AN ANALYTIC UNDERSTANDING OF JET SUBSTRUCTURE

Transcription

1 AN ANALYTIC UNDERSTANDING OF JET SUBSTRUCTURE Simone Marzani Institute for Particle Physics Phenomenology Durham University NIKHEF Amsterdam, 7 th November 213 Dasgupta, Fregoso, SM, Powling EPJ C Dasgupta, Fregoso, SM, Salam, JHEP Dasgupta, Khelifa-Kerfa SM, Spannowsky, JHEP Banfi, Dasgupta, Khelifa-Kerfa and SM JHEP

2 Outline A very brief introduction to jets The jet mass distribution Grooming and Tagging QCD analysis of trimming, pruning and mass-drop tagger The modified mass drop tagger 2

3 Quarks, gluons and jets We usually discuss high-energy interactions in terms of quarks and gluons This is neither what we collide nor what we observe in the detectors Initial state: QCD factorisation theorems allow us to separate long-distance physics (proton) from hard interactions (partons) Final states: QCD splittings are enhanced in the collinear region so we are left with collimated sprays of hadrons: jets 3

4 JETS Collimated, energetic bunches of particles Ubiquitous in collider phenomenology 4

5 Jet definition(s) Jet algorithms: sets of (simple) rules to cluster particles together Implementable in experimental analyses and in theoretical calculations Must yield to finite cross sections First example : Sterman and Weinberg, Phys. Rev. Lett. 39, 1436 (1977): 5

6 Sequential recombination A large class of modern jet definitions is given by sequential recombination algorithms Starting with a list of particles, compute all distances dij and dib Find the minimum of all dij and dib dib can be an external parameter (e.g. Jade algorithm), a distance from the beam... If the minimum is a dij, recombine i and j and iterate Otherwise call i a final-state jet, remove it from the list and iterate for a complete review see Salam, Towards jetography (29) 6

7 Most common jet algorithms Common choices for the distance are d ij =min d ib = p 2p ti p 2p ti,p2p tj R 2 ij R 2 with R 2 ij =(y i y j ) 2 +( i j ) 2 p = 1 kt algortihm (Catani et al., Ellis and Soper) p = Cambridge / Aachen (Dokshitzer et al., Wobish and Wengler) p = -1 anti-kt algorithm (Cacciari, Salam, Soyez) Different algorithms serve different purposes Anti-kt clusters around hard particles giving round jets (default choice for ATLAS and CMS) Anti-kt is less useful for substructure studies, while C/A reflects angular ordering 7

8 Inclusive jet distributions (pb/gev) σ dy 2 T d dp s = 8TeV anti-k T R=.7 L = 1.71fb -1 CMS Preliminary 5. < y <.5 ( 1 ) 4.5 < y < 1. ( 1 ) 3 1. < y < 1.5 ( 1 ) < y < 2. ( 1 ) 1 2. < y < 2.5 ( 1 ) 2.5 < y < 3. ( 1 ) NNPDF 2.1 NLO NP Jet p T (GeV) ATLAS, Phys.Rev. D86 (212) 1422 CMS-PAS-SMP Inclusive jet observables are well-described by fixed-order QCD State of the art is NLO and several codes are publicly available (NLOJET++ by Nagy, NJet by Badger et al.). Towards jet cross-sections at NNLO (Glover et al.) 8

9 The boosted regime The LHC is exploring phenomena at energies above the EW scale Z/W/H/top can no longer be considered heavy particles These particles are abundantly produced with a large boost Their hadronic decays are collimated and can be reconstructed within a single jet. Need to distinguish: R R from QCD h p t > 2m/R q 9

10 Jet mass It s the simplest variable describing the structure of a jet How well can we compute it? Jet mass distributions are affected by double (soft & collinear) logarithms 1 d dm 2 J = 1 m 2 J apple s A 1 ln m2 J p 2 T + 2 sa 2 ln 3 m 2 J p 2 T +... Reliable estimates of jet shapes should include: fixed-order calculations at NLO (OK with public codes) resummed (N)NLL predictions 1

11 Jet mass: all-order calculations First NLL calculation of the jet mass in p-p collision Banfi, Dasgupta, Khelifa-Kerfa and S.M. (21) Dasgupta, Khelifa-Kerfa, S.M. and Spannowsky (212) Calculations also in SCET Chien, Kelley, Schwartz and Zhu (212) Jouttenus, Stewart, Tackmann and Waalewijn (213) For an isolated jet (small-r limit) the NLL cumulative distribution is ( ) 1 Z d d d = e D( ) = m2 j p 2 t R 2 independent emissions non-global logs: difficult to resum dependence on the jet algorithm e multiple emissions ED ( ) (1 + D ( )) N ( ) correlated emissions k 1 k 2 p 1 p 2 11

12 Z+jet.8.7 Z+jet, R=1., p TJ > 2 GeV LO NLL NLL+LO Z+jet, R=.6, p TJ > 2 GeV Jet Functions with O(R 2 ) terms (global only) with non-global logs.6 1 1/ d / d / d / d = m J /p TJ = m J /p TJ Fixed-order QCD is inadequate: we need resummation Precision QCD requires resummation beyond the naive isolated jet approximation : initial-state radiation and non-global logs Dasgupta, Khelifa-Kerfa, S.M. and Spannowsky (212) 12

13 Non-perturbative effects Z+jet, R=.6, p TJ > 2 GeV 1/ d / d NLL+LO Pythia 8 PS We have to include the effect of NP physics = m J /p TJ 13

14 Non-perturbative effects Z+jet, R=.6, p TJ > 2 GeV 1/ d / d NLL+LO with shift = 2. GeV Pythia 8 with hadronisation We have to include the effect of NP physics First consider hadronisation: large effect but fairly understood = m J /p TJ 14

15 Non-perturbative effects Z+jet, R=.6, p TJ > 2 GeV 1/ d / d NLL+LO with shift = 2. GeV Pythia 8 with hadronisation We have to include the effect of NP physics First consider hadronisation: large effect but fairly understood = m J /p TJ But we also have to consider the possibility of multiple interactions: the underlying event and pile-up Arbitrary units ATLAS -1 Ldt = 4.7 fb, s = 7 TeV Data 211 anti-k t with R=1. LCW, No jet grooming applied jet 6 p < 8 GeV, η <.8 T 1 N PV 4 5 N PV 7 8 N PV 11 N PV 12 Theoretical control over these effects is less good Leading jet mass, m jet 1 [GeV] ATLAS, JHEP 139 (213) 76 15

16 Beyond the mass: substructure Let s have a closer look: background peaks in the EW region Need to go beyond the mass and exploit jet substructure Grooming and Tagging: 1. clean the jets up by removing soft junk 2. identify the features of hard decays and cut on them Arbitrary units.1.8 ATLAS -1 Ldt = 4.7 fb, s = 7 TeV Data 211 anti-k t with R=1. LCW, No jet grooming applied jet 6 p < 8 GeV, η <.8 T 1 N PV 4 5 N PV 7 8 N PV 11 N PV Leading jet mass, m jet 1 [GeV] ATLAS, JHEP 139 (213) 76 16

17 Beyond the mass: substructure Let s have a closer look: background peaks in the EW region Need to go beyond the mass and exploit jet substructure Grooming and Tagging: 1. clean the jets up by removing soft junk 2. identify the features of hard decays and cut on them Grooming provides a handle on UE and pile-up Arbitrary units ATLAS -1 Ldt = 4.7 fb, s = 7 TeV Data 211 anti-k t with R=1. LCW, No jet grooming applied jet 6 p < 8 GeV, η <.8 T 1 N PV 4 5 N PV 7 8 N PV 11 N PV 12 Arbitrary units.14 ATLAS -1 Ldt = 4.7 fb, s = 7 TeV Data 211 anti-k with R=1. LCW, Trimmed (f t 6 p jet T < 8 GeV, η <.8 1 N PV 4 5 N PV 7 8 N PV 11 N PV 12 =.5, R =.3) cut sub.4.2 grooming Leading jet mass, m jet 1 [GeV] ATLAS, JHEP 139 (213) Leading jet mass, m jet 1 [GeV] ATLAS, JHEP 139 (213) 76 17

18 Grooming and tagging The last few years have seen a rapid development in substructure techniques: Very active (and growing) field with dedicated theory / experiment conference series (BOOST) O(1-2) powerful methods to tag jet substructure Substructure techniques are being used in searches and QCD measurements: they will be crucial in the years to come The existence of many methods can lead to some confusion Do we understand how / why they work? Only analytic understanding can make this field robust 18

19 Trimming Where to start? Cannot possibly study all tools These 3 are widely used We concentrate on background (QCD jets) recluster on scale Rsub discard subjets with < zcut pt Pruning Krohn, Thaler and Wang (21) recluster Rprune ~ mj/pt discard large-angle soft clusterings Mass-drop tagger (MDT, aka BDRS) Ellis, Vermillion and Walsh (29) decluster & discard soft junk repeat until find hard struct Butterworth, Davison, Rubin and Salam (28) 19

20 Our understanding so far Boost 21 proceedings: The [Monte Carlo] findings discussed above indicate that while [pruning, trimming and filtering] have qualitatively similar effects, there are important differences. For our choice of parameters, pruning acts most aggressively on the signal and background followed by trimming and filtering. To what extent are the taggers above similar? How does the statement of aggressive behaviour depend on the taggers parameters and on the jet s kinematics? Let s start with the right Monte Carlo study 2

21 Comparison of taggers / d / d quark jets: m [GeV], for p t = 3 TeV plain jet mass = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), qq qq, p t > 3 TeV 3 / d / d gluon jets: m [GeV], for p t = 3 TeV plain jet mass = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), gg gg, p t > 3 TeV Plain jet mass: characteristic Sudakov peak 21

22 Comparison of taggers / d / d quark jets: m [GeV], for p t = 3 TeV plain jet mass Trimmer (z cut =.5, R sub =.3) Pruner (z cut =.1).2.1 MDT (y cut =.9, µ=.67) = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), qq qq, p t > 3 TeV 3 / d / d gluon jets: m [GeV], for p t = 3 TeV plain jet mass Trimmer Pruner.2 MDT = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), gg gg, p t > 3 TeV Different taggers appear to behave quite similarly 22

23 Comparison of taggers / d / d quark jets: m [GeV], for p t = 3 TeV plain jet mass Trimmer (z cut =.5, R sub =.3) Pruner (z cut =.1).2.1 MDT (y cut =.9, µ=.67) = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), qq qq, p t > 3 TeV 3 / d / d gluon jets: m [GeV], for p t = 3 TeV plain jet mass Trimmer Pruner.2 MDT = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), gg gg, p t > 3 TeV But only for a limited kinematic region! 23

24 Comparison of taggers / d / d quark jets: m [GeV], for p t = 3 TeV plain jet mass Trimmer (z cut =.5, R sub =.3) Pruner (z cut =.1).2.1 MDT (y cut =.9, µ=.67) = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), qq qq, p t > 3 TeV 3 / d / d gluon jets: m [GeV], for p t = 3 TeV plain jet mass Trimmer Pruner.2 MDT = m 2 /(p t 2 R 2 ) Jets: C/A with R=1. MC: Pythia 6.4, DW tune, parton-level (no MPI), gg gg, p t > 3 TeV Let s translate from QCD variables to ``search variables: ρ m, for pt = 3 TeV, R =1. 24

25 Questions that arise Can we understand the different shapes (flatness vs peaks)? What s the origin of the transition points? How do they depend on the taggers parameters? A theorist s worry: complicated algorithms and distributions Are we giving up on calculability / precision QCD? precision QCD grooming M. Schwartz (Boost 212) 25

26 Questions that arise Can we understand the different shapes (flatness vs peaks)? What s the origin of the transition points? How do they depend on the taggers parameters? A theorist s worry: complicated algorithms and distributions Are we giving up on calculability / precision QCD? We have shown how to compute groomed-jet distributions grooming precision QCD M. Schwartz (Boost 212) 26

27 Trimming 1. Take all particles in a jet and re-cluster them with a smaller jet radius Rsub < R 2. Keep all subjets for which pt subjet > zcut pt 3. Recombine the subjets to form the trimmed jet 27

28 Trimming at LO ρ/σ dσ / dρ.2.1 trimmed quark jets: LO m [GeV], for p t = 3 TeV, R= Emissions within Rsub are never tested for zcut: double logs ρ = m 2 /(p t 2 R 2 ) Intermediate region in which zcut is effective: single logs r 2 z cut z cut d (trim,lo) s C F s C F s C F ln r2 d 3 4 ln 1 3 z cut 4 ln 1 = 3 4 r = R sub R 28

29 Trimming: all orders One gets exponentiation of LO (+ running coupling) d trim,resum d = d trim,lo apple exp d Z d 1 d trim,lo d.3 Pythia 6 MC: quark jets m [GeV], for p t = 3 TeV, R = Trimming.3 Analytic Calculation: quark jets m [GeV], for p t = 3 TeV, R = Trimming / d / d.2.1 R sub =.2, z cut =.5 R sub =.2, z cut =.1 3 / d / d.2.1 R sub =.2, z cut =.5 R sub =.2, z cut = = m 2 /(p t 2 R 2 ) = m 2 /(p t 2 R 2 ) All-order calculation done in the small-zcut limit 29

30 Pruning 1. From an initial jet define pruning radius Rprune ~ m / pt 2. Re-cluster the jet, vetoing recombination for which z = min(p ti,p ti ) ~p ti + ~p ti <z cut d ij >R prune i.e. soft and wide angle 3

31 Pruning at LO The pruning radius is set dynamically: Rprune < dij The 2 prongs are always tested for zcut pruned quark jets: LO.2 m [GeV], for p t = 3 TeV, R= ρ/σ dσ / dρ.1 single-log region 3 z cut Interesting result: at LO we only have single logs! ρ = m 2 /(p t 2 R 2 ) 31

32 Beyond LO R R prune p 1 p 2 R prune What pruning is meant to do Choose an Rprune such that different hard prongs (p1, p2) end up in different hard subjets. Discard any softer radiation. p 1 R prune p 2 What pruning sometimes does Chooses Rprune based on a soft p3 (dominates total jet mass), and leads to a single narrow subjet whose mass is also dominated by a soft emission (p2, within Rprune of p1, so not pruned away). R p 3 32

33 Beyond LO R R prune p 1 Y-pruning p 2 R prune What pruning is meant to do Choose an Rprune such that different hard prongs (p1, p2) end up in different hard subjets. Discard any softer radiation. p 1 R prune p 2 What pruning sometimes does Chooses Rprune based on a soft p3 (dominates total jet mass), and leads to a single narrow subjet whose mass is also dominated by a soft emission (p2, within Rprune of p1, so not pruned away). R I-pruning p 3 33

34 Structure beyond LO The all-order pruned mass distribution is NOT given by exponentiation of LO Two distinct contributions with different resummations: Y-pruning: essentially Sudakov suppression of LO ~ αs n L 2n-1 I-pruning: convolution between the pruned and the original mass ~ αs n L 2n Because of its anomalous component the logarithmic structure at NLO worsens: ~ αs 2 L 4 (for ρ<zcut 2, as plain jet mass) A simple fix: require at least one successful merging with ΔR > Rprune and z > zcut (Y-pruning) 34

35 All-order results Full Pruning: single-log region for zcut 2 <ρ<zcut We control αs n L 2n and αs n L 2n-1 in the expansion NG logs present but deferred to NNLO Pythia 6 MC: quark jets m [GeV], for p t = 3 TeV, R = Analytic Calculation: quark jets m [GeV], for p t = 3 TeV, R = Pruning, z cut =.1 Y-pruning, z cut =.1 I-pruning, z cut =.1.2 Pruning, z cut =.1 Y-pruning, z cut =.1 I-pruning, z cut =.1 / d / d.1 / d / d = m 2 /(p t 2 R 2 ) = m 2 /(p t 2 R 2 ) Y-pruning already being used by CMS CMS-PAS-BTV

36 Mass Drop Tagger at LO 1. Undo the last stage of the C/A clustering. Label the two subjets j 1 and j 2 (m 1 > m 2 ) 2. If m1< μm (mass drop) and the splitting was not too asymmetric (yij > ycut), tag the jet. 3. Otherwise redefine j = j1 and iterate. In the small-ycut limit the result is identical to LO pruning: single-log distribution 3 ρ/σ dσ / dρ pruned quark jets: LO m [GeV], for p t = 3 TeV, R= single-log region y cut ρ = m 2 /(p t 2 R 2 ) 36

37 Complications at NLO p 1 p 2 p 3 What MDT does wrong: If the yij condition fails, MDT iterates on the more massive subjet. It can follow a soft branch (p2+p3 < ycut ptjet), when the right answer was that the (massless) hard branch had no substructure This can be considered a flaw of the tagger It worsens the logarithmic structure ~αs 2 L 3 The all-order distribution is NOT given by exponentiation of LO It calls for a modification 37

38 The modified Mass Drop Tagger 1. Undo the last stage of the C/A clustering. Label the two subjets j 1 and j 2 (m 1 > m 2 ) 2. If m1< μm (mass drop) and the splitting was not too asymmetric (yij > ycut), tag the jet. 3. Otherwise redefine j to be the subjet with highest transverse mass and iterate. In practice the soft-branch contribution is very small However, this modification makes the all-order structure particularly interesting / d / d Pythia 6 MC: quark jets m [GeV], for p t = 3 TeV, R = MDT, y cut =.9 wrong branch mmdt 1-4 y cut = m 2 /(p t 2 R 2 ) 38

39 All-order structure of mmdt In the small ycut limit, it is just the exponentiation of LO The mmdt has single logs to all orders (i.e. αs n L n ).2 Pythia 6 MC: quark jets m [GeV], for p t = 3 TeV, R = mmdt y cut =.3 y cut =.13 y cut =.35.2 Analytic Calculation: quark jets m [GeV], for p t = 3 TeV, R = mmdt y cut =.3 y cut =.13 y cut =.35 (some finite y cut ) / d / d.1 / d / d = m 2 /(p t 2 R 2 ) = m 2 /(p t 2 R 2 ) Remarkable agreement! 39

40 All-order structure of mmdt In the small ycut limit, it is just the exponentiation of LO The mmdt has single logs to all orders (i.e. αs n L n ) / d / d LO v. NLO v. resummation (quark jets).1 m [GeV], for p t = 3 TeV, R = p t,jet > 3 TeV mmdt (y cut =.13) Leading Order Next-to-Leading Order Resummed = m 2 /(p t 2 R 2 ) Single logs: extended validity of FO calculations Single logs of collinear origi Remarkable consequence: mmdt is free of non-global 1/ d / d logs! plain mass Z+jet, R=1., p TJ > 2 GeV = m J /p TJ LO NLL NLL+LO only a qualitative comparison: different process/kinematics! 4

41 All-order structure of mmdt In the small ycut limit, it is just the exponentiation of LO The mmdt has single logs to all orders (i.e. αs n L n ) / d / d LO v. NLO v. resummation (quark jets).1 m [GeV], for p t = 3 TeV, R = p t,jet > 3 TeV mmdt (y cut =.13) Leading Order Next-to-Leading Order Resummed = m 2 /(p t 2 R 2 ) Single logs: extended validity of FO calculations Single logs of collinear origin Remarkable consequence: mmdt is free of non-global logs! 41

42 Other properties of mmdt Flatness of the background is a desirable property (data-driven analysis, side bands) ycut can be adjusted to obtain it (analytic relation) Role of μ, not mentioned so far It contributes to subleading logs and has small impact if not too small (μ>.4) Filtering only affects subleading (N nfilt LL) terms Effect of µ parameter: quark jets m [GeV], for p t = 3 TeV, R = Effect of filtering: quark jets m [GeV], for p t = 3 TeV, R = µ = 1. mmdt (y cut =.13) / d / d.1 µ =.67 µ =.4 µ =.3 µ =.2 / d / d.1 mmdt + filtering = m 2 /(p t 2 R 2 ) = m 2 /(p t 2 R 2 ) 42

43 Non-perturbative effects hadron / parton hadron / parton hadronisation summary (quark jets) m [GeV], for p t = 3 TeV, R = plain mass trimmer pruning Y-pruning mmdt (z cut ) = m 2 /(p t 2 R 2 ) hadron (with UE) / hadron (no UE) wue / noue UE summary (quark jets) m [GeV], for p t = 3 TeV, R = Plain mass Trimmer pruning Y-pruning mmdt = m 2 /(p t 2 R 2 ) Most taggers have reduced sensitivity to NP physics mmdt particularly so (it s the most calculable) Y-pruning sensitive to UE because of the role played by the fat jet mass 43

44 Hadronisation effects for mmdt hadron / parton hadronisation v. analytics (quark jets) m [GeV], for p t = 3 TeV, R = mmdt (z cut =.1) -mass mmdt (z cut =.1) -mass mmdt (y cut =.11) mmdt (y cut =.11) analytics analytics ( 2.4) = m 2 /(p t 2 R 2 ) Hadronisation produces: 1.a shift in jet mass 2.a shift in the jet s (or prong s) momentum Same power behaviour but with competing signs: d NP dm ' d PT dm apple 1+a NP m 44

45 Different Monte Carlos Analytic studies of the taggers reveal their properties mmdt is the most calculable (single-logs, small NP effects) Useful tool if MCs don t agree Different showers m [GeV], for p t = 3 TeV, R = / d / d.1 v6.425 (DW) virtuality ordered v6.425 (P11) p t ordered v6.428pre (P11) p t ordered v8.165 (4C) p t ordered Analytics p t,jet > 3 TeV mmdt (y cut =.13) = m 2 /(p t 2 R 2 ) 45

46 In summary... Jet substructure is playing an increasingly important role in LHC phenomenology (searches and QCD) I have presented the first comprehensive field-theoretical understanding of these algorithms Analytic studies of groomers and taggers reveal their properties indicate how to develop better tools (Y-pruning, mmdt) provide solid checks on MC simulations mmdt: precision QCD not only possible but even easier! 46

47 Outlook Phenomenology of the taggers presented here for signal and background (work in progress with Dasgupta, Salam and Siodmok) New family of taggers inspired by the analytic properties of mmdt (work in progress with Larkoski, Soyez and Thaler) Understanding correlations between taggers 47

48 Outlook Phenomenology of the taggers presented here for signal and background (work in progress with Dasgupta, Salam and Siodmok) New family of taggers inspired by the analytic properties of mmdt (work in progress with Larkoski, Soyez and Thaler) Understanding correlations between taggers THANK YOU! 48

49 BACKUP SLIDES 49

50 Lund diagrams for jet mass Lund kinematic diagram ln k t ~ ln z soft large angle region hard collinear region soft collinear region line of constant jet mass large angles y ~ ln 1/ small angles 5

51 Summary table highest logs transition(s) Sudakov peak NGLs NP: m 2 plain mass α n s L2n L 1/ ᾱ s yes µ NP p t R trimming α n s L 2n z cut, r 2 z cut L 1/ ᾱ s 2lnr yes µ NP p t R sub pruning α n s L2n z cut, z 2 cut L 2.3/ ᾱ s yes µ NP p t R MDT α n s L2n 1 y cut, 1 4 y2 cut, y3 cut yes µ NP p t R Y-pruning α n s L2n 1 z cut (Sudakov tail) yes µ NP p t R mmdt α n s Ln y cut no µ 2 NP /y cut 51

52 Lund diagrams for trimming ln z > z cut z cut r 2 < < z cut < z cut r 2 Trimming = z cut = z cut = z cut = z cut r 2 = z cut r 2 E gluon = z cut E jet = R sub E gluon = z cut E jet = R sub E gluon = z cut E jet ln 1/ ln 1/ ln 1/ 52

53 Lund diagrams for pruning ln z > z cut z cut fat < < z cut < z cut fat Pruning = z cut = z cut = z cut I E gluon = z cut E jet emission that sets fat and R prune Y = R prune fat = z cut E gluon = z cut E jet = R prune fat = z cut E gluon = z cut E jet ln 1/ ln 1/ ln 1/ 53

54 Lund diagrams for mmdt ln z < z cut mmdt = z cut b a Egluon = z cut Ejet ln 1/ 54

55 Examples of NLO checks 15 1 Coefficient of (C F s / ) 2 for modified mass-drop R=.8, y cut =.1 Event2 Event2 - Analytic Coefficient of (C F s / ) 2 for pruning R=.8, z cut =.4 Event2 Event2 - Analytic d / d ln v d / d ln v ln v ln v Coefficient of C F C A ( s / ) 2 for modified mass-drop R=.8, y cut =.2 Event2 Event2 - Analytic 1 5 Coefficient of (C F s / ) 2 for trimming R=.8, R sub =.2, z cut =.15 Event2 Event2 - Analytic 14 d / d ln v d / d ln v ln v ln v 55

56 ρ σ dσ (I-prune) dρ = zcut ρ e S(ρ fat,ρ) +Θ ( z cut dρ fat ρ fat 1 ρ fat ( zcut e D(ρ fat) ρ dz α s (ρ fat z p 2 t R 2 ) C F ρ fat z π dz p gq (z) α s(ρzp 2 t R 2 ) C F ρ/ρ fat π ρ ) ( zcut ρ fat dρ zcut exp ρ [ Θ ) ( ) ρ z cut + ρ fat ρ /ρ fat dz z C F π α s(ρ z p 2 t R 2 ) )] ( ) ( ) ρ σ dσ (Y-prune) dρ + = e D(ρ) 1 min(zcut,ρ/z cut ) ρ dz p gq (z) α s(ρzp 2 t R 2 ) C F z cut π ( e D(ρ fat) dρ fat ρ fat e S(ρ fat,ρ) zcut ρ fat dz + α s (ρ fat z p 2 ) t R2 ) C F z π ρ/ρfat z cut dz p gq (z) α s(ρzp 2 t R 2 ) C F π 56

57 ATLAS MDT GeV 1 dm 1 d MC / Data ATLAS Cambridge-Aachen R=1.2 Split/Filtered with R >.3 5 < p < 6 GeV T N PV = 1, y < 2 qq Data, L = 35 pb Statistical Unc. Total Unc. Pythia Herwig Jet Mass [GeV] This cut significantly changes the tagger s behaviour: mass minimum The single-log region is reduced (and can even disappear) We hope that future studies will be able to avoid this ATLAS measured the jet mass with MDT Different version of the tagger with Rmin=.3 between the prongs / d / d.1 ATLAS MDT (Pythia 6 MC, quarks) m [GeV], for p t = 3 TeV, R = MDT (y cut =.9) ATLAS MDT (R min =.3, y cut =.9) = m 2 /(p t 2 R 2 ) 57

58 Performances for finding signals (Ws) signal significance with quark bkgds signal significance with gluon bkgds 5 5 ε S / ε B 4 3 mmdt (y cut =.11) pruning (z cut =.1) Y-pruning (z cut =.1) trimming (R sub =.3, z cut =.5) ε S / ε B 4 3 mmdt (y cut =.11) pruning (z cut =.1) Y-pruning (z cut =.1) trimming (R sub =.3, z cut =.5) 2 hadron level with UE 2 hadron level with UE p t,min [GeV] p t,min [GeV] Y-pruning gives a visible improvement 58