Introduction to Monte Carlo generators - II

Transcription

1 Introduction to Monte Carlo generators - II (Fully exclusive modeling of high-energy collisions) Andrzej Siódmok CTEQ School - University of Pittsburgh, USA July 2017 Thanks to: S. Gieseke, S.Höche, F. Krauss,L. Lonnblad, W. Placzek, S. Prestel, M. H. Seymour, T. Sjöstrand, P. Skands, M. Schönherr, B. Webber

2 Reminder: Building blocks of Monte Carlo Generators taken from Stefan Gieseke c The general approach is the same in different programs but the models and approximations used are different. 2 / 63

3 1st lecture Monte Carlo methods why and how? Parton Shower 1st tutorial Build your own Parton Shower (in Python)! 2nd lecture Hadronization Multiple Parton Interaction Tuning 2nd tutorial Shower uncertainties (in Python) or (see Marek s lecture) matching in Python 3rd tutorial Real life example - work with Herwig, Sherpa and Pythia! Plan 3 / 63

4 Hadronization (non-perturbative semi-empirical models) Hadronization Two main models: Lund string model and Cluster model also older: Flux tube model and Independent fragmentation (Feynman-Field fragmentation 78) Hadronization factorizes from hard process (process-independent) Both main models contain many parameters to be determined from data, preferably LEP. 4 / 63

5 Lund String model [Andersson,Gustafson,Ingelman,Sjostrand] Phys.Rept.97(1983)31 Originally invented without parton showers in mind. We start with 2-jet events in e + e hadrons. Lund string model: like rubber band that is pulled apart and breaks into pieces, or like a magnet broken into smaller pieces. 5 / 63

6 Lund model - Physical motivation κ = 1 GeV/fm potential energy gain lifting a 16 ton truck. Flux tube uniform traversal shape (in the central region) simple description as a dimensional object - a string 6 / 63

7 Lund model - QCD potential Lund string: like rubber band that is pulled apart and breaks into pieces 7 / 63

8 Lund model - string motion As a q q pair moves apart, they are slowed down and more and more energy is stored in the string. If the energy is small, the q q pair will eventually stop and move together again. We get a YoYo - state which we interpret as a meson. If high enough energy, the string will break as the energy in the string is large enough to create a new q q pair. Assume negligibly small quark masses. Then linearity between space-time and energy-momentum gives: 8 / 63

9 Combine yo-yo-style string motion with string breakings. Motion of quarks and antiquarks with intermediate string pieces. A quarks from one string break combines with a antiquarks from an adjacent one. 9 / 63

10 How does the string break? The quarks obtain a mass and a transverse momentum in the breakup through a tunneling mechanism Probablity of tunneling: Suppression of heavy quarks: uū : d d : s s : c c 1 : 1 : 0.3 : Diquark (qq - q q breakups) antiquark simple model for baryon production. String model has very good energy-momentum picture however it is unpredictive in understanding of hadron mass effects many parameters, depending on how you count. 10 / 63

11 The Lund model - gluons Gluon a kink in the string. The Lund string model predicted the string effect measured by Jade. In a three-jet event there are more energy between the gq and g q jets than between q q. 11 / 63

12 The cluster model [Webber NPB238(1984)492] What if we have PS (more perturbative input before hadronization). Can we get a simpler model? Cluster Model: i j QCD parton showers provide pre-confinement of colour: Planar approximation: gluon = colour-anticolour pair k l 12 / 63

13 The cluster model [Webber NPB238(1984)492] What if we have PS (more perturbative input before hadronization). Can we get a simpler model? Cluster Model: QCD parton showers provide pre-confinement of colour: Planar approximation: gluon = colour-anticolour pair colour-singlet pairs end up close in phase space and form highly excited hadronic states, the clusters Clusters ( excited hadrons) decay into hadrons Mass spectrum of colour-singlet pairs asymptotically independent of energy, production mechanism 13 / 63

14 Cluster model - Mass spectrum Mass spectrum of primordial clusters independent of cm energy Primary Light Clusters 1 10 M/GeV Q = 35 GeV Q = 91.2 GeV Q = 189 GeV Q = 500 GeV Q = 1000 GeV Peaked at low mass (1-10 GeV) typically decay into 2 hadrons. Project colour singlets onto continuum of high-mass mesonic resonances (clusters). Decay to lighter well-known resonances and stable hadrons. 14 / 63

15 Heavy cluster Although cluster mass spectrum peaked at small m, broad tail at high m. Small fraction of clusters too heavy for isotropic two-body decay to be a good approximation heavy cluster decay first (Longitudinal cluster fission) into lighter cluster, or radiate a hadron C CC C HC, it is rather string-like. 15% of primary clusters get split but 50% of hadrons come from them! 15 / 63

16 Taken from T. Sjöstrand Hadronization - comparison of the model 16 / 63

17 Multiple Particle Interaction 17 / 63

18 How do we know MPI exists? Data makes you smarter! UA5 experiment at the SPS - proton-antiproton 540 GeV c.m. 18 / 63

19 Motivation - how do we know MPI exists? 19 / 63

20 Motivation - how do we know MPI exists? Direct observation of multiple interactions Five studies: AFS (1987), UA2 (1991), CDF (1993, 1997), D0 (2009) Order 4 jets p 1 > p 2 > p 3 > p 4 and define ϕ as angle between p 1 p 2 and p 3 p 4 for AFS/CDF Double Parton Scattering 2 3 Double BremsStrahlung p 1 + p 2 0 p 1 + p 2 0 p 3 + p 4 0 p 3 + p 4 0 dσ/dϕ flat dσ/dϕ peaked at ϕ 0/π for AFS/CDF 20 / 63

21 Motivation - how do we know MPI exists? CDF: Double parton scattering in p p collisions at s = 1.8 [Phys. Rev. D 56, (1997)] 21 / 63

22 Motivation - how do we know MPI exists? CDF Run II 22 / 63

23 Motivation - how do we know MPI exists? CDF Run II 23 / 63

24 Motivation: Motivation - is it really important? The minimum bias/underlying event is an unavoidable background to most collider observables and having good understand of it leads to more precise collider measurements! First LHC results are Minimum Bias and Underlying Event! Alice: [ ], CMS [ ], ATLAS [ ] so it must be important ;) These will be particularly relevant for the LHC as, when it is operated at design luminosity, rare signal events will be embedded in a background of more than 20 near-simultaneous minimum-bias collisions. Any realistic experiment simulation event generator needs to be able to model these effects. Don t worry, we will measure and subtract it But... fluctuations and correlations on an event-by-event basis are crucial. 24 / 63

25 Multiple Partonic Interactions Inclusive hard jet cross section in pqcd: σ inc (s, p min t ) = i,j dp 2 t p min 2 t dx 1 dx 2 MPI model basics f i (x 1, Q 2 ) f j (x 2, Q 2 ) dˆσ ij dp 2 t Figure 4.3: Total cross secut on o- or erlly m- inpen D tal m 250 : DL '92 σ(mb)σtot σtot : DL '04 QCD2 2, p T >2GeV s (GeV) σ inc > σ tot eventually Interpretation: σ inc counts all partonic scatters in a single pp collision more than a single interaction σ inc = n dijets σ inel 25 / 63

26 Assumptions: MPI model basics (Herwig++) the distribution of partons in hadrons factorizes with respect to the b and x dependence average number of parton collisions: n( b, s) = L partons (x 1, x 2, b) ij = 1 dx 1 dx 2 d 2 b 1 + δ ij ij dˆσ ij dp 2 t dp 2 t dˆσ ij dp 2 t dp 2 t D i/a (x 1, p 2 t, b )D j/b (x 2, p 2 t, b b ) = 1 dx 1 dx 2 d 2 b dp 2 dˆσ ij t 1 + δ ij dp 2 ij t f i/a (x 1, p 2 t )G A ( b )f j/b (x 2, p 2 t )G B ( b b ) = A( b)σ inc (s; p min t ). at fixed impact parameter b, individual scatterings are independent (leads to the Poisson distribution) 26 / 63

27 From assumptions: Eikonal model basics at fixed impact parameter b, individual scatterings are independent, the distribution of partons in hadrons factorizes with respect to the b and x dependence. we get the average number of partonic collisions at a given b value is n(b, s) = A(b)σ inc (s; p min t ) = 2χ(b, s) where A(b) is the partonic overlap function of the colliding hadrons 27 / 63

28 Semi hard underlying event 28 / 63

29 Hot Spot model Extension to soft MPI, p t < p min t Fix the two parameters µ soft and σ inc soft in n tot ( ( b, s) = A( b; µ)σ inc hard(s; p min t ) + A( ) b; µ soft )σ inc from two constraints. Require simultaneous description of σ tot and b el (measured/well predicted), σ tot (s) =! 2 d 2 b (1 ) e χtot( b,s), b el (s) =! d 2 b 2 ( ) b 1 e χtot( b,s). σ tot soft 29 / 63

30 Extension to soft MPI, p t < p min t Continuation of the differential cross section into the soft region p t < p min t (here: p t integral kept fixed) 1/ (5 GeV) d /dp t (1/GeV) pt min =3 GeV, = 0.5 GeV 2 pt min =5 GeV, =0.06 GeV 2 d soft dp t p t e (p 2 t p min,2 t ) p t (GeV) 30 / 63

31 Detailed look at observables: Transverse Region <N chg > transv data, uncorrected pt min =3.5, 2 =1.50, 2 tot pt min =3.5, 2 =1.25, 2 tot pt min =4.0, 2 =1.50, 2 tot /N =3.1 /N =2.9 /N =2.8 Tevatron Run1 2 1 MC/Data p ljet t (GeV) Notice Jet pedestal effect. 31 / 63

32 Look at LHC results (900 GeV) ATLAS charged particles in Min Bias (N ch 1, p T > 500MeV, η < 2.5) p [GeV] MC/data Average transverse momentum as function of N ch ATLAS data cteq, mu=1, pt=3.0 mrts mu=1, pt=3.0 mrts mu=2, pt=5.0 cteq mu=2, pt=5.0 cteq mu=1.5, pt=4.0 mrst, mu=1.5, pt= N ch oops, not so nice... 1/NevdN ch/dη MC/data Charged particle multiplicity as function of η ATLAS data cteq, mu=1, pt=3.0 mrts mu=1, pt=3.0 mrts mu=2, pt=5.0 cteq mu=2, pt=5.0 cteq mu=1.5, pt=4.0 mrst, mu=1.5, pt= despite very good agreement with Rick Field s CDF UE analysis. choice of PDF set (CTEQ61l vs MSTW LO** (our default)) Failure of a physically motivated model usually points to more, interesting physics... colour structure? η 32 / 63

33 Colour Structure of the Underlying Event Colour Structure of the Underlying Event multiple interactions, even when soft, can cause non-trivial changes to the colour topology of the colliding system as a whole, with potentially major consequences for the particle multiplicity in the final state 33 / 63

34 Colour Structure of the Underlying Event Colour Structure of the Underlying Event multiple interactions, even when soft, can cause non-trivial changes to the colour topology of the colliding system as a whole, with potentially major consequences for the particle multiplicity in the final state 34 / 63

35 Colour reconnection (CR) in Herwig++ Extending Herwig s hadronization model: QCD parton showers provide pre-confinement colour-anticolour pairs form highly excited hadronic states, the clusters 35 / 63

36 Implementation Colour reconnection (CR) in Herwig++ Allow CR if the cluster mass decreases, Extending Herwig s hadronization model: QCD parton showers provide pre-confinement colour-anticolour pairs form highly excited hadronic states, the clusters CR in the cluster hadronization model: allow reformation of clusters, e.g. (il) + (jk) Physical motivation: exchange of soft gluons during non-perturbative hadronization phase M il + M kj < M ij + M kl, where M 2 ab = (p a + p b ) 2 is the (squared) cluster mass Accept alternative clustering with probability p reco (model parameter) this allows to switch on CR smoothly 36 / 63

37 MinBias ATLAS 900 GeV 1/NevdN ch/dη MC/data Charged particle multiplicity as function of η (0.9TeV,N ch 6) Read off from ATLAS Herwig Herwig η 1/NevdNev/dN ch MC/data Charged particle density (0.9TeV,N ch 6) Read off from ATLAS Herwig Herwig N ch 37 / 63

38 MinBias ATLAS 900 GeV 1/Nev 1/p dnch/dp [GeV 2 ] MC/data 10 1 Charged particle multiplicity as function of p (0.9TeV,N ch 6) Read off from ATLAS Herwig Herwig p [GeV] p [GeV] MC/data Average transv. momentum as function of N ch (0.9TeV,N ch 6) Read off from ATLAS Herwig Herwig N ch 38 / 63

39 d soft Underlying event in Herwig++ - key components Matter distribution (µ 2 ) Aµ(b) [fm 2 ] µ 2 = 2 GeV 2 µ 2 = 0.71 GeV b [fm] Extension to soft MPI (p t < p min t ) 1/ (5 GeV) d /dp t (1/GeV) p t (GeV) pt min pt min =3 GeV, = 0.5 GeV 2 =5 GeV, =0.06 GeV 2 dp t p t e (p Gaussian extension below p min t Energy dependent p min t t p 2 min,2 t ) Colour structure (p reco, p CD ) Based on electromagnetic form factor (radius of the proton free parameter) Main parameters: Possibility of change of color structure (color reconnection) [Gieseke, Röhr, AS, EPJC 72 (2012)] The least understood part of modeling µ 2 - inverse hadron radius squared (parametrization of overlap function) p min t - transition scale between soft and hard components p min t p reco - colour reconnection = p min t,0 ( s ) b E 0 39 / 63

40 d soft Underlying event in Herwig++ - key components Matter distribution (µ 2 ) Aµ(b) [fm 2 ] µ 2 = 2 GeV 2 µ 2 = 0.71 GeV b [fm] Based on electromagnetic form factor (radius of the proton free parameter) Pythia: - Many options including double Gaussian (similar shape to EE) - x-depended overlap [Corke, Sjostrand, JHEP 1105:009] Extension to soft MPI (p t < p min t ) 1/ (5 GeV) d /dp t (1/GeV) dp t p t e (p t p 2 min,2 t ) p t (GeV) pt min pt min =3 GeV, = 0.5 GeV 2 =5 GeV, =0.06 GeV 2 Gaussian extension below p min t Energy dependent p min t Pythia: Regularise cross section with p min t as free parameter: dσ dp 2 α2 (p 2 T ) p T 4 α2 (p 2 T +pmin 2 t ) T (p 2 T +pmin 2 t ) 2 Colour structure (p reco, p CD ) Possibility of change of color structure (color reconnection) [Gieseke, Röhr, AS, EPJC 72 (2012)] The least understood part of modeling (very active area research) Pythia: Recent development: String Formation Beyond Leading Colour J. Christiansen, P. Skands [arxiv: ] 40 / 63

41 Min Bias/Underlying Event Herwig++ MPI model with independent hard and soft processes, showered and with colour reconnection. Just few parameters. Min bias without integrated diffraction (work in progress). Pythia MPI interleaved with showering. MPI ordered in p T. The most sophisticated model. Many options and parameters (Pythia has strong emphasis on NP physics) many tune families. Sherpa New model - SHRiMPS with integrated diffraction based on KMR (Khoze-Martin-Ryskin model). Model in development - currently not suitable for UE studies (work in progress - this winter?). Currently for UE there is cheap version of Pythia s UE model (F. Krauss) 41 / 63

42 UE measurements - Energy Overview 42 / 63

43 Run II results - UE [ATL-PHYS-PUB ] Many LHC UE observables (not tuned since not available) and well described by most of the models! 43 / 63

44 Problems - very soft MinBias ATLAS Need of the colour reconnection. 44 / 63

45 Problems - very soft MinBias ATLAS Need of the colour reconnection. MB 7000 TeV, problem at low p T, high Nch (CMS ridge) 45 / 63

46 Problems - Identified particles More plots: mcplots.cern.ch 46 / 63

47 Tuning MC models have parameters such as pt cutoff, energy evolution, colour-reconnection... + many parameters of hadronization models Tuning (fixing) of parameters required to constrain models No unique way of tuning: which data samples should be used? Divide and conquer (split parameters in subgroups which can be tune separately)... manual tunning - hard and inefficient - lots of man and CPU power needed. new tools help to automatize this process -> however still you need to think it is not Fire-and-forget 47 / 63

48 Tuning Rivet and Professor 48 / 63

49 Rivet and Professor Tuning Tuning procedure in Professor (1D, 1Bin) 1 Random sampling: N parameter points in n-dimensional space 2 Run generator and fill histograms 3 For each bin: use N points to fit interpolation (2 nd or 3 rd order polynomial) 4 Construct overall (now trivial) χ 2 bins (interpolation data) 2 error 2 5 and Numerically minimize pyminuit, SciPy data bin b b bin interpolation b b best p p Professor 4 / / 63

50 Tuning Rivet and Professor 50 / 63

51 Tuning Rivet and Professor 51 / 63

52 Semi hard underlying event Taken from Peter Skands: 52 / 63

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55 Colour reconnections in Herwig++ [Gieseke, Röhr, AS, Eur.Phys.J. C72 (2012) 2225] f a (m cut ) N a (m cut )/ b=h,i,n N b (m cut ) = N a(m cut ) N cl, (1) n type cluster n-type i-type h-type fi h type cluster 0.4 i type cluster mcut/gev Since these n-clusters can lie at very different rapidities (the extreme case being the two opposite beam remnants), the strings or clusters spanned between them can have very large invariant masses (though normally low pt), and give rise to large amounts of (soft) particle production. 55 / 63

56 Colour reconnections in Herwig++ [Gieseke, Röhr, AS, Eur.Phys.J. C72 (2012) 2225] f a (m cut ) N a (m cut )/ b=h,i,n N b (m cut ) = N a(m cut ) N cl, (1) 1/n dn/dmcl/gev s = 7 TeV fi n-type i-type h-type Mcluster [GeV] mcut/gev Since these n-clusters can lie at very different rapidities (the extreme case being the two opposite beam remnants), the strings or clusters spanned between them can have very large invariant masses (though normally low pt), and give rise to large amounts of (soft) particle production. 56 / 63

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59 Summary Summary: Tremendous amount of new developements in GPMCs. Parton showers well established. Hard matrix element - NLO revolution and more - see Marek s lectures. Hadronization crucial to obtain fully exclusive simulation of the collisions. Two main models: string and cluster. MPI models under constant improvement (new MPI model Shrimps in Sherpa, improvements in Pythia and Herwig, for LHC)! Good first round of LHC data well described but still a lot space for improvements. Not-too-soft not-too-high-multiplicity physics under good control (if you use modern models with modern tunes). 59 / 63

60 The Road Ahead Event generators crucial since the start of LHC studies. Qualitatively predictive already 25 years ago Quantitatively steady progress, continuing today: continuous dialogue with experimental community, more powerful computational techniques and computers, new ideas. As LHC needs to study more rare phenomena and more subtle effects, generators must keep up by increased precision. 60 / 63

61 Thank you for the attention!

62 MCnet Short-term studentships

63 Enjoy the rest of the school!