New results for parton showers

Transcription

1 New results for parton showers Gavin P. Salam* Rudolf Peierls Centre for Theoretical Physics & All Souls College, Oxford including work with M. Dasgupta, F. Dreyer, K. Hamilton, P. Monni * on leave from CERN and CNRS Annual Theory Meeting IPPP Durham, 7/2/208

2 at colliders, you can probe big unanswered questions about fundamental particles & their interactions (dark matter, matter-antimatter asymmetry, nature of dark energy, hierarchy of scales ) and big answerable questions (structure of Higgs sector, determining fundamental parameters of Lagrangian of particle physics) 2

3 Higgs precision (H γγ) : optimistic estimate v. luminosity & time 50 extrapolation of µ γγ precision from 7+8 TeV results 7+8 TeV one expt. extrapolated precision [%] ATLAS CMS two-expt. combination µ lumi at 3/4 TeV [fb - ] fb - = 0 4 collisions 3

4 Higgs precision (H γγ) : optimistic estimate v. luminosity & time 50 extrapolation of µ γγ precision from 7+8 TeV results 7+8 TeV one expt. The LHC has the extrapolated precision [%] ATLAS CMS two-expt. combination µ statistical potential to take Higgs physics from observation to 2% precision But only if we learn how to connect experimental observations with theory at that precision lumi at 3/4 TeV [fb - ] fb - = 0 4 collisions 3

5 how is all of this made quantitative? whether new-physics searches, Higgs physics, or other SM studies 4

6 UNDERLYING THEORY EXPERIMENTAL DATA how do you make quantitative connection? 5

7 UNDERLYING THEORY EXPERIMENTAL DATA how do you make quantitative connection? through a chain of experimental and theoretical links [in particular Quantum Chromodynamics (QCD)] 6

8 What are the links? ATLAS and CMS (big LHC expts.) have written 850 articles since 204 fraction of ATLAS & CMS papers that cite them GEANT4 Anti-k t jet alg. Pythia 6.4 MC Pythia 8. CT0 PDFs POWHEG Box POWHEG (2007) CTEQ6 PDFs CL(s) technique (A.Read) POWHEG (2004) MG5aMCatNLO Papers commonly cited by ATLAS and CMS ( ) MSTW2008 PDFs FastJet Manual Likelihood tests for new physics Sherpa. MadGraph 5 top++ NNLO ttbar Herwig 6 MC Pileup subtraction PDF4LHC (20) NNPDF23 PDFs links papers they cite as of , excluding self-citations; all papers > 0.2 quantum chromodynamics (QCD) theory papers experimental & statistics papers CL(s) technique (T.Junk) NNPDF30 PDFs Perugia tunes (200) Herwig++ MC Plot by GP Salam based on data from InspireHEP 7

9 knowing what goes into a collision i.e. proton structure fraction of ATLAS & CMS papers that cite them GEANT4 Anti-k t jet alg. Pythia 6.4 MC Pythia 8. CT0 PDFs POWHEG Box POWHEG (2007) CTEQ6 PDFs CL(s) technique (A.Read) POWHEG (2004) MG5aMCatNLO [rich UK involvement] Papers commonly cited by ATLAS and CMS ( ) as of , excluding self-citations; all papers > 0.2 MSTW2008 PDFs FastJet Manual Likelihood tests for new physics Sherpa. MadGraph 5 top++ NNLO ttbar Herwig 6 MC Pileup subtraction PDF4LHC (20) NNPDF23 PDFs CL(s) technique (T.Junk) NNPDF30 PDFs Perugia tunes (200) Herwig++ MC Plot by GP Salam based on data from InspireHEP 8

10 knowing what goes into a collision i.e. proton structure PROTON 0.8 fraction of ATLAS & CMS papers that cite them GEANT4 Anti-k t jet alg. Pythia 6.4 MC Pythia 8. CT0 PDFs POWHEG Box POWHEG (2007) CTEQ6 PDFs CL(s) technique (A.Read) POWHEG (2004) MG5aMCatNLO MSTW2008 PDFs FastJet Manual Papers commonly cited by ATLAS and CMS ( ) Likelihood tests for new physics Sherpa. MadGraph 5 top++ NNLO ttbar Herwig 6 MC [rich UK involvement] as of , excluding self-citations; all papers > 0.2 PDF4LHC (20) NNPDF23 PDFs CL(s) technique (T.Junk) NNPDF30 PDFs Perugia tunes (200) Herwig++ MC Pileup subtraction Plot by GP Salam based on data from InspireHEP 8

11 organising event information ( jets ) fraction of ATLAS & CMS papers that cite them GEANT4 Anti-k t jet alg. Pythia 6.4 MC Pythia 8. CT0 PDFs POWHEG Box POWHEG (2007) CTEQ6 PDFs CL(s) technique (A.Read) POWHEG (2004) MG5aMCatNLO Papers commonly cited by ATLAS and CMS ( ) as of , excluding self-citations; all papers > 0.2 MSTW2008 PDFs FastJet Manual Likelihood tests for new physics Sherpa. MadGraph 5 top++ NNLO ttbar Herwig 6 MC Pileup subtraction PDF4LHC (20) NNPDF23 PDFs CL(s) technique (T.Junk) NNPDF30 PDFs Perugia tunes (200) Herwig++ MC Plot by GP Salam based on data from InspireHEP 9

12 0

13 0

14 the question of organising information from hundreds of particles will come back later

15 predicting full particle structure that comes out of a collision fraction of ATLAS & CMS papers that cite them GEANT4 Anti-k t jet alg. Pythia 6.4 MC Pythia 8. CT0 PDFs POWHEG Box POWHEG (2007) CTEQ6 PDFs CL(s) technique (A.Read) POWHEG (2004) MG5aMCatNLO [rich UK involvement] Papers commonly cited by ATLAS and CMS ( ) as of , excluding self-citations; all papers > 0.2 MSTW2008 PDFs FastJet Manual Likelihood tests for new physics Sherpa. MadGraph 5 top++ NNLO ttbar Herwig 6 MC Pileup subtraction PDF4LHC (20) NNPDF23 PDFs CL(s) technique (T.Junk) NNPDF30 PDFs Perugia tunes (200) Herwig++ MC Plot by GP Salam based on data from InspireHEP 2

16 energy scale TeV hard process Z' time 00 GeV 0 GeV parton shower [ PanScales ] project schematic view of key components of QCD predictions and Monte Carlo event simulation GeV hadronisation π Κ π ρ p..... Κ π π Κ π π 3

17 energy scale TeV hard process Z' time 00 GeV 0 GeV parton shower [ PanScales ] project schematic view of key components of QCD predictions and Monte Carlo event simulation GeV hadronisation π Κ π ρ p..... Κ π π Κ π π 4

18 energy scale TeV hard process Z' time 00 GeV parton schematic view of key shower components of QCD 0 GeV [ PanScales ] project predictions and Monte Carlo event simulation pattern of particles in MC can be directly GeV hadronisation π Κ π ρ p..... Κ π π Κ π π compared to pattern in experiment 5

19 general purpose Monte Carlo event generators: THE BIG 3 Herwig 7 Pythia 8 Sherpa 2 they do an amazing job of simulation vast swathes of data; collider physics would be unrecognisable without them 6

20 energy scale major advances of past 20yrs: TeV hard process Z' time hard process (NLO, NNLO) & its interface with shower 00 GeV parton shower 0 GeV [ PanScales ] project GeV hadronisation π Κ π ρ p..... Κ π π Κ π π 7

21 energy scale major advances of past 20yrs: TeV hard process Z' time hard process (NLO, NNLO) & its interface with shower 00 GeV parton shower POHWEG 0 GeV [ PanScales ] project BOX MC@NLO (in Herwig&Sherpa) MINLO MLM, CKKW Vincia, FxFx GeV hadronisation UNNLOPS π Κ π ρ p..... Κ π π Κ π π [ ] 7

22 energy scale TeV hard process Z' time 00 GeV parton shower this talk 0 GeV [ PanScales ] project GeV hadronisation π Κ π ρ p..... Κ π π Κ π π 8

23 ttom panels to guide the eye. Fundamental experimental calibrations (jets) Relative JES uncertainty [%] ATLAS - s = 3 TeV, 3.2 fb Direct Balance with γ+jet anti-k t R = 0.4, EM+JES jet η < 0.8 Total uncertainty MC generator Out-of-cone Photon purity Second-jet veto Δφ JVT Photon scale Photon res. Statistical unc. Jet energy scale, which feeds into hundreds of other measurements Largest systematic errors ( 2%) come from differences between MC generators 2 (here Sherpa v. Pythia) 0 fundamental limit on jet p T [GeV] LHC precision potential 9

24 ATLAS anti-k t R=0.4, η < GeV<p <80 GeV T - L dt = 4.7 fb, s = 7 TeV Data + Stat. Pythia Herwig++ Syst. MC Simulation Gluon Efficiency Gluon Efficiency using full event information (quark/gluon tagging) data Syst. Data + Stat. MC Enriched Data use more info L dt = 4.7 fb, s = 7 TeV Pythia MC Simulation become more sensitive to MC limitations 60 GeV<p <80 GeV T - up to 35% differences in MCs v. data 0.2 a concern given trend 2.0 towards use of.5 Quark Efficiency maximal info, e.g. with machine 0.0 learning Pythia6 MC Other/Data MC/Data Herwig++0.8MC Quark Efficiency Quark Efficiency ATLAS anti-k t R=0.4, η < 0.8 Quark Efficiency 20

25 Matching with hard process is hitting a limit (e.g. Jäger, Karlberg, Scheller ) d σ/d z j3 [fb] pythia6 - default shower pythia8 - default shower pythia8 - dipole shower herwig7 - default shower d σ/d z j3 [fb] 0-2 hard matrix-element Limits effectiveness of current matching methods showers (here POWHEG) p T,j3 > 0 GeV 0-4 Parton structure also gets in way of Ratio to pythia6 - default better (NNLOPS) hard-process + shower matching schemes z j3 2

26 what is a parton shower? illustrate with dipole / antenna showers Gustafson & Pettersson 988, Ariadne 992, main Sherpa & Pythia8 showers, option in Herwig7, Vincia shower & (partially) Deductor shower 22

27 At its simplest n=0 n i= ( ) = iteration of 2 3 (or 2) splitting kernel 23

28 in practice: an evolution equation (in evolution scale v, e.g. /trans.mom.) Start with q-qbar state. Evolve a step in v and throw a random number to decide if state remains unchanged Z dp 2 (v) dv = f q q (v) P 2(v)

29 in practice: an evolution equation (in evolution scale v, e.g. /trans.mom.) Start with q-qbar state. Evolve a step in v and throw a random number to decide if state remains unchanged Z dp 2 (v) dv = f q q (v) P 2(v)

30 in practice: an evolution equation (in evolution scale v, e.g. /trans.mom.) Start with q-qbar state. Evolve a step in v and throw a random number to decide if state remains unchanged At some point, rand.numb. is such that state splits (2 3, i.e. emits gluon). Evolution Z equation changes dp 3 (v) dv = [ f qg (v) + f g q (v) ] P 3(v) gluon is part of two dipoles (qg, qg) 26

31 in practice: an evolution equation (in evolution scale v, e.g. /trans.mom.) self-similar Z evolution continues until it reaches a nonperturbative scale 27

32 recent directions of parton-shower work?. including 2 4 (or 3) splittings 2. subleading colour corrections (dipole picture is large N C ) 3. EW showers 28

33 Including 3 splittings ( 2 4) Jadach et al, e.g , Li & Skands, Höche, Krauss & Prestel, , Höche & Prestel, , Dulat, Höche & Prestel, D (0) ji (z, µ) = ij ( z) $ j z i D () ji (z, µ) = " P (0) ji (z) $ i j z i D (2) ji (z, µ) = 2" P () ji (z)+ 0 4" 2 P (0) ji (z)+ 2" 2 Z z dx x P (0) jk! (x)p (0) ki (z/x) $ i j z + i j z i Equations from slides by Höche $ 29

34 Including 3 splittings ds/d log 0 (y23) [nb] Dire PS just 2 splittings + 3 soft splittings 0 5 LO NLO soft k/2 apple µ apple 2k LO k/2 apple µ apple 2k LO no CMW Ratio log 0 (y 23 ) Dulat, Höche & Prestel,

35 Hierarchy of subleading colour corrections N 3 3 Angeles, De Angelis, Forshaw, Plätzer, Seymour JHEP 05 (208) 044 Gieseke, Kirchgaesser, Plätzer, Siodmok arxiv: De Angelis, Forshaw, Plätzer arxiv:8y.xxxxx Forshaw, Holguin, Plätzer arxiv:8y.xxxxx Plätzer, Sjödahl, Thorén, arxiv: N 2 2 N 2 N N N 2 3 N 3 Plugin approach can accommodate anything from (N)GLs to full parton showers. 0 s s 2 s 3 s cf. also work by Hatta & Ueda, ; Nagy & Soper papers; some subleading colour also in DIRE2 work 3

36 Bauer, Ferland & Webber, , EW showers (esp. beyond LHC) see also Chen, Han & Tweedie, & Sjostrand & collab W & Z emissions come with double logarithms α EW ln 2 Q m W right-handed up quarks left-handed up quarks W emission affects only left-handed quarks strong polarisation of quarks in unpolarised proton (at high enough energies) 32

37 what does a parton shower achieve? not just a question of ingredients, but also the final result of assembling them together Dasgupta, Dreyer, Hamilton, Monni & GPS,

38 what should a parton shower achieve? not just a question of ingredients, but also the final result of assembling them together Dasgupta, Dreyer, Hamilton, Monni & GPS,

39 it s a complicated issue For a total cross section, e.g. for Higgs production, it s easy to talk about systematic improvements (LO, NLO, NNLO, ). But they re restricted to that one observable 35

40 it s a complicated issue For a total cross section, e.g. for Higgs production, it s easy to talk about systematic improvements (LO, NLO, NNLO, ). But they re restricted to that one observable With a parton shower (+hadronisation) you produce a realistic full set of particles. You can ask questions of arbitrary complexity: the multiplicity of particles the total transverse momentum with respect to some axis (broadening) the angle of 3rd most energetic particle relative to the most energetic one [machine learning might learn many such features] 35

41 it s a complicated issue For a total cross section, e.g. for Higgs production, it s easy to talk about systematic improvements (LO, NLO, NNLO, ). But they re restricted to that one observable With a parton shower (+hadronisation) you produce a realistic full set of particles. You can ask questions of arbitrary complexity: the multiplicity of particles the total transverse momentum with respect to some axis (broadening) the angle of 3rd most energetic particle relative to the most energetic one [machine learning might learn many such features] 35

42 The standard answer so far It s common to hear that showers are Leading Logarithmic (LL) accurate. That language, widespread for multiscale problems, comes n T from analytical resummations. E.g. for (famous) Thrust T = max n T i p i. n T i p i 2-jet event: T 36

43 The standard answer so far It s common to hear that showers are Leading Logarithmic (LL) accurate. That language, widespread for multiscale problems, comes n T from analytical resummations. E.g. for (famous) Thrust T = max n T i p i. n T i p i 2-jet event: T σ( T < e L ) = σ tot exp [Lg (α s L) + g 2 (α s L) + α s g 3 (α s L) + α 2 s g 4 (α s L) + ] [α s, L ] LL NLL NNLL N 3 LL Catani, Trentadue, Turnock & Webber 93 Becher & Schwartz 08 36

44 The standard answer so far Sometimes you may see statements like Following standard practice to improve the logarithmic accuracy of the parton shower, the soft enhanced term of the splitting functions is rescaled by +α s (t)/(2π)k Questions: ) Which is it? LL or better? 2) For what known observables does this statement hold? 3) What good is it to know that some handful of observables is LL (or whatever) when you want to calculate arbitrary observables? 4) Does LL even mean anything when you do machine learning? 5) Why only LL when analytic resummation can do so much better? 37

45 Our proposal for minimal criteria for a shower Resummation Establish logarithmic accuracy for all known classes of resummation: global event shapes (thrust, broadening, angularities, jet rates, energy-energy correlations, ) non-global observables (cf. Banfi, Corcella & Dasgupta, hep-ph/062282) fragmentation / parton-distribution functions (multiplicity, cf. original Herwig angular-ordered shower from 980 s) Matrix elements Establish in what sense iteration of (e.g. 2 3) splitting kernel reproduces N-particle tree-level matrix elements for any N. 38

46 Examine two showers Pythia8 shower: because it s the most widely used DIRE shower (205 version, with just 2 3 splitting), because it s unique in being available for two General Purpose MC programs (Pythia8 & Sherpa2) The results I ll talk about will be the same for both and they ll be limited to fixed order for simplicity (though it s easy enough to generalise to an all-order study) 39

47 Matrix element for single emission: it s correct P P dpĩ j!ikj dp dp 2 S C dp? p? d e 2 +e 2 2 S C dp? p? d e 2 +e 2 40

48 Matrix element for single emission: it s correct P P dpĩ j!ikj dp dp 2 C S dp? p? d e 2 +e 2 2 C S dp? p? d e 2 +e ratio to full matrix element P? q! qg q! qg q! qg + q! qg

49 Matrix element for single emission: it s correct P P dpĩ j!ikj dp dp 2 C S dp? p? d e 2 +e 2 2 C S dp? p? d e 2 +e ratio to full matrix element P? q! qg q! qg q! qg + q! qg

50 Matrix element for single emission: it s correct P P dpĩ j!ikj dp dp 2 C S dp? p? d e 2 +e 2 2 C S dp? p? d e 2 +e ratio to full matrix element P? q! qg q! qg q! qg + q! qg

51 Matrix element for single emission: it s correct P P dpĩ j!ikj dp dp 2 C S dp? p? d e 2 +e 2 2 C S dp? p? d e 2 +e ratio to full matrix element P? q! qg q! qg q! qg + q! qg

52 Two emissions 4

53 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] 3 η g gluon rapidity Dire Pythia η g2 42

54 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 43

55 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 44

56 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 45

57 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 46

58 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 47

59 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 48

60 Two emissions impact of gluon-2 emission on gluon- momentum q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] p,g / ~ p,g gluon momentum Dire Pythia q[g ] qg 2 [g ] g [ q] g g 2 [ q] g [q] g g 2 [q] q[g ] qg 2 [g ] η g gluon rapidity Dire Pythia η g2 also noticed in 992 by Andersson, Gustafson & Sjogren special fudge in Ariadne 49

61 Two emissions matrix-element Phasespace map Correct radiation pattern ln p? ln p? C F C A /2 g analogous effect commented on by Nagy & Soper for DY recoil, but wider relevance not appreciated? 50

62 Two emissions matrix-element ratio of dipole-shower double-soft ME to correct result Phasespace map Correct radiation pattern ln p? C F C A /2 g ln p? ratio to correct 2-emission matrix-element r = p,2 / p, M 2 shower(p a,p b ) / M 2 correct(p a,p b ) 0.05 Applies to "diamond" rapidity region -π -π/2 0 π/2 π 0 Δφ 2 analogous effect commented on by Nagy & Soper for DY recoil, but wider relevance not appreciated? 50

63 Prevents shower from getting NLL accuracy for any e+e- event shape numerically, coefficients are Observable NLL ln discrepancy not large compared to other T L 3 vector p t sum L 3 B T L 2 y cam L 2 FC L 2 effects, cf. CMW 0.65ᾱ 2 L 2 (because all these observables are quite inclusive) but machine-learning uses all info including large phasespace regions with 00% deficiencies 5

64 so far took C F = C A /2, i.e. leading N C limit In real life they re not equal & common choice for allocating them assigns C A /2 to large part of phasespace that is actually gluon emission from quark (i.e. C F ) Correct radiation pattern ln p? Dipole radiation pattern ln p? C F C F C A /2 C A /2 g g 52

65 another view of the colour issue The dipole shower phase space partitioning of g 2 s radiation pattern is: Angular ordering implies a partitioning more like the following: 53

66 impact on observables? Z Z Has LL subleading-n C effect on 3-jet rates, thrust, but not for things like broadening, 2- jet rate (which are physically close the evolution variable, i.e. transverse momentum). E.g. for thrust (L) = 64 2 L 4 CA 2C F 54

67 closing 55

68 Conclusions Parton showers are a crucial element in collider physics Seeing many developments (subleading colour for non-global logarithms, multi-particle emission kernels, etc.) But maybe we need to go back to foundations: improving parton showers is not just a question of better components (e.g. higher-order splitting kernels) question of how components are assembled is equally crucial we must identify & state what a parton shower should be achieving new studies along these lines are teaching us important things about existing showers 56

69 BACKUP 57

70 Constant evolution variable contours in the Lund plane 0 Pythia 2 v Q =0 Dire ln p? 4 6 Phase space boundary v Q =0 2 v Q =0 3 Phase space boundary 8 v Q =

71 two soft emissions : boost dipole partitions back into the event COM Consider we emitted soft gluon g from hard qq, so we end up with a qg and a gq dipole: g _ q q To get us from the event COM to the gq dipole COM [blue line] requires a BIG BOOST Dipole partitioned at η= 0 in that frame: g _ q q To get us back to the event COM from the gq dipole COM undo the same BIG BOOST g _ q q In event COM partition comes out very close to q ; instead of equidistant in angle between g & q g _

72 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

73 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

74 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

75 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

76 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

77 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

78 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

79 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

80 jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 20 θ (or η = ln tan θ 2 ) k t = p t ΔR [GeV] p t [GeV] 0 5 p t = Eθ 2 Introduced for understanding Parton Shower Monte Carlos by B. Andersson,G. Gustafson L. Lonnblad and Pettersson θ ΔR The Lund Plane

81 organise phasespace: Lund diagrams LUND DIAGRAM JET t ln k (a) (b) (c) (b) (c) t ln k (a) (b) (c) (b) (c) ln / ln / 69

82 The path forward: collect 20-30x more collisions by ~2035 [GeV] 0 χ m CMS pp χ ± χ 0 2 WZ χ χ Observed ± σ theory Expected ± σ experiment fb NLO-NLL excl m χ ±=m (3 TeV) χ 0 2 [GeV] Suppose we had a choice between HL-LHC (4 TeV, 3ab - ) or going to higher c.o.m. energy but limited to 80fb -. How much energy would we need to equal % CL upper limit on cross section [pb] the HL-LHC? today s reach (3 TeV, 80fb - ) HL-LHC reach (4 TeV 3ab - ) energy needed for same reach with 80fb TeV SSM Z 6.7 TeV 20 TeV 2 TeV weakly coupled Z 680 GeV chargino 3.7 TeV 37 TeV.4 TeV 54 TeV 70

83 Hard processes: to 3rd order (NNLO) in perturbation theory strong coupling constant (α s ) 2 explosion of calculations in past 3 years as of April c.c. + c.c. 2 7