QCD (for Colliders) Lecture 3 Gavin Salam, CERN Fourth Asia-Europe-Pacific School of High-Energy Physics September 2018, Qhy Nhon, Vietnam

Transcription

1 QCD (for Colliders) Lecture 3 Gavin Salam, CERN Fourth Asia-Europe-Pacific School of High-Energy Physics September 208, Qhy Nhon, Vietnam

2 2 the real world? µ B + π K... Z H µ + B u σ _ u proton proton

3 GLUON EMISSION FROM A QUARK Consider an emission with energy E s ( soft ) σ 0 θ ke p angle θ ( collinear wrt quark) Examine correction to some hard process with cross section σ 0 d ' 0 2 sc F de E d This has a divergence when E 0 or θ 0 [in some sense because of quark propagator going on-shell] 3

4 Suppose we re not inclusive e.g. calculate probability of emitting a gluon Probability P g of emitting gluon from a quark with energy Q: P g ' 2 sc F Z Q de E We cut off the integral for transverse momenta (p T E θ) below some non-perturbative threshold Q 0. Z d (E >Q 0) On the grounds that perturbation theory doesn t apply for p T ~ Λ QCD i.e. language of quarks and gluons becomes meaningless With this cutoff, the result is P g ' sc F ln 2 Q Q 0 + O ( s ln Q) this is called a double logarithm [it crops up all over the place in QCD] 4

5 <latexit sha_base64="vwlyvp7d9lzds6szqoon5tpo8w=">aaade3iczzlnbtnaemfx5iuer6qcuayiinfakv0hwbgikulsklfjw6kbrpf6nay6xpvddratfk/b03bdxhkarjwj4ysqknqke8fz+4893v+mlzlwrdhfilx+87de6377qcphz+0unundlybrgy8kv5iifk5tuyuyku+kimgkkvinz9oqw4eefhbgyb/cohktaqza5pkdwls+tzmpprzwyhplougun9nyolh8q72rjik9p9hcwelt/ljcjqurlva22vpsjfghe8zzoxrspcq7lzm2ea3zzak06vwgqlypetoj0iprgcbd4dvlsj4vhhzcgbwxcvs5iqfjjfeibro5frxwk5iks0wfmjo/hksmvaxktg8nhhpr5fvzq4phbwlikvlaw5mdltvgb9twjzfap97qlc/mbipa7mtmi+gicfk+pk2nhbm2ked2qbcxaj8r8onwhuleph2kyll7wsctczr09w0bvm0hsvy2qfnfl5srx5zhfofkgzw9qflj7vioij7vo+dqfg70lhp/mdpnju5sgzfguqtets/bha3i0avewdues3yjdwnl0hmxpmd8p4myzhw8i9obdgl/wr/gx/hb9x0jby9zwlwxh++q8suwej</latexit> <latexit sha_base64="vwlyvp7d9lzds6szqoon5tpo8w=">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</latexit> <latexit sha_base64="vwlyvp7d9lzds6szqoon5tpo8w=">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</latexit> <latexit sha_base64="vwlyvp7d9lzds6szqoon5tpo8w=">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</latexit> Suppose we re not inclusive e.g. calculate probability of emitting a gluon Probability P g of emitting gluon from a quark with energy Q: P g ' 2 sc F Z Q Q 0 de E We cut off the integral for transverse momenta (p T E θ) below some non-perturbative threshold Q 0. Z Q 0 E On the grounds that perturbation theory doesn t apply for p T ~ Λ QCD i.e. language of quarks and gluons becomes meaningless d With this cutoff, the result is P g ' sc F ln 2 Q Q 0 + O ( s ln Q) this is called a double logarithm [it crops up all over the place in QCD] 5

6 Suppose we re not inclusive e.g. calculate probability of emitting a gluon Suppose we take Q 0 ~ Λ QCD, what do we get? P g ' sc F Let s use α s = α s (Q) = /(2b ln Q/Λ) [Actually over most of integration range this is optimistically small] ln 2 Q! C F Q 0 2b ln Put in some numbers: Q = 00 GeV, Λ QCD 0.2 GeV, C F =4/3, b( b 0 ) 0.6 P g ' 2.2 Q! C F QCD 4b 2 s This is supposed to be an O(αs) correction. But the final result ~ /αs QCD hates to not emit gluons! 6

7 correct way of doing it: with running coupling inside the integral Adding running coupling is straightforward: just use α s (p t ) with p t Eθ, in the integrand: P g = 2C F π Q dp t α Q 0 p s (p t ) t p t /Q dz z = C F πb 0 ( ln Q Λ ln ln Q Λ + ) Structure of answer changes a bit: it s larger than /α s (Q), by a factor ln ln Q/Λ. Βut to keep expressions simple in these lectures we ll often restrict ourselves to a fixed-coupling approximation. 7

8 Picturing a QCD event q q Start off with a qqbar system 8

9 Picturing a QCD event q q a gluon gets emitted at small angles 9

10 Picturing a QCD event q q it radiates a further gluon 0

11 Picturing a QCD event q q and so forth

12 Picturing a QCD event q q meanwhile the same happened on the other side 2

13 Picturing a QCD event q q then a non-perturbative transition occurs 3

14 Picturing a QCD event q π, K, p,... q giving a pattern of hadrons that remembers the gluon branching (hadrons mostly produced at small angles wrt qqbar directions two jets ) 4

15 5 resummation and parton showers the previous slides applied in practice

16 Resummation Analytical, or semi-numerical, calculation of dominant logarithmically enhanced terms, to all orders in the strong coupling. Applies when you place a strong constraint on an observable. Calculations are often specific to a single observable. Parton shower Monte Carlo Simulation of emission of arbitrary number of particles, usually ordered in angle or p t. Underlying algorithm should reproduce many of the singular limits of multi-particle QCD amplitudes, including virtual corrections. Can be used to calculate arbitrary observables. 6

17 Resummation: one way of seeing the underlying key idea Calculate cross section for some observable v(p, p m ), a function of the event momenta, to be less than some cut V. Illustrate structure in soft limit, fixed coupling, ignore secondary emissions from soft gluons. (v(emissions) < V )= X 0 lim!0 m! X n=0 my m=0 i= m+n n! Y i=m+ 2 s C F 2 s C F Z Z de i E i de i E i Z Z d i i d i i Z 2 0 Z 2 0 d i 2 d i 2 (V v(p,...,p m )) 7

18 Resummation: one way of seeing the underlying key idea Calculate cross section for some observable v(p, p m ), a function of the event momenta, to be less than some cut V. Illustrate structure in soft limit, fixed coupling, ignore secondary emissions from soft gluons. (v(emissions) < V )= X 0 lim!0 m! X n=0 my m=0 i= m+n n! Y i=m+ 2 s C F 2 s C F Z Z de i E i de i E i Any number of real gluons (independent of each other if angles are all very different) Z Z d i i d i i Z 2 0 Z 2 0 d i 2 d i 2 (V v(p,...,p m )) 7

19 Resummation: one way of seeing the underlying key idea Calculate cross section for some observable v(p, p m ), a function of the event momenta, to be less than some cut V. Illustrate structure in soft limit, fixed coupling, ignore secondary emissions from soft gluons. (v(emissions) < V )= X 0 lim!0 m! X n=0 my m=0 i= m+n n! Y i=m+ Any number of virtual gluons 2 s C F 2 s C F Z Z de i E i de i E i Any number of real gluons (independent of each other if angles are all very different) Z Z d i i d i i Z 2 0 Z 2 0 d i 2 d i 2 (V v(p,...,p m )) 7

20 Resummation: one way of seeing the underlying key idea Calculate cross section for some observable v(p, p m ), a function of the event momenta, to be less than some cut V. Illustrate structure in soft limit, fixed coupling, ignore secondary emissions from soft gluons. (v(emissions) < V )= X 0 lim!0 m! X n=0 my m=0 i= m+n n! Y i=m+ Any number of virtual gluons 2 s C F 2 s C F Z Z de i E i de i E i Any number of real gluons (independent of each other if angles are all very different) Z Z d i i d i i Z 2 0 Z 2 0 d i 2 d i 2 (V v(p,...,p m )) constraint from observable, involves just real gluons 7

21 <latexit sha_base64="sptxsjw/3lwcyzzmwyhpahc0js=">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</latexit> <latexit sha_base64="sptxsjw/3lwcyzzmwyhpahc0js=">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</latexit> <latexit sha_base64="sptxsjw/3lwcyzzmwyhpahc0js=">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</latexit> <latexit sha_base64="sptxsjw/3lwcyzzmwyhpahc0js=">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</latexit> Resummation example result It s common to ask questions like what is the probability that a Z boson is produced with transverse momentum < p T Answer is given (~) by a Sudakov form factor, i.e. the probability of not emitting any gluons with transverse momentum > p T. P (Z trans.mom. <p T ) ' exp apple 2 s C F ln 2 M Z p T when p T is small, the logarithm is large and compensates for the smallness of α s so you need to resum log-enhanced terms to all orders in α s. 8

22 What do we know about resummation? You ll sometimes see mention of NNLL or similar This means next-next-to-leading logarithmic Most common definition of Leading logarithmic (LL): you sum all terms with p=n+ (for n= ) in exp " X n,p n s ln p M H p T NLL: include all terms with p=n (for n= ) NNLL: include all terms with p=n (for n= ) In real life, the function that appears in the resummation is sometimes instead a Fourier or Mellin transform of an exponential # 9

23 Resummation of Higgs p T spectrum (same formula, with C F C A ) dσ/d p t H [pb/gev] ratio to N 3 LL+NNLO NNLO N 3 LL+NNLO RadISH+NNLOJET, 3 TeV, m H = 25 GeV µ R = µ F = m H /2, Q = m H /2 PDF4LHC5 (NNLO) uncertainties with µ R, µ F, Q variations p t H [GeV] NNLO, ill-behaved at small pt. NNLO+N3LL, resummation ensures sensible, reliable predictions at small pt. This kind of resummation is an input to nearly all LHC Higgs studies Bizon et al

24 NNLO N3 LL+NNLO T NNLL+NLO Data 0.02 Resummation of Z p spectrum v. data NNPDF3.0 (NNLO) Ratio to data /dptz (/ )d uncertainties with µr, µf, NNLO 3 N LL+NNLO 0.08 NNLL+NLO 0.06 Data (ATLAS) ptz RadISH+NNLOJET + 8 TeV, pp Z( )+X 0.0 < Y < 2.4, 66 < M < 6 GeV NNPDF3.0 (NNLO) uncertainties with µr, µf, Q variations Bizon et al

25 (Threshold resummation) If you produce a system near threshold, i.e. mass M close to the pp centre-of-mass energy s, there are so-called threshold logarithms, which modify the total cross section. Steeply falling PDFs may also result in threshold logarithms. Driven by a quantity N, N = d ln σ d ln s Resummation involves terms Valid if N. (α s ln 2 N) n, often enhance σ In practice, for some applications (e.g. top, Higgs production), M s and N ~ 2. Opinions differ about validity of threshold resummation in this regime 22

26 resummation v. parton showers (the basic idea, ignoring secondary emsn. from gluons) a resummation predicts one observable to high accuracy a parton shower takes the same idea of a Sudakov form factor and uses it to generate emissions from probability of not emitting gluons above a certain p T, you can deduce p T distribution of first emission. use a random number generator (r) to sample that p T distribution deduce p T by solving r =exp " 2 s C A ln 2 p2 T,max p 2 T # 2. repeat for next emission, etc., until p T falls below some nonperturbative cutoff very similar to radioactive decay, with time ~ /pt and a decay rate ~ pt log /pt 23

27 A toy shower (fixed coupling, primary branching only, only pt, no energy conservation, no PDFs, etc.) #!/usr/bin/env python # an oversimplified (QED-like) parton shower # for Zuoz lectures (206) by Gavin P. Salam from random import random from math import pi, exp, log, sqrt pthigh = 00.0 ptcut =.0 alphas = 0.2 CA=3 def main(): for iev in range(0,0): print "\nevent", iev event() def event(): # start with maximum possible value of Sudakov sudakov = while (True): # scale it by a random number sudakov *= random() # deduce the corresponding pt pt = ptfromsudakov(sudakov) # if pt falls below the cutoff, event is finished if (pt < ptcut): break print " primary emission with pt = ", pt def ptfromsudakov(sudakovvalue): """Returns the pt value that solves the relation Sudakov = sudakovvalue (for 0 < sudakovvalue < ) """ norm = (2*CA/pi) # r = Sudakov = exp(-alphas * norm * L^2) # --> log(r) = -alphas * norm * L^2 # --> L^2 = log(r)/(-alphas*norm) L2 = log(sudakovvalue)/(-alphas * norm) pt = pthigh * exp(-sqrt(l2)) return pt main() 24

28 A toy shower (fixed coupling, primary branching only, only pt, no energy conservation, no PDFs, etc.) #!/usr/bin/env python # an oversimplified (QED-like) parton shower # for Zuoz lectures (206) by Gavin P. Salam from random import random from math import pi, exp, log, sqrt pthigh = 00.0 ptcut =.0 alphas = 0.2 CA=3 def main(): for iev in range(0,0): print "\nevent", iev event() def event(): # start with maximum possible value of Sudakov sudakov = while (True): # scale it by a random number sudakov *= random() # deduce the corresponding pt pt = ptfromsudakov(sudakov) # if pt falls below the cutoff, event is finished if (pt < ptcut): break print " primary emission with pt = ", pt def ptfromsudakov(sudakovvalue): """Returns the pt value that solves the relation Sudakov = sudakovvalue (for 0 < sudakovvalue < ) """ norm = (2*CA/pi) # r = Sudakov = exp(-alphas * norm * L^2) # --> log(r) = -alphas * norm * L^2 # --> L^2 = log(r)/(-alphas*norm) L2 = log(sudakovvalue)/(-alphas * norm) pt = pthigh * exp(-sqrt(l2)) return pt main() % python./toy-shower.py Event 0 primary emission with pt = primary emission with pt = primary emission with pt = Event primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = Event 2 primary emission with pt = primary emission with pt = primary emission with pt = Event 3 primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = Event 4 primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt =

29 A toy shower (fixed coupling, primary branching only, only pt, no energy conservation, no PDFs, etc.) #!/usr/bin/env python # an oversimplified (QED-like) parton shower # for Zuoz lectures (206) by Gavin P. Salam from random import random from math import pi, exp, log, sqrt pthigh = 00.0 ptcut =.0 alphas = 0.2 CA=3 def main(): for iev in range(0,0): print "\nevent", iev event() def event(): # start with maximum possible value of Sudakov sudakov = while (True): # scale it by a random number sudakov *= random() # deduce the corresponding pt pt = ptfromsudakov(sudakov) # if pt falls below the cutoff, event is finished if (pt < ptcut): break print " primary emission with pt = ", pt def ptfromsudakov(sudakovvalue): """Returns the pt value that solves the relation Sudakov = sudakovvalue (for 0 < sudakovvalue < ) """ norm = (2*CA/pi) # r = Sudakov = exp(-alphas * norm * L^2) # --> log(r) = -alphas * norm * L^2 # --> L^2 = log(r)/(-alphas*norm) L2 = log(sudakovvalue)/(-alphas * norm) pt = pthigh * exp(-sqrt(l2)) return pt main() % python./toy-shower.py Event 0 primary emission with pt = primary emission with pt = primary emission with pt = Event primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = Event 2 primary emission with pt = primary emission with pt = primary emission with pt = Event 3 primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = primary emission with pt = If you want to play: replace CA=3 (emission from gluons) with CF=4/3 (emission from quarks) and see how pattern Event 4 primary emission with pt = primary emission with pt = primary with pt = primary of emissions emission with pt changes = primary emission with pt = (multiplicity, pt of hardest... emission, etc.) 24

30 Secondary, tertiary gluons: many showers use colour dipoles (Pythia, Sherpa & option in Herwig) Original dipole MC: Ariadne (90 s) q q Use large-n C idea of colour structure g Initial q q qq event = colour dipole. q q Radiated gluon turns dipole 2 dipoles q g g q Each dipole then radiates independently (different colour no interference), creating new colour dipoles at each step 25

31 Event record from a real-world shower (Herwig6 old shower with compact record) u Z _ u proton proton 26

32 combining showers & fixed order essential for accurate cross sections & multijet states 27

33 E.g. jet multiplicity in events with a W v. Pythia CMS σ(w + n-jets) σ(w) Pythia (shower only) data energy scale unfolding MadGraph Z2 MadGraph D6T Pythia Z2-36 pb jet E T at s W eν = 7 TeV > 30 GeV arxiv: shower MCs on their own cannot reproduce pattern of hard multijet states (there are topologies that are almost inaccessible via showering) σ( inclusive jet multiplicity, n 28

34 MLM matching Z+parton 29

35 MLM matching shower Z+parton 30

36 MLM matching + shower Z+parton Z+2partons 3

37 MLM matching + shower Z+parton shower Z+2partons 32

38 MLM matching + v. shower Z+parton shower Z+2partons shower of Z+parton generates hard gluon 33

39 MLM matching + v. shower Z+parton shower Z+2partons shower of Z+parton generates hard gluon 34

40 MLM matching DOUBLE COUNTING + v. shower Z+parton shower Z+2partons shower of Z+parton generates hard gluon 35

41 MLM matching + v. shower Z+parton shower Z+2partons shower of Z+parton generates hard gluon 36

42 MLM matching ACCEPT ACCEPT REJECT Q merge p t cut + v. shower Z+parton shower Z+2partons shower of Z+parton generates hard gluon Hard jets above scale Qmerge have distributions given by tree-level ME Rejection procedure eliminates double-counted jets from parton shower Rejection generates Sudakov form factors between individual jet scales An alternative approach is called CKKW (similar in spirit, Sudakov put in manually) 37

43 Combining NLO accuracy with parton showers () ideas Frixione & Webber 02 Expand your Monte Carlo branching to first order in α s MC@NLO cont. Rather non-trivial requires deep understanding of MC Calculate differences wrt true O (α s ) both in real and virtual pieces Let s imagine a problem with one phase-space dimension, e.g. E. Expand Monte If your Carlo Monte cross Carlo section givesfor correct emission softwith and/or energy collinear E: limits, those differences are finite σ MC δ(e)+α s σr MC (E)+α sσv MC δ(e)+o ( α 2 ) s Generate extra partonic configurations with phase-space distributions With proportional true NLOto real/virtual those differences terms and as αshower s σ R (E) them andα s σ V δ(e), define ( ) MC@NLO = MC +α s (σ V σv MC )+α s de(σ R (E) σr MC (E)) All weights finite, but can be ± Processes include Frixione, Laenen, Motylinski, Nason, Webber, White Higgs boson, single vector boson, vector boson pair, heavy quark pair, single top (with and without associated W), lepton pair and associated 38

44 Combining NLO accuracy with parton showers (2) POWHEG ideas Aims to work around limitations Nason 04 the (small fraction of) negative weights the tight interconnection with a specific MC Principle Write a simplified Monte Carlo that generates just one emission (the hardest one) which alone gives the correct NLO result. Essentially uses special Sudakov (k t )=exp( exact real-radition probability above k t ) Lets your default parton-shower do branchings below that k t. 39

45 Recent developments and research directions (Much) more efficient ways of combining tree-level and showers: Vincia Getting shower samples that are simultaneously NLO accurate at different multiplicities (FxFx, Sherpa NLO matching) Showers that are NNLO accurate: MiNLO, Geneva, UNNLOPS Understanding the underlying resummation accuracy of showers (going beyond LL, leading colour) and its interplay with merging / matching 40

46 [pb] fb CMS (8 TeV) Data MG5 + PY6 ( 4j LO + PS) SHERPA 2 ( 2j NLO 3,4j LO + PS) MG5_aMC + PY8 ( 2j NLO + PS) dσ/dn jets MG5/Data anti-k T (R = 0.5) jets jet jet p > 30 GeV, y < 2.4 T Z/γ* ll channel Stat. unc. Modern tools give good predictions for multijet rates with vector bosons (up to ~ 4 jets, sometimes beyond) SHERPA/Data Stat. unc. MG5_aMC/Data Stat. theo. PDF α s unc N jets 4

47 d σ d N jet σ MC/Data MC/Data ATLAS Powheg+Pythia8 MG5_aMC@NLO+Herwig++ Sherpa v Data Stat. Stat.+Syst. 3 TeV, 3.2 fb add. jet p T Number of additional jets - 60 GeV Number of additional jets.4 Powheg+Pythia6 (RadLo) Powheg+Pythia6 (RadHi) Powheg+Pythia Number of additional jets d σ d N jet σ Modern tools give good 2 0predictions for Sherpa v2.2 multijet rates with top quarks MC/Data MC/Data arxiv: Powheg+Pythia8 MG5_aMC@NLO+Herw 205 Data Stat. Stat.+Syst. 0 Numbe 0 Number o.4 Powheg+Pythia6 (RadLo) Powheg+Pythia6 0 Number of 42

48 hadronisation & MPI essential models for realistic events i.e. events with hadrons 43

49 two main models for the parton hadron transition ( hadronisation ) String Fragmentation (Pythia and friends) Cluster Fragmentation (Herwig) (& Sherpa) Pictures from ESW book 44

50 two main models for the parton hadron transition ( hadronisation ) String Fragmentation (Pythia and friends) Cluster Fragmentation (Herwig) (& Sherpa) Pictures from ESW book 44

51 multi-parton interactions (MPI, a.k.a. underlying event) n type cluster h type cluster taken from R. Field i type cluster taken from Allow 2 2 scatterings of multiple other partons in the incoming protons 45

52 Underlying event properties v. MCs /(N ev η ϕ)n Ratio ch ALICE Preliminary Uncertainties: stat.(vertical), syst.(box) p T 403 ALI PREL Transverse region > 0.5 GeV/c and η < 0.8 charged particle density pp@3tev published pp@7tev Pythia8(Monash203) EPOS-LHC 2 3TeV/7TeV Pythia8/Data EPOS-LHC/Data p leading T (GeV/c) e toward region in pp collisions at p s = e transverse region. inclusive /dη ch dn / /dη ch dn Data/MC ALICE Preliminary pp, s = 3 TeV, INEL > 0 Multiplicity Class 0-0.0% % Data PYTHIA 8 Monash 203 PYTHIA 8 Monash 203 no CR PYTHIA 6 Perugia 20 EPOS LHC.5. η ALI-PREL-4039 η 46

53 jets i.e. how we make sense of the hadronic part of events 47

54 µ + µ B + π K... B jets i.e. how we make sense of the hadronic part of events proton proton Interpretation µ + µ Z _ b H b u σ _ u proton proton 48

55 Why do we see jets? Gluon emission quark non perturbative hadronisation π + K L π 0 K + π Z s de E d Non-perturbative physics s 49

56 Why do we see jets? Gluon emission quark non perturbative hadronisation π + K L π 0 K + π Z s de E d Non-perturbative physics s While you can see jets with your eyes, to do quantitative physics, you need an algorithmic procedure that defines what exactly a jet is 49

57 make a choice, specify a Jet Definition {p } jet definition {j } i k particles, 4-momenta, calorimeter towers,... jets Which particles do you put together into a same jet? How do you recombine their momenta (4-momentum sum is the obvious choice, right?) Jet [definitions] are legal contracts between theorists and experimentalists -- MJ Tannenbaum They re also a way of organising the information in an event 000 s of particles per events, up to ,000 events per second 50

58 what should a jet definition achieve? 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 jet 2 jet jet 2 jet jet 2 jet jet 2 projection to jets should be resilient to QCD effects 5

59 Reconstructing jets is an ambiguous task 52

60 Reconstructing jets is an ambiguous task 2 clear jets 52

61 Reconstructing jets is an ambiguous task 2 clear jets 3 jets? 52

62 Reconstructing jets is an ambiguous task 2 clear jets 3 jets? or 4 jets? 53

63 Jet definition ingredients Jet algorithm A set of rules that you apply to combine particles into jets Jet algorithm parameters Thresholds that help specify when two particles belong to the same jet or not. Most hadron collider jet algorithms have two threshold parameters: Jet angular radius parameter R: particles closer in angle than R get recombined (NB: usually implemented as a condition on the distance parameter on the standard hadron collider rapidity-azimuth [y,φ] cylinder) Transverse momentum threshold: jets should have p T > p T,min 54

64 the main jet algorithm at the LHC A Sequential recombination algorithm R 2 ij =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Involves calculating clustering distance between pairs of particles d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti. Find smallest of d ij, d ib 2. If ij, recombine them 3. If ib, call i a jet and remove from list of particles 4. repeat from step until no particles left Only use jets with p t > p t,min anti-k t algorithm Cacciari, GPS & Soyez,

65 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

66 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm dmin is dij = e 05 How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

67 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

68 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm dmin is dij = How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

69 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

70 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm dmin is dij = How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

71 Jet clustering: anti-k t p t /GeV 50 anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

72 Jet clustering: anti-k t p t /GeV anti-k t algorithm dmin is dij = How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

73 Jet clustering: anti-k t p t /GeV anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

74 Jet clustering: anti-k t p t /GeV anti-k t algorithm dmin is dij = How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

75 Jet clustering: anti-k t p t /GeV anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

76 Jet clustering: anti-k t p t /GeV anti-k t algorithm dmin is dij = How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

77 Jet clustering: anti-k t p t /GeV anti-k t algorithm How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

78 Jet clustering: anti-k t p t /GeV anti-k t algorithm dmin is dib = How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

79 Jet clustering: anti-k t p t /GeV anti-k t algorithm Good Jet (p T > p T,min ) How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

80 Jet clustering: anti-k t p t /GeV anti-k t algorithm dmin is dib =.96 Good Jet (p T > p T,min ) How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core. 20 d ij = max(p 2 ti,p2 tj ) R 2 ij R y d ib = p 2 ti [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

81 Jet clustering: anti-k t p t /GeV anti-k t algorithm Good Jet (p T > p T,min ) How do di erent sequential recombination jet algorithms build up the jet? Anti-k t gradually makes its way through the secondary blob: only hierarchy in clustering is distance from hard core Too soft for a jet (p T < p T,min ) y d ij = d ib = max(p 2 ti,p2 tj ) p 2 ti R 2 ij R 2 [here R=2.0 p T,min =20 GeV at LHC: R=0.4.0] Rij 2 =(y i y j ) 2 +( i j ) 2 y = 2 ln E + p z E p z Gavin Salam (CERN) Jets Physics at the LHC Edinburgh May/June / 5

82 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

83 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

84 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

85 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

86 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

87 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

88 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

89 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

90 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

91 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

92 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

93 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

94 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

95 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

96 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= 73

97 anti-k t in action [full simulated event] Clustering grows around hard cores d ij = max(p 2 ti,p2 tj ) R 2 ij R 2, d ib = p 2 ti R= Anti-kt gives circular jets ( cone-like ) in a way that s infrared safe 73

98 conclusions 74

99 ATLAS H WW* ANALYSIS [ ] 3 Signal and background models The ggf and VBF production modes for H! WW are modelled at next-to-leading order (NLO) in the strong coupling S with the Powheg MC generator [22 25], interfaced with Pythia8[26] (version 8.65) for the parton shower, hadronisation, and underlying event. The CT0 [27] PDF set is used and the parameters of the Pythia8 generator controlling the modelling of the parton shower and the underlying event are those corresponding to the AU2 set [28]. The Higgs boson mass set in the generation is 25.0 GeV, which is close to the measured value. The Powheg ggf model takes into account finite quark masses and a running-width Breit Wigner distribution that includes electroweak corrections at NLO [29]. To improve the modelling of the Higgs boson p T distribution, a reweighting scheme is applied to reproduce the prediction of the next-to-next-to-leading-order (NNLO) and next-to-next-to-leading-logarithm (NNLL) dynamic-scale calculation given by the HRes 2. program [30]. Events with 2 jets are further reweighted to reproduce the pt H spectrum predicted by the NLO Powheg simulation of Higgs boson production in association with two jets (H + 2 jets) [3]. Interference with continuum WW production [32, 33] has a negligible impact on this analysis due to the transverse-mass selection criteria described in Section 4 and is not included in the signal model. The inclusive cross sections at p s 8 TeV for a Higgs boson mass of 25 0 GeV, calculated at NNLO NNL Jets are reconstructed from topological clusters of calorimeter cells [50 52] using the anti-k t algorithm with a radius parameter of R = 0.4 [53]. Jet energies are corrected for the e ects of calorimeter noncompensation, signal losses due to noise threshold e ects, energy lost in non-instrumented regions, con- 75

100 WHAT DO ATLAS & CMS USE MOST FREQUENTLY? 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 Papers commonly cited by ATLAS and CMS ( ) CL(s) technique (A.Read) POWHEG (2004) MG5aMCatNLO 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 as of , excluding self-citations; all papers > 0.2 Perugia tunes (200) Herwig++ MC Plot by GP Salam based on data from InspireHEP 76

101 WHAT DO ATLAS & CMS USE MOST FREQUENTLY? 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 Likelihood tests for new physics Sherpa. Papers commonly cited by ATLAS and CMS ( ) as of , excluding self-citations; all papers > 0.2 QCD tools 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 77

102 CONCLUSIONS A huge number of ingredients goes into hadron-collider predictions and studies (α s, PDFs, matrix elements, resummation, parton showers, non-perturbative models, jet algorithms, etc.) a key idea is the separation of (time) scales, factorisation short timescales: the hard process long timescales: hadronic physics in between: parton showers, resummation, DGLAP as long as you ask the right questions (e.g. look at jets, not individual hadrons), you can exploit this separation for quantitative, accurate, collider physics maximising accuracy and information extracted is today s research frontier 78

103 Extra resources Introductory level QCD lecture notes from CERN schools, e.g. Peter Skands, arxiv: GPS, arxiv:0.53 More advanced Slides from QCD and Monte Carlo specific schools CTEQ schools: MCNet schools: Books QCD and collider physics, Ellis, Stirling & Webber The Black Book of Quantum Chromodynamics, Campbell, Huston & Krauss 79

104 EXTRA SLIDES 80

105 GLUON V. HADRON MULTIPLICITY It turns out you can calculate the gluon multiplicity analytically, by summing all orders (n) of perturbation theory: N g n (n!) 2 ( CA πb ln Q Λ ) n exp 4CA πb ln Q Λ Compare to data for hadron multiplicity (Q s) Including some other higher-order terms and fitting overall normalisation Agreement is amazing! charged hadron multiplicity in e + e events adapted from ESW 8

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sha_base64="njz5wufmnxliaqplicfnlqmlsdc=">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</latexit> <latexit sha_base64="go7l2ogay8yuie02dt7ifboswwm=">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</latexit> <latexit sha_base64="go7l2ogay8yuie02dt7ifboswwm=">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</latexit> <latexit sha_base64="go7l2ogay8yuie02dt7ifboswwm=">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</latexit> <latexit 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sha_base64="j+jldveqxwcrxraoj8xn3n5ruo=">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</latexit> <latexit sha_base64="j+jldveqxwcrxraoj8xn3n5ruo=">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</latexit> <latexit sha_base64="j+jldveqxwcrxraoj8xn3n5ruo=">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</latexit> <latexit sha_base64="j+jldveqxwcrxraoj8xn3n5ruo=">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</latexit> Resummation of p T : steps along the way v(p,...,p m )= mx i= ~p T,i ' max(p T,...,p Tm ) Z my (V v(p,...,p m )) = (V p Ti ) Z V )= i= <latexit sha_base64="njz5wufmnxliaqplicfnlqmlsdc=">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</latexit> X my Z Z Z 2 s C F de i d 2 i d i (V v(p m! m=0 i= E i i 0 2,...,p m )) Y Z apple Z Z Z 2 s C X Y Z Z F ZdE d =exp E (V E )! X n=0 n! m+n Y i=m+ 2 s C F Z de i E i Z d i i Z 2 0 d i 2 = expapple 2 s C F Z de E Z d 82