Jets, UE and early LHC data

Transcription

1 Jets, UE and early LHC data Gavin P. Salam LPTHE, UPMC Paris 6 & CNRS LHC@BNL Joint Theory/Experiment Workshop on Early Physics at the LHC 8 February 2010 Brookhaven National Laboratory, Upton, USA Based on work with Jon Butterworth, Andrea Banfi, Matteo Cacciari, John Ellis, Are Raklev, Sebastian Sapeta, Gregory Soyez, Giulia Zanderighi

2 early LHC (p. 2) Introduction LHC is a parton collider Quarks and gluons are inevitable in initial state and ubiquitous in the final state Partons quarks and gluons are key concepts of QCD. Lagrangian is in terms of quark and gluon fields Perturbative QCD only deals with partons Though we often talk of quarks and gluons, we never see them Not an asymptotic state of the theory because of confinement But also even in perturbation theory because of collinear divergences (in massless approx.) The closest we can get to handling final-state partons is jets

3 early LHC (p. 3) Introduction Jets as projections p π π φ K LO partons NLO partons parton shower hadron level Jet Def n Jet Def n Jet Def n Jet Def n jet 1 jet 2 jet 1 jet 2 jet 1 jet 2 jet 1 jet 2 Projection to jets provides universal view of event

4 early LHC (p. 4) Introduction QCD jets flowchart Jet (definitions) provide central link between expt., theory and theory And jets are an input to almost all analyses

5 early LHC (p. 4) Introduction QCD jets flowchart Jet (definitions) provide central link between expt., theory and theory And jets are an input to almost all analyses

6 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(kti 2,k2 tj ) R2 ij /R2 and d ib = ki 2 Recombine i,j (if ib: i jet) Repeat Bottom-up jets: Sequential recombination (attempt to invert QCD NB: hadron branching) collider variables Rij 2 = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

7 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

8 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

9 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

10 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

11 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

12 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

13 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat R ij > R NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle

14 early LHC (p. 5) Introduction Sequential recombination algorithms k t algorithm Catani, Dokshizter, Olsson, Seymour, Turnock, Webber Ellis, Soper 93 Find smallest of all d ij = min(k 2 ti,k2 tj ) R2 ij /R2 and d ib = k 2 i Recombine i,j (if ib: i jet) Repeat R ij > R NB: hadron collider variables R 2 ij = (φ i φ j ) 2 + (y i y j ) 2 rapidity y i = 1 2 ln E i+p zi E i p zi R ij is boost invariant angle R sets minimal interjet angle NB: d ij distance QCD branching probability α s dk 2 tj dr2 ij d ij

15 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

16 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

17 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

18 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

19 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

20 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

21 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

22 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

23 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

24 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

25 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

26 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08

27 early LHC (p. 6) Introduction Adapting seq. rec. to give circular jets Soft stuff clusters with nearest neighbour k t : d ij = min(k 2 ti, k2 tj ) R2 ij anti-k t: d ij = R 2 ij max(k 2 ti, k2 tj ) Hard stuff clusters with nearest neighbour Privilege collinear divergence over soft divergence Cacciari, GPS & Soyez 08 anti-k t gives cone-like jets without using stable cones

28 early LHC (p. 7) Introduction ATLAS: first dijet event, with anti-k t

29 early LHC (p. 8) Introduction CMS: first dijet event, with anti-k t

30 early LHC (p. 9) Introduction With ATLAS and CMS having adopted anti-k t as their default jet algorithm, LHC is the first hadron collider experiment to start running with a clear prospect for infrared and collinear jet-finding. Crucial for future comparisons to QCD.

31 early LHC (p. 10) Early data Early data? Limited luminosity Jet energy scale poorly constrained (±10%?) Steeply falling jet cross sections not well measured Strategy? Use purely hadronic events (large X-sct) Measure ratios of jet p t s, ratios of cross sections

32 early LHC (p. 11) Early data y 23, a simple event shape 1) Select events with two central jets, hardest with p t1 > 100 GeV σ = O (100 7 TeV 2) Define d 23 = maximum of 3rd hardest jet, p 2 t3 k t splitting scale of either of two central jets cf. substructure studies 3) Normalise to Q 2 = (p t1 + p t2 ) 2, y 23 = d 23 /Q 2 cancel (most of) Jet Energy Scale uncertainty 4) Plot differential distribution within selected events uncertainty on selected X-section cancels

33 early LHC (p. 12) Early data You can compare to Monte Carlo parton showers Pythia, Herwig, Sherpa Parton showers matched to tree-level matrix elements Alpgen (MLM), Madgraph (MLM), Sherpa (CKKW) Non-MC predictions: NLL resummation + NLO CAESAR + NLOJET: controlled approximations Banfi, GPS & Zanderighi 10

34 early LHC (p. 13) Early data NLL+NLO v. showers Low p t, gluon dominated NLO+NLL (all uncert.) NLO+NLL (sym. scale uncert.) Herwig 6.5 Pythia 6.4 virtuality ordered shower (DW tune) Pythia 6.4 p t ordered shower (S0A tune) σ dσ dln y 3,g LHC, 14 TeV p t1 > 200 GeV, y jets < 1, η C = 1.5 PARTON LEVEL NO UE

35 early LHC (p. 14) Early data NLL+NLO v. showers High p t, quark dominated 0.2 NLO+NLL (all uncert.) NLO+NLL (sym. scale uncert.) Herwig 6.5 Pythia 6.4 virtuality ordered shower (DW tune) Pythia 6.4 p t ordered shower (S0A tune) σ dσ dln y 3,g -8-4 LHC, 14 TeV p t1 > 1 TeV, y jets < 1, η C = 1.5 PARTON LEVEL NO UE

36 early LHC (p. 15) Early data Several showers High p t, quark dominated 0.2 DW S0A Pto pt0 Perugia σ dσ dln y 3,g -8-4 LHC, 14 TeV p t1 > 1 TeV, y jets < 1, η C = 1.5 PARTON LEVEL NO UE

37 early LHC (p. 16) Early data NLL+NLO v. Alpgen+Herwig Low p t, gluon dominated 0.3 NLO+NLL (all uncert.) NLO+NLL (sym. scale uncert.) Alpgen + Herwig (partons) σ dσ dln y 3,g LHC, 14 TeV p t1 > 200 GeV, y jets < 1, η C = 1.5 PARTON LEVEL NO UE

38 early LHC (p. 17) Early data Other event shapes [ τ,g 10 5 τ,e 2 T m,g 2 T m,r ρ T,E B T,E ρ H,E B W,E ln y 3,g ln y 3,E F g S g B T,R 4 2 B W,R NLO+NLL (all uncert.) PARTON LEVEL NLO+NLL (sym. scale uncert.) NO UE Alpgen + Herwig (partons) LHC, 14 TeV p t1 > 200 GeV, y jets < 1, η C = 1.5 There are many other ways of combining event particle momenta to get event shapes e.g. transverse thrust Each with different sensitivity to QCD branching.

39 early LHC (p. 18) Early data Hadronic observables not just for constraining Monte Carlos

40 early LHC (p. 19) Neutralinos R-parity violating SUSY As an example, a search for neutralinos in R-parity violating supersymmetry. Normal SPS1A type SUSY scenario, except that neutralino is not LSP, but instead decays, χ 0 1 qqq. Jet combinatorics makes this a tough channel for discovery Produce pairs of squarks, m q 500 GeV. Each squark decays to quark + neutralino, m χ GeV Neutralino is somewhat boosted jet with substructure Butterworth, Ellis, Raklev & GPS 09 q q q q ~ q ~ 0 χ1 ~ q q ~ g ~ 0 χ1 q ~ q q ~ q q q q

41 early LHC (p. 19) Neutralinos R-parity violating SUSY As an example, a search for neutralinos in R-parity violating supersymmetry. Normal SPS1A type SUSY scenario, except that neutralino is not LSP, but instead decays, χ 0 1 qqq. Jet combinatorics makes this a tough channel for discovery Produce pairs of squarks, m q 500 GeV. Each squark decays to quark + neutralino, m χ GeV Neutralino is somewhat boosted jet with substructure Butterworth, Ellis, Raklev & GPS 09 q q boosted q q ~ q ~ 0 χ1 ~ q q ~ g ~ 0 χ1 q ~ q q ~ q boosted q q q

42 early LHC (p. 20) Neutralinos Analytics (back-of-the-enveolope) Subjet decomposition procedures are not just trial and error. Mass distribution for undecomposed jet: 1 dn N dm 2Cα s lnrp t /m m e Cαs ln2 Rp t/m+ Strongly shaped, with Sudakov peak, etc. Mass distribution for hardest (largest Jade distance) substructure within C/A jet that satisfies a symmetry cut (z > z min ): 1 dn N dm C α s (m) m C α s (Rp t ) m e C α s lnrp t/m+ [ 1 + (2b0 C ) α }{{} s lnrp t /m + O ( α 2 s ln 2)] partial cancellation Procedure gives nearly flat distribution in mdn/dm Neutralino procedure involves 2 hard substructures, but ideas are similar

43 early LHC (p. 21) Neutralinos RPV SUSY, SPS1a, 1 fb 1 [14 TeV] m 1 /(100GeV) dn/dbin per fb signal + background background (just dijets) Cam/Aachen R=0.7 p t1 > 500 GeV signal Herwig Jimmy m 1 [GeV] Keep it simple: Look at mass of leading jet m dn Plot 100 GeV dm for hardest jet (p t > 500 GeV) Require 3-pronged substructure And third jet And fourth central jet 99% background rejection scale-invariant procedure so remaining bkgd is flat Once you ve found neutralino: Look at m 14 using events with m 1 in neutralino peak and in sidebands Out comes the squark!

44 early LHC (p. 21) Neutralinos RPV SUSY, SPS1a, 1 fb 1 [14 TeV] m 1 /(100GeV) dn/dbin per fb signal + background background (just dijets) signal 2000 Cam/Aachen + filt, R=0.7 p t1 > 500 GeV, z split > 0.15, m bc > 0.25 m abc Herwig Jimmy m 1 [GeV] Keep it simple: Look at mass of leading jet m dn Plot 100 GeV dm for hardest jet (p t > 500 GeV) Require 3-pronged substructure And third jet And fourth central jet 99% background rejection scale-invariant procedure so remaining bkgd is flat Once you ve found neutralino: Look at m 14 using events with m 1 in neutralino peak and in sidebands Out comes the squark!

45 early LHC (p. 21) Neutralinos RPV SUSY, SPS1a, 1 fb 1 [14 TeV] m 1 /(100GeV) dn/dbin per fb signal + background background (just dijets) signal 1000 Cam/Aachen + filt, R=0.7 p t1 > 500 GeV, z split > 0.15, m bc > 0.25 m abc 0 Herwig Jimmy 4.3 p t3 > 100 GeV m 1 [GeV] Keep it simple: Look at mass of leading jet m dn Plot 100 GeV dm for hardest jet (p t > 500 GeV) Require 3-pronged substructure And third jet And fourth central jet 99% background rejection scale-invariant procedure so remaining bkgd is flat Once you ve found neutralino: Look at m 14 using events with m 1 in neutralino peak and in sidebands Out comes the squark!

46 early LHC (p. 21) Neutralinos RPV SUSY, SPS1a, 1 fb 1 [14 TeV] m 1 /(100GeV) dn/dbin per fb signal + background background (just dijets) signal Cam/Aachen + filt, R=0.7 p t1 > 500 GeV, z split > 0.15, m bc > 0.25 m abc 0 p t3 > 100 GeV, y 13 < m 1 [GeV] Keep it simple: Look at mass of leading jet m dn Plot 100 GeV dm for hardest jet (p t > 500 GeV) Require 3-pronged substructure And third central jet And fourth central jet 99% background rejection scale-invariant procedure so remaining bkgd is flat Once you ve found neutralino: Look at m 14 using events with m 1 in neutralino peak and in sidebands Out comes the squark!

47 early LHC (p. 21) Neutralinos RPV SUSY, SPS1a, 1 fb 1 [14 TeV] m 1 /(100GeV) dn/dbin per fb signal + background background (just dijets) signal 200 Cam/Aachen + filt, R=0.7 p t1 > 500 GeV, z split > 0.15, m bc > 0.25 m abc 0 p t3, p t4 > {100,80} GeV, y 13, y 14 < m 1 [GeV] Keep it simple: Look at mass of leading jet m dn Plot 100 GeV dm for hardest jet (p t > 500 GeV) Require 3-pronged substructure And third central jet And fourth central jet 99% background rejection scale-invariant procedure so remaining bkgd is flat Once you ve found neutralino: Look at m 14 using events with m 1 in neutralino peak and in sidebands Out comes the squark!

48 early LHC (p. 21) Neutralinos RPV SUSY, SPS1a, 1 fb 1 [14 TeV] dn/d(20 GeV) per fb < m 1 < < m 1 < < m 1 < 120 Cam/Aachen + filt, R=0.7 p t1 > 500 GeV, z split > 0.15, m bc > 0.25 m abc 0 p t3, p t4 > {100,80} GeV, y 13, y 14 < m 14 [GeV] Keep it simple: Look at mass of leading jet m dn Plot 100 GeV dm for hardest jet (p t > 500 GeV) Require 3-pronged substructure And third central jet And fourth central jet 99% background rejection scale-invariant procedure so remaining bkgd is flat Once you ve found neutralino: Look at m 14 using events with m 1 in neutralino peak and in sidebands Out comes the squark!

49 early LHC (p. 22) Neutralinos RPV SUSY: significance v. mass scale All points use 1 fb 1, 14 TeV Divide significance by 3 for 7 TeV as m χ increases, m q goes from 530 GeV to 815 GeV Same cuts as for main SPS1A analysis no particular optimisation

50 early LHC (p. 23) UE Constraining low-p t part of Monte Carlos Underlying Event

51 early LHC (p. 24) UE For each event Traditional approach [Marchesini & Webber (1988), UA1 (1988), Field et al.] 1. take charged particles with p t > 0.5 GeV and y < 1 2. cluster with cone jet algorithm with R = 0.7 to find the leading jet 3. define typical p t of UE as p t in TransMin, TransMax or TransAv regions 2π Leading Jet φ TransMin TransAv: O(α s ) φ Leading Jet TransMin TransMax TransMax: O(α s ) TransMax TransMin: O(α 2 s ) 0 1 y +1 topological separation: UE defined as particles entering certain region of (y, φ) space

52 early LHC (p. 25) UE Area/median approach For each event. cluster particles with an infrared safe jet finding algorithm (all particles are clustered so we have set of jets ranging from hard to soft) only k t or C/A algs. from the list of all jets (no cuts required!) determine [{ pt,j }] ρ = median A j and its uncertainty σ median gives a typical value of pt /A for a given event using median is a way to dynamically separate hard and soft parts of the event [Cacciari, Salam, Soyez ( 08),

53 early LHC (p. 25) UE Area/median approach For each event. cluster particles with an infrared safe jet finding algorithm (all particles are clustered so we have set of jets ranging from hard to soft) only k t or C/A algs. from the list of all jets (no cuts required!) determine [{ pt,j }] ρ = median A j and its uncertainty σ median gives a typical value of pt /A for a given event using median is a way to dynamically separate hard and soft parts of the event [Cacciari, Salam, Soyez ( 08), 1/n dn/d(p tj /A j ) ρ-σ/ A j ρ th percentile for σ median 50 th percentile for ρ p tj /A j

54 early LHC (p. 26) UE How do you decide when one method works better than another? Cacciari, GPS & Sapeta 10

55 early LHC (p. 27) UE What is the underlying event? Questions should initial and final state radiation be called part of the underlying event? jet 2 are multiple parton interactions responsible for most of the underlying activity? what about correlations? BFKL chains? jet 1 jet 2 jet 2 jet 1 jet 1

56 early LHC (p. 28) UE A toy model for the UE Do the methods measure UE or perturbative radiation? If you can t define what UE is, you can t answer the question So try a simplistic, but well-defined toy model Soft component (UE) Independent emission with spectrum 1 dn = 1 n dp t µ e pt/µ Number of emissions and p t = µ set its characteristics Hard component (PT) Independent emission with spectrum dn dp t dydφ = C i π 2 α s (p t ) p t up to scale Q p t,hard /2 (C i is C A = 3 or C F = 4 3 )

57 early LHC (p. 29) UE Fluctuations in estimation of ρ In the toy model: the same ρ distribution used to generate all events nevertheless: event-to-event fluctuations of ρ due to restricted area this sets the lower limit for the uncertainty of ρ determination

58 early LHC (p. 29) UE Fluctuations in estimation of ρ In the toy model: the same ρ distribution used to generate all events nevertheless: event-to-event fluctuations of ρ due to restricted area this sets the lower limit for the uncertainty of ρ determination 2 area/med, S d /ρ = 0.21 trad-min, S d /ρ = 0.30 trad-av, S d /ρ = area/med-sub, S d /ρ = 0.33 area/med, S d /ρ = 0.40 trad-min, S d /ρ = 0.90 trad-av, S d /ρ = 1.81 ρ/n dn/dρ ext 1 soft UE y < 1.0 ν = 5 ρ/n dn/dρ ext 1 soft+pert+2 Born y < 1.0 ν = ρ ext /ρ ρ ext /ρ lower fluctuations for area/median approach due to larger available area traditional approach suffers more from the hard contamination S Q

59 early LHC (p. 29) UE Fluctuations in estimation of ρ In the toy model: the same ρ distribution used to generate all events nevertheless: event-to-event fluctuations of ρ due to restricted area this sets the lower limit for the uncertainty of ρ determination 2 area/med, S d /ρ = 0.21 trad-min, S d /ρ = 0.30 trad-av, S d /ρ = area/med-sub, S d /ρ = 0.33 area/med, S d /ρ = 0.40 trad-min, S d /ρ = 0.90 trad-av, S d /ρ = 1.81 ρ/n dn/dρ ext 1 soft UE y < 1.0 ν = 5 ρ/n dn/dρ ext 1 soft+pert+2 Born y < 1.0 ν = ρ ext /ρ ρ ext /ρ lower fluctuations for area/median approach due to larger available area traditional approach suffers more from the hard contamination S Q

60 early LHC (p. 30) UE UE in Monte Carlo with median method?

61 early LHC (p. 31) UE Average ρ as a function of y dijets at the LHC, s = 10 TeV, p t > 100 GeV, y < Herwig Jimmy 4.31 Pythia DWT Pythia S0A Pythia DW ρ [GeV] pp, s = 10 TeV, a-k t +C/A, R= y significant y dependence strips of y=2 sufficient for robust ρ determination

62 early LHC (p. 32) UE Fluctuations within an event from event to event within an event S d / ρ 1.4 pp, s = 10 TeV, a-k t +C/A, R= Herwig Jimmy 4.31 Pythia DWT 0.2 Pythia DW Pythia S0A y σ / ρ 1.4 Herwig Jimmy 4.31 Pythia DWT 1.2 Pythia DW Pythia S0A pp, s = 10 TeV, a-k t +C/A, R= y large inter-event and intra-event two patterns of rapidity dependence sizable difference between Herwig+Jimmy and Pythia

63 early LHC (p. 32) UE Fluctuations within an event from event to event within an event S d / ρ 1.4 pp, s = 10 TeV, a-k t +C/A, R= Herwig Jimmy 4.31 Pythia DWT 0.2 Pythia DW Pythia S0A y σ / ρ 1.4 Herwig Jimmy 4.31 Pythia DWT 1.2 Pythia DW Pythia S0A pp, s = 10 TeV, a-k t +C/A, R= y large inter-event and intra-event two patterns of rapidity dependence sizable difference between Herwig+Jimmy and Pythia

64 early LHC (p. 33) UE Correlations < y 1 < 1 corr(y 1, y 2 ) = ρ(y1 )ρ(y 2 ) ρ(y 1 ) ρ(y 2 ) S d (y 1 )S d (y 2 ) corr (y 1, y 2 ) Hw+Jim Atlas 0.2 a-k t +C/A, R= 0.6 Pythia DWT Pythia DW pp, s = 10 TeV Pythia S0A y 2 y 1,y 2 rapidity bins of width y = 2... average over many events significant difference between Herwig + Jimmy and Pythia qualitatively consistent with σ / ρ : smaller fluctuations within event larger correlations

65 early LHC (p. 33) UE Correlations < y 1 < 1 corr(y 1, y 2 ) = ρ(y1 )ρ(y 2 ) ρ(y 1 ) ρ(y 2 ) S d (y 1 )S d (y 2 ) corr (y 1, y 2 ) Hw+Jim Atlas 0.2 a-k t +C/A, R= 0.6 Pythia DWT Pythia DW pp, s = 10 TeV Pythia S0A y 2 y 1,y 2 rapidity bins of width y = 2... average over many events significant difference between Herwig + Jimmy and Pythia qualitatively consistent with σ / ρ : smaller fluctuations within event larger correlations

66 early LHC (p. 33) UE Correlations corr (y 1, y 2 ) < y 1 < 1 Hw+Jim Atlas 0.2 a-k t +C/A, R= 0.6 Pythia DWT Pythia DW pp, s = 10 TeV Pythia S0A y 2 corr(y 1, y 2 ) = significant difference between Herwig + Jimmy and Pythia qualitatively consistent with σ / ρ : smaller fluctuations within event larger correlations ρ(y1 )ρ(y 2 ) ρ(y 1 ) ρ(y 2 ) S d (y 1 )S d (y 2 ) y 1,y 2 rapidity bins of width y = 2... average over many events σ / ρ Herwig Jimmy 4.31 Pythia DWT Pythia DW Pythia S0A pp, s = 10 TeV, a-k t +C/A, R= y

67 early LHC (p. 34) Conclusions Conclusions In early data, look at ratios of observables. Much scope for constraining our QCD predictions There s more information in the Underlying Event than we re extracting currently Jets offer a way of extracting it Searches, e.g. multi-jet + jet-substructure, have interesting potential in data

68 early LHC (p. 35) Extras EXTRAS

69 early LHC (p. 36) Extras Cross sections Some high-p t cross sections 7 TeV LHC (leading order, from Herwig 6.5): dijets, p t > 100 GeV pb 65% glue dijets, p t > 300 GeV 1000 pb dijets, p t > 500 GeV 53 pb 30% glue W e/µ+ν +j, p tw > 50 GeV 620pb W e/µ+ν +j, p tw > 100 GeV 90pb Z µ + µ /e + e +j, p tz > 50 GeV 66pb t t 70pb t t, p t,t > 300 GeV 1.5 pb

70 early LHC (p. 37) Extras UE Area/median approach ρ ext / ρ Two component UE ν = 5, y < π Two component model: soft UE + hard PT R with 2 Born analytic appr. without Born analytic appr. pure soft ρ ext ρ (soft) πcj ext + 2 σr n h A tot n h number of perturbative part. σ measure of fluctuations ρ true value of p t /A ρ (soft) ext c J R 2 ν ln 2 ρ c J R 2 ν ln Θ(R cr ) 2 n h n b + C i 1 A tot A tot π 2 ln α s(q 0 ) 2b 0 α s (Q) the two terms bias ρ ext in opposite directions for R (used in most MC analysis of UE) the biases largely cancel similar picture and conclusions for σ

71 early LHC (p. 38) Extras UE Comparison of characteristics: toy model vs MC 5 ρ [GeV] Pythia DWT pp, s = 10 TeV a-k t +C/A, y < 5 1/n dn/(dp t /A) [GeV -1 ] Pythia DWT pp, s = 10 TeV a-k t +C/A, y < R p t /A [GeV] the pattern for ρ(r) from the toy model present in MC events: (i) turn-on at low R, (ii) linear growth at larger R variation in the curves indicative of the inter-event fluctuations growth of ρ with R produced by the tails of distributions of p t /A