questions

12 colour reconnections and friends (Fischer, Sjostrand, 1610:09818) (slide stolen from Torbjorn Sjostrand)

13 strange strangeness (ALICE collaboration) universality of hadronisation assumed parameters tuned to LEP data in particular: strangeness suppression for strangeness: flat ratios but data do not reproduce this looks like SU(3) restoration not observed for protons needs to be investigated Ratio of yields to (π +π + ) KS Λ+Λ ( 2) + Ξ +Ξ ( 6) + Ω +Ω ( 16) ALICE pp, s = 7 TeV p-pb, s NN = 5.02 TeV Pb-Pb, s NN = 2.76 TeV PYTHIA8 DIPSY EPOS LHC dn /dη ch 3 η < 0.5

14 beyond factorization

15 example: multi-parton interactions protons = extended objects possibility of more parton pairs interacting resulting final states may be hard in perturbative regime p few GeV but: no factorization theorem available no first-principles theory simplistic parameterization σ (DPS) X +Y = σ X σ Y σ eff with σ eff 15 mb (measured) (σ tot 100 mb = m 2 at LHC)

16 example: the ridge momentum conservation in transverse plane: in 2 2 collisions particles produced back-to-back decorrelation by additional radiation well understood in pert.qcd

17 Introduction Lessons from the LHC Precision Future directions Summary however: surprising structure in high-multiplicity pp cannot be reproduced in standard pert.qcd Monte Carlo typically explained as collective effect in heavy-ion collisions: hydrodynamics in pp: colour-ropes, glasma ( colour-glass condensate = non-pert. in weak coupling, glasma = Bose enhancement + Pauli blocking) conceptually different from textbook perturbation theory F. Krauss IPPP

18 the quest for precision

19 precision at fixed order

20 complex inputs I: parton distribution functions PDFs not known from first principles, only their scaling with µ F (from the Altarelli-Parisi equations) fitted from data at different processes, at different, µ F, at different experiments, with different systematics current accuracy: next-to next-to leading order (NNLO) (various collaborations: CTEQ, MMHT, NNPDF, ABM, GRV, HeraPDF) needs NNLO calculations and three-loop kernels driving the evolution (4-loop kernels partially known; Moch et al., ) but: αs 2 is O(1%) must also include electromagnetic and weak evolution at (N)LO (current frontier: LUXqed; Manohar PRL 117 (2016) ) determining reliable PDFs a complex endeavour

21 complex inputs II: partonic cross sections ˆσ fully automated evaluation of ˆσ at LO and NLO, integral over phase space dφ X with 3n 2 dimensions for n particles Monte Carlo methods with involved sampling strategies problem beyond LO: occurrence of divergent structures when momenta k ( ultraviolet divergence ) regularization and renormalization or k 0 ( infrared divergence ) regularization and exact cancellation between contributions (Kinoshita Lee Nauenberg theorem) regularization by analytic continuation d 4 k d D k with D = 4 + 2ɛ divergences manifest as poles 1/ɛ straightforward for UV divergences but tricky for IR divergences: cancellation is between contributions of different multiplicity (and phase space integrals are usually done with Monte Carlo methods)

22 the aftermath of the NLO (QCD) revolution establishing a wide variety of automated tools for NLO calculations BLACKHAT, GOSAM, MADGRAPH, NJET, OPENLOOPS, RECOLA + automated IR subtraction methods (MADGRAPH, SHERPA) first full NLO (EW) results with automated tools technical improvements still mandatory start discussing scale setting prescriptions (higher multis, higher speed, higher efficiency, easier handling,... ) (simple central scales for complicated multi-scale processes? test smarter prescriptions?) steep learning curve still ahead: NLO phenomenology (example: methods for uncertainty estimates beyond variation around central scale)

23 pushing the perturbative order: gg H NLO O(α S ) (Dawson; Djouadi et al.; 1990) NNLO O(α 2 S ) (Harlander et al., Anastasiou et al.; 2002) NNNLO O(α 3 S ) (Anastasiou et al.; 2015) 1,000 Feynman diagrams at NNLO 100,000 Feynman diagrams at N 3 LO reduced to 1000 master integrals Symbols

24 technological/complexity limit

25 the looming revolution: going beyond NLO H in ggf at N 3 LO (Anastasiou, Duhr and others) explosive growth in NNLO (QCD) 2 2 results t t ( ; ; ) single-t ( ) VV ( ; ; ; ) HH ( ) VH ( ; ; ) V γ ( ) γγ ( ; ) Vj ( ; ; ; ; ) Hj ( ; ; ; ; ) jj ( ; ) NLO corrections to gg VV ( ) WBF at NNLO ( ) and N 3 LO ( ) (apologies for any unintended omissions) different IR subtraction schemes: N-jettiness slicing, antenna subtraction, sector decomposition,

26 living with the revolution we will include them into full simulations (I am willing to place a bet: 3 years at most!) practical limitations/questions to be overcome: dealing with IR divergences at NNLO: slicing vs. subtracting (I m not sure we have THE solution yet) how far can we push NNLO? are NLO automated results stable enough for NNLO at higher multiplicity? matching for generic processes at NNLO? (MINLO or UN 2 LOPS or something new?) more scales (internal or external) complicated need integrals more philosophical questions: going to higher power of N often driven by need to include larger FS multiplicity maybe not the most efficient method limitations of perturbative expansion: breakdown of factorisation at HO (Seymour et al.) higher-twist: compare (α S /π) n with Λ QCD/M Z

27 a scale puzzle at NNLO J. Currie et al., Acta Phys.Polon. B48 (2017) 955 common lore: higher orders stabilise/reduce scale dependence but: look at inclusive jet-p

28 status of precision simulations

29 embedding in full simulations fixed-order perturbation theory does not give full picture of pp collisions at LHC. more particles produced by radiation of secondaries all-orders PT in approximation transition from quarks & gluons to hadrons decays of unstable hadrons & QED radiation multiple interactions all in numerical simulation combination of first principles PT, effective theories, heavy modelling, and fitting to data

30 reminder: how parton showers work parton showers are approximations, based on leading colour, leading logarithmic accuracy, spin-average parametric accuracy by comparing Sudakov form factors: { [ ]} dk 2 = exp k 2 A log k2 Q 2 + B, where A and B can be expanded in α S (k 2 ) Q T resummation includes A 1,2,3 and B 1,2 (transverse momentum of Higgs boson etc.) showers usually include terms A 1,2 and B 1 A = cusp terms ( soft emissions ), B anomalous dimensions γ

31 a new shower implementation DIRE (S.Höche & S.Prestel, Eur.Phys.J. C75 (2015) 461) evolution and splitting parameter ((ij) + k i + j + k): κ 2 j,ik = 4(p i p j )(p j p k ) Q 4 and z j = 2(p j p k ) Q 2. splitting functions including IR regularisation (a la Curci, Furmanski & Petronzio, Nucl.Phys. B175 (1980) 27-92) P qq (0) ) = [ 1 z 2C F (1 z) 2 + κ z ], 2 P qg (0) ) = [ z 2C F z 2 + κ 2 2 z ], 2 [ ] P gg s(0) 1 z z(1 z) ) = 2C A (1 z) 2 1 +, + κ2 2 P gq (0) ) ] = T R [z 2 + (1 z) 2 renormalisation/factorisation scale given by µ = κ 2 Q 2 combine gluon splitting from two splitting functions with different spectators k accounts for different colour flows

32 LO results for Drell-Yan (example of accuracy in description of standard precision observable) 1 dσ fid σ fid dp [GeV 1 T ] MC/Data MC/Data MC/Data pt spectrum, Z ee (dressed) yz yz 2 ( 0.1) < yz 2.4 ( 0.01) ATLAS data JHEP 09 (2014) 145 ME+PS (1-jet) 5 Qcut 20 GeV 0 yz yz < yz p T,ll [GeV] Sherpa MC 1 dσ fid. σ fid. dφ η MC/Data MC/Data MC/Data φ η spectrum, Z ee (dressed) yz < yz 1.6 ( 0.1) 1.6 < yz ( 0.01) ATLAS data Phys.Lett. B720 (2013) 32 ME+PS (1-jet) 5 Qcut 20 GeV yz < yz < yz φ η Sherpa MC

33 g Q Q a systematic nightmare parton showers geared towards collinear & soft emissions of gluons (double log structure) g q q only collinear old measurements at LEP of g b b and g c c rate fix this at LHC for modern showers (important for t tb b) questions: kernel, scale in α S (example: k vs. m bb )

34 flagship measurements: VH b b, t th b b,... many searches with b s influences b-tag rate ( double -b jets = gluon jets) can cause problems in highly boosted regime

35 Introduction Lessons from the LHC Precision Future directions Summary ATLAS measurement in b b production use decay products in B J/Ψ(µµ) + X and B µ + X use muons as proxies, most obvious observable R(JΨ, µ) F. Krauss IPPP

36 matching at NLO and NNLO avoid double-counting of emissions two schemes at NLO: and POWHEG mismatches of K factors in transition to hard jet region MC@NLO: visible structures, especially in gg H POWHEG: high tails, cured by h dampening factor well-established and well-known methods (no need to discuss them any further) two schemes at NNLO: MINLO & UN 2 LOPS (singlets S only) different basic ideas MINLO: S + j at NLO with p (S) T 0 and capture divergences by reweighting internal line with analytic Sudakov, NNLO accuracy ensured by reweighting with full NNLO calculation for S production UN 2 LOPS identifies and subtracts and adds parton shower terms at FO from S + j contributions, maintaining unitarity available for two simple processes only: DY and gg H

37 NNLOPS for H production: MINLO K. Hamilton, P. Nason, E. Re & G. Zanderighi, JHEP 1310 also available for Z/W /VH production

38 NNLOPS for Z production: UN 2 LOPS S. Hoche, Y. Li, & S. Prestel, Phys.Rev.D90 & D91 [pb] - e + e dσ/dy Ratio to NLO s = 7 TeV 60 GeV<m <120 GeV ll NNLO NLO' FEWZ m ll /2< µ <2m NLO' R/F ll m ll /2< µ <2m NNLO R/F ll y 4 - e + e Sherpa+BlackHat 1/σ dσ/dpt,z [1/GeV] MC/Data 10 1 Z pt reconstructed from dressed electrons ATLAS PLB705(2011)415 UN 2 LOPS m ll/2 < µ R/F < 2 m ll m ll/2 < µ Q < 2 m ll pt,z [GeV] also available for H production

39 NNLOPS: shortcomings/limitations MINLO relies on knowledge of B 2 terms from analytic resummation to date only known for colour singlet production MINLO relies on reweighting with full NNLO result one parameter for H (y H ), more complicated for Z,... UN 2 LOPS relies on integrating single- and double emission to low scales and combination of unresolved with virtual emissions potential efficiency issues, need NNLO subtraction UN 2 LOPS puts unresolved & virtuals in zero-emission bin no parton showering for virtuals (?)

40 merging example: p,γγ in vs. NNLO (arxiv: [hep-ex]) [pb/gev] dσ/dp T,γγ ATLAS s = 7 TeV 1 Data 2011, Ldt = 4.9 fb PYTHIA MC11c SHERPA MC11c 1.3 (MRST2007) 1.3 (CTEQ6L1) [pb/gev] dσ/dp T,γγ ATLAS s = 7 TeV 1 Data 2011, Ldt = 4.9 fb DIPHOX+GAMMA2MC (CT10) 2γNNLO (MSTW2008) data/sherpa data/diphox data/pythia p [GeV] T,γγ data/2γnnlo p [GeV] T,γγ

41 multijet-merging at NLO sometimes more legs wins over more loops basic idea like at LO: towers of MEs with increasing jet multi (but this time at NLO) combine them into one sample, remove overlap/double-counting maintain NLO and LL accuracy of ME and PS this effectively translates into a merging of MC@NLO simulations and can be further supplemented with LO simulations for even higher final state multiplicities different implementations, parametric accuracy not always clear starts being used, still lacks careful cross-validation (MEPS@NLO, FxFx, UNLOPS)

42 illustration: p H dσ/dp [pb/gev] 10 1 in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets Sherpa S-MC@NLO first emission by MC@NLO p (h) [GeV]

43 illustration: p H dσ/dp [pb/gev] 10 1 in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO first emission by MC@NLO, restrict to Q n+1 < Q cut p (h) [GeV]

44 illustration: p H dσ/dp [pb/gev] 10 1 in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut p (h) [GeV]

45 illustration: p H dσ/dp [pb/gev] in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut restrict emission off pp h + jet to Q n+2 < Q cut p (h) [GeV]

46 illustration: p H dσ/dp [pb/gev] in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO pp h + NLO first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut restrict emission off pp h + jet to Q n+2 < Q cut MC@NLO pp h + 2jets for Q n+2 > Q cut p (h) [GeV]

47 illustration: p H dσ/dp [pb/gev] in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO pp h + NLO first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut restrict emission off pp h + jet to Q n+2 < Q cut MC@NLO pp h + 2jets for Q n+2 > Q cut iterate p (h) [GeV]

48 illustration: p H dσ/dp [pb/gev] in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO pp h + NLO pp h + LO first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut restrict emission off pp h + jet to Q n+2 < Q cut MC@NLO pp h + 2jets for Q n+2 > Q cut iterate p (h) [GeV]

49 illustration: p H dσ/dp [pb/gev] in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO pp h + NLO pp h + LO first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut restrict emission off pp h + jet to Q n+2 < Q cut MC@NLO pp h + 2jets for Q n+2 > Q cut iterate sum all contributions p (h) [GeV]

50 illustration: p H dσ/dp [pb/gev] in MEPS@NLO Transverse momentum of the Higgs boson pp h + jets pp h + NLO pp h + NLO pp h + NLO pp h + LO p (h) [GeV] first emission by MC@NLO, restrict to Q n+1 < Q cut MC@NLO pp h + jet for Q n+1 > Q cut restrict emission off pp h + jet to Q n+2 < Q cut MC@NLO pp h + 2jets for Q n+2 > Q cut iterate sum all contributions eg. p (h)>200 GeV has contributions fr. multiple topologies

51 Z+jets at 13 Tev: comparison with ATLAS data various merging codes at LO and NLO ) [pb] jets σ(z/γ*+n ATLAS Preliminary 1 13 TeV, 3.16 fb anti-k t jets, R = 0.4 jet jet p > 30 GeV, y < 2.5 T + Z/γ *( l l ) + jets Data BLACKHAT + SHERPA SHERPA 2.1 ALPGEN + PY6 MG5_aMC+ PY8 CKKWL MG5_aMC+ PY8 FxFx [pb/gev] T dσ/dh ATLAS Preliminary 1 13 TeV, 3.16 fb anti-k t jets, R = 0.4 jet jet p > 30 GeV, y < 2.5 T + Z/γ *( l l ) + 1 jet Data Z + 1 jet N NNLO jetti BLACKHAT + SHERPA SHERPA 2.1 ALPGEN + PY6 MG5_aMC+ PY8 CKKWL MG5_aMC+ PY8 FxFx Pred./Data Pred./Data Pred./Data N jets N jets Pred./Data Pred./Data Pred./Data [GeV] H T H T H T [GeV] [GeV] [GeV] H T

52 pushing the envelope: showering at NLO accuracy

53 Including NLO splitting kernels expand splitting kernels as ( Hoeche, FK & Prestel, , and Hoeche & Prestel, ) P(z, κ 2 ) = P (0) (z, κ 2 ) + α S 2π P(1) (z, κ 2 ) aim: reproduce DGLAP evolution at NLO include all NLO splitting kernels three categories of terms in P (1) : cusp (universal soft-enhanced correction) corrections to 1 2 new flavour structures (e.g. q q ), identified as 1 3 new paradigm: two independent implementations (already included in original showers)

54 validation of 1 3 splittings dσ/d log 10 yn n+1 [pb] Jet resolution at parton level (Durham algorithm) e + e q 91.2 GeV 200 y y23 Dire PS dσ/d log 10 (dn n+1/gev) [pb] Jet resolution at parton level (kt algorithm) 50 pp e + 8 TeV 0 d d01 Dire PS Sherpa Pythia Sherpa Pythia Deviation 2 σ 0 σ -2 σ y23 Deviation 2 σ 0 σ -2 σ d01 Deviation 2 σ 0 σ -2 σ y 34 Deviation 2 σ 0 σ -2 σ d log 10 y n n log 10 (d n n+1/gev)

55 impact of 1 3 splittings Jet resolution at parton level (Durham algorithm) Jet resolution at parton level (kt algorithm) Ratio to LOPS e + e q 91.2 GeV y23 LO LO Dire PS Ratio to LOPS pp e + 8 TeV d01 LO LO Dire PS dσ/d log 10 y 34 [pb] dσ/d log 10 y 45 [pb] one y34 all y45 one all log 10 y n n+1 dσ/d log 10 (d23/gev) [pb] dσ/d log 10 (d 12/GeV) [pb] d one 1 3 all one all d log 10 (d n n+1/gev)

56 physical results: e e + hadrons (Hoeche, FK & Prestel, ) dσ/dy Differential 2-jet rate with Durham algorithm (91.2 GeV) Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Dire PS dσ/dy Differential 3-jet rate with Durham algorithm (91.2 GeV) Data NLO /4 t µ 2 R 4 t LO 1/4 t µ 2 R 10 4 t 2 Dire PS MC/Data y Durham 23 MC/Data y Durham 34 Thrust (E CMS = 91.2 GeV) C-Parameter (E CMS = 91.2 GeV) 1/σ dσ/dt Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Dire PS 1/σ dσ/dc Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Dire PS MC/Data MC/Data T C

57 physical results: DY at LHC (untuned showers vs. 7 TeV ATLAS data) 1 σ fid dσ fid dp T [GeV 1 ] MC/Data Z ee dressed, Inclusive Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Z pt [GeV] Dire PS 1 σ fid dσ fid dp T [GeV 1 ] MC/Data < yz < 1.0, dressed Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Z pt [GeV] Dire PS 1.0 < yz < 2.0, dressed 2.0 < yz < 2.4, dressed 1 σ fid dσ fid dp T [GeV 1 ] MC/Data Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Z pt [GeV] Dire PS 1 σ fid dσ fid dp T [GeV 1 ] MC/Data Data NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Z pt [GeV] Dire PS

58 physical results: differential jet rates at LHC dσ/d log 10 (d01/gev) [pb] 10 3 pp e + 7 TeV NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Dire PS dσ/d log 10 (d01/gev) [pb] pp 8 TeV NLO 1/4 t µ 2 R 4 t LO 1/4 t µ 2 R 4 t Dire PS Ratio to LO log 10 (d01/gev) Ratio to LO log 10 (d01/gev)

59 limitations and future challenges

60 theory challenges

61 limitation: computing short-distance cross sections LO (Childers, Uram, LeCompte, Benjamin, Hoeche, CHEP 2016) challenge of efficiency on tomorrow s (& today s) computers 2000 s paradigm: memory free, flops expensive (example: 16-core Xeon, 20MB L2 Cache, 64GB RAM) 2020 s paradigm: flops free, memory expensive & must be managed (example: 68-core Xeon KNL, 34MB L2 Cache, 16GB HBM, 96GB RAM) Code mayimprovements trigger rewrites enable of code scaling to account on KNLfor changing paradigm 9hr run-time matrix element contributions (figures stolen from Taylor Childers talk at CHEP) New results from two days ago next test on Mira to see if we see similar improvements

62 theory limitations/questions we have constructed lots of tools for precision physics at LHC but we did not cross-validate them careful enough (yet) but we did not compare their theoretical foundations (yet) we also need unglamorous improvements on existing tools: account for new computer architectures and HPC paradigms systematically check advanced scale-setting schemes (MINLO) automatic (re-)weighting for PDFs & scales scale compensation in PS is simple (implement and check) 4 vs. 5 flavour scheme really? how about α S : range from to (yes, I know, but still - it bugs me) is there any way to settle this once and for all (measurements?)

63 achievable goals (I believe we know how to do this) NLO for loop-induced processes: fixed-order starting, tedious but straightforward EW NLO corrections with tricky/time-consuming calculation setup but important at large scales: effect often QCD, but opposite sign need maybe faster approximation for high-scales (EW Sudakovs) work out full matching/merging instead of approximations improve parton shower: beyond (next-to) leading log, leading colour, spin-averaged HO effects in shower and scale uncertainties start including next-to leading colour include spin-correlations important for EW emissions

64 more theory uncertainties/issues? with NNLOPS approaching 5% accuracy or better: non-perturbative uncertainties start to matter: PDFs, MPIs, hadronization, etc. question (example): with hadronization tuned to quark jets (LEP) how important is the chemistry of jets for JES? can we fix this with measurements? example PDFs: to date based on FO vs. data will we have to move to resummed/parton showered? g q q at accuracy limit of current parton showers: how bad are 25% uncertainty on g b b? can we fix this with measurements? (reminder: LO was not a big hit, though)

65 opportunities at 100 TeV

66 some general observations (sea-) parton luminosities go with x λ steep increase in soft jet production LHC 100 TeV interesting opportunities for double-parton scattering ridge with 10 GeV p hadrons? interface perturbative non-perturbative? jets will be more collimated challenges for sub-jet measurements

67 cross sections potpourri Leading-order cross sections at a 100 TeV pp collider pp inelastic j 2 j 3 pp! X at LO, p s = 100 TeV anti-kt jets R =0.4 pt,j/ > 50 GeV, Rj, > 0.4 1b 1mb [pb] j 4 j 5 j 6 j 7 j 8 t t Ht t (t t) 2 H 2 t t (t t) 3 H 3 t t W + W W + W W ± H (W + W ) 2 W ± H 2 (W + W ) 3 W ± H 3 Z Z 2 ZH Z 3 ZH 2 Z 4 ZH 3 Z W + W Z W + W Z 2 H 2 j 2 (VBF) (W + W ) 2 Z W + W Z 3 QCD & tth W Z Photons Higgs mixed V Process Category j W ± H (GF) Hj 2 (VBF) H 2 (GF) H 3 j 2 (VBF) Hj Hj 2 Hj 3 1 µb 1nb 1 pb 1 fb 1 ab

68 scaling of jet rates with c.m. energy more jets higher transverse momenta jets more collimated σ(p 10TeV) 100 ab pt > 50 GeV different scaling patterns σ( Njet) [pb] 10 9 s = 14 TeV 10 8 s = 100 TeV Sherpa pp Njet jets at LO 10 3 anti-kt jets R = 0.4 Njet dσ/dpt [pb/gev] BlackHat+Sherpa pp jj at NLO s = 14 TeV anti-kt jets R = pt [GeV] BlackHat+Sherpa pp jj at NLO s = 100 TeV anti-kt jets R = pt [GeV] 0.0 < y < < y < 1.0, SF: < y < 2.0, SF: < y < 3.0, SF: < y < 4.0, SF: < y < 5.0, SF: < y < 6.0, SF: 10 6

69 typical jet-p in W + jets σ N excl jet (p j T )/σtot 10 0 Inclusive N-Jet Fractions Njet = 1 Njet = 2 Njet = 3 σ N excl jet (p j T )/σtot 10 0 Inclusive N-Jet Fractions Njet = 1 Njet = 2 Njet = Sherpa MENLOPS pp lνl + X s = 7 TeV p j T [GeV] 10 2 Sherpa MENLOPS pp lνl + X s = 100 TeV p j T [GeV]

70 staircase to Poisson scaling patterns in multijet production may provide insight where precise calulcations fail two extreme cases: staircase vs. Poissonian N-jet exclusive cross section σn jet [pb] anti-kt jets R = 0.4 pt,min = 50 GeV Sherpa MENLOPS pp lνl + X s = 100 TeV p j lead T p j lead T p j lead T p j lead T p j lead T > 50 GeV > 200 GeV > 500 GeV > 700 GeV > 1000 GeV Njet

71 jet substructure n subjets n subjets for inclusive QCD R C/A = 1.0 jets at FCC 20 s = 100 TeV p subjet T > 20 GeV, R subjet = 0.1 p subjet T > 10 GeV, R subjet = p subjet T > 20 GeV, R subjet = 0.05 p subjet T > 10 GeV, R subjet = 0.05 anti-k T jets parton-shower level p T fat jet [GeV]

72 summary

73 summary QCD at energy frontier full of challenges & surprises increasing accuracy and precision of LHC drives rapid development of calculational techniques (with a lot of exciting mathematical developments) rapid development of ever more detailed simulations first measurements with boosted topologies jet substructures become analysis tool (stress-testing computational abilities in soft- and hardware) not covered, but: novel analysis methods (ML & friends)

74