How not to use the Monte Carlo Stan Bentvelsen Nordic LHC workshop

How not to use the Monte Carlo

Stan BentvelsenNordic LHC workshop

Stan Bentvelsen Nordic LHC

P 2

Remarks 1

Proton-proton collisions are extremely complexDetectors like Atlas and CMS are extremely complex

Do not thrust too much your event generatorDo not thrust too much your detector simulation

without explicit and full checks with the ‘data’ itself

‘Data’ can be any of the following and more: Other experiments (Tevatron) Internal (sub-) detector consistency Test-beam Cosmic rays Proton-proton collisions


P 3

Remarks 2

For reliable results the game to play is: reduce the dependency on MC as much as possible

(best to eliminate any dependence)

‘Shake down’ of detector (simulation) in many ways Redundancy between detectors Straight tracks, energy clusters, etc, etc…

Use Physics: available ‘candlelight’ signals Mass of the J/ψ, W±, Z0, top-quark Presence of b-jets

Use constraints: e.g. energy-momentum Difficult in pp collisions: Partonic cm not known Balance in PT


P 4

Remarks 3

This does not mean to sit back and wait for data to come!

Make clever use of MC to construct ‘MC correction free’ observables

Realistically not always possible – find balance

This talk: just warn against using MC and simulation ‘blindly’…


P 5

Use of MC’s

Not so straightforward to talk for one hour about “how not to use the Monte Carlo”

Instead, I like to discuss a few examples in which “awareness of Monte Carlo limitations”

plays an important role

It is also closely connected to “commissioning of the LHC detectors”


P 6

Event generation

Preliminaries: Every generated physics process consists of two parts: Hard process: Obtained using

perturbative (LO,NLO) calculation of the probability amplitude (matrix element)

Soft(er) effects:

Initial and final state radiation (DGLAP parton showers)

Underlying event

Fragmentation and hadronisation

See talk by Leif Lonnblad


P 7 How not to use the event generator

“Pythia tells me that W+multijets is negligible background for my top study”

Make conscious choice of event generator Is process (with phase space) implemented in the Generator?

ttbar spin-correlations not implemented in Pythia or MC@NLO Don’t take ‘Herwig’ or ‘Pythia’ as the absolute truth

Clarify what aspect you want to test with the generator Sensitivity to underlying matrix element

E.g. multi-jet physics Sensitivity to soft component

E.g. exclusive resonance study Underlying events

In most practical cases both!


P 8

Ignore new/better calculations?

A major step forward occurred with the introduction of NLO generator MC@NLO Full NLO QCD calculations

Practicalities: Deal with negative weights: ±w

Many generators available for multi-parton final states AlpGen, VecBos, AcerMC, Sherpa


P 9

ttbar system: MC@NLO, Herwig, Pythia

PT(tt system) Herwig & MC@NLO agree at low PT,

At large PT MC@NLO ‘harder’ PYTHIA completely off

Huge difference in PT from ‘ISR’,MC@NLO coincides with NLO QCDcalculations

Example: distributions on top-anti-top characteristic – PT of the whole system

PT of t-tbar system is balanced by ISR & FSR


P 10

Next step: the simulation

Detector response Parameterization, smeared

Simple detector geometry (e.g. cells in grid eta-phi) Smear 4 vector of final state particles

Photons: resolution by EM calorimeter Electrons, muons: resolutions by EM calorimeter and Inner Detector Hadrons: collected in cells – cell smearing – jet finding

E.g. b-tagging of jets implemented by overall tagging efficiency and truth information.

Detailed simulation of material interactions Geant4 (C++) packages (Geant3 is currently phased out) Detailed description of material interactions of the detector

Detailed detector geometry description Definition of ‘sensitive materials’: energy lost accumulated Creation and tracking of daughter particles: shower development


P 11

Digitization / reconstruction

Digitization Transform accumulated energy

deposits into detector output Energy deposit in Si wafer

readout channel Physics modeling quite involved


P 12

Simulation/data analysis flow

Energy depositions

HitsG4 Sim

PileUp

Digitization Raw Data

Objects

Simulation response

Services:

-Atlas geometry

-Alignment dBase

Reconstruction

ATLAS Bytestream

Atlas detector response

Physics analysis

objects

Postscript

(publications)

Reconstruction and analysis

Event generation

Event generation (Pythia…)

Fast simulation / parametrization


P 13

How not to use the simulation

Fast / full simulation have both their merits and are useful

Judge for each problem what to use CPU power available Time Status

Probably not efficient to: Study cracks in the calorimeter with parameterized simulation Asses signal of various models of black hole evaporation with full simulation

(event generation should be enough!)

If time and CPU power permits – full simulation seems always ‘better’ But life is not that straightforward ‘back of envelope’ calculations often useful to test new ideas

Rule of thumb:

Detector simulation takes 1s for 1 GeV dumped energy on modern PC.

I.e. ~1 hour to generate 1 ‘heavy’ event


P 14

How to check the Monte Carlo itself?

Tune the Monte Carlo response with test-beam data Absolutely essential! Few examples in last part of this talk

Internal consistency checks Does the detector respond symmetrically in z? Uniform in φ? Any other symmetry axis?

Inspection of the geometry – material distribution All detectors-components installed that should be installed? Compare the total ‘weight’ of a sub-detector with the weight in the

simulation


P 15

Monte Carlo validation

Validate the full Monte Carlo simulation itself. Is geometry correct?

R (cm)

Z (cm)

Location of secondaries from truth.

TRT C-wheels missing

2nd layer pixel missing


P 16

A few case studies

Using data to set the energy scales Calorimeter scale: using Z0

B-jet scale: using Z0

Et-miss

Using data to check/study data B-jet calibration W-mass determination Top physics

Underlying event B-taggin efficiencies Non W QCD background

Testbeam We have already data!

What do we learn from that?


P 17

Event rates in ATLAS or CMS at L = 1033 cm-2 s-1

Already in first year, large statistics expected from: -- known SM processes understand detector and physics at s = 14 TeV -- several New Physics scenarios

Which physics in first year?

Process N/s N/yearTotal collected before start LHC

W e 15 108 104 LEP / 107 FNAL

Z ee 1.5 107 107 LEP

tt 1 107 104 Tevatron

bb 106 1012-13 109 Belle/BaBar ?

H (130) 0.02 105 ?

Low lumi


P 18

Energy scale calibration

Make use of physics signals to understand the detector Abundance of Z and W particles being produced Top quark Various combinations of these with associated particles

Z-boson: Properties extensively determined at LEP Mass and width known up-to approx 2 MeV Mass and couplings described by Standard Model

W-boson: Current precision on mass approx 42 MeV

Ultimate goal at LHC to bring down to ~15 MeV

Top-quark Current mass at 178±4 GeV

Ultimate goal at LHC aprox 1 GeV

PDG Mass (GeV) Width (GeV)

Z 91.1876±0.0021 2.4952±0.0023

W 80.425±0.038 2.124±0.041

Top 178±4


P 19

Z0e+e- calibration

Use the Z0 mass to calibrate the EM calorimeterCan we get non-uniformity and absolute energy scale from data? Divide the calorimeter in regions i Introduce bias for each region by The Z0 invariant mass

Can be written as:

By giving all αi a suitable variance, a likelihood fit can be constructed Determine βij with lots of Z0

Untangle the αi

)1( itruei

newi EE

)cos1(2 truej

truei

trueij EEM

21

21 ijtrue

ijjitrue

ijnewij MMM


P 20

Ze+e- calibration

Method works well From parametrized MC study a

good correlation is observed between the fitted and injected values for α

Test method on full simulation events Expect non-uniformity due to

material distribution

Difference αinj and αfit

Integrated over regions in φ as function of η

Energy-loss due to material


P 21

Hadronic shower components

A hadronic shower consists of EM energy (e.g. ),

O(50%) Visible non-EM energy (e.g.

dE/dx from , , etc), O(25%) Invisible energy (e.g. breakup

of nuclei and nuclear excitation) O(25%)

Escaped energy (e.g. Ν) Each fraction is E

dependent and subject to large fluctuations

Calibration has to take into account both visible and invisible energy fractions: delicate process

Energy scale of jets can have miscalibration as large as 5-10%

Invisible energy is the main source of the non-compensating nature of hadron calorimeters


P 22

Jet energy calibration

Can we utilize the EM scale to say something on hadronic scale?

Use lepton balancing in PT to calibrate the jet energy Again – use the MC to check if the method works in an unbiased way. But method should be independent of MC as possible

Jets energy calibration not straightforward Both hadronic and electromagnetic energy content. No unambiguous assignment of energy-flow to a jet.

Which particles belong to the jet and which don’t?

%3%50)(

%9)(

EE

EE

e


P 23

Calibration of b-jets using Z or

B-jet response different from light quark jet

fragmentation – invisible component …

Rely on relatively rare process Process :

g + b b + Z0 b jet + +-

Constraint : pT(b) pT(Z0)

First estimation of calibration constant : = pT(2)/ pT(jet)

Use precise muon tracking to study the scale of b-jets

M(Z)=91.2 GeV

(b-tagged) Jet

MC study:

g + q q + Z0 signal

q + q g + Z0 with g qq background

Jet reconstruction with Cone algorithm

R = 0.7

pTseed = 5 GeV; pT threshold = 15 GeV


P 24

Event selection: Z0+jet

Statistics not great for Z0+jet – but enough to do the analysis

-1 bjet + +- reproducing invariant mass of Z0

-no photons, no electrons

Event generated : 30 000 000; events selected : 20 000pT(2) in GeV Nb of events pT(2) in GeV

40-50 7589 44.5

50-60 4494 54.5

60-75 3552 66.6

75-120 3554 91.7

120-200 931 145.0

> 200 119 257.0

Expected number of events in 3 years of low luminosity runs


P 25

Imbalance in PT

Due to Initial State Radiations :

the pT balance is not fully verified

the reconstructed b jet can come from ISR

PT(2) [GeV/c]

pT(b) / pT(2)

40-50 0.961 0.003

50-60 0.969 0.003

60-75 0.973 0.003

75-120 0.971 0.003

120-200 0.979 0.006

>200 0.98 0.03


P 26

Use the MC to evaluate the balance between pT(b) and pT() Introduce dependence on ISR of MC Check the MC by evaluate distribution in φ

K= (pT(jet) + pT().cos(φ/2) is sensitive to ISR

φ is the angle between pT(jet) and pT()

RMS (K) can be used to evaluate ISR effects from real data side

How to deal with imbalance?

φ


P 27

Potential of + jet

The statistics is much better in this case

Analysis: selection, optimized for jet rejection

• Opposite hemisphere : most energetic jet + loose back-to-back requirement ±0.3 in

azimuth

Pt balance mean

Quark 2.6 %

Jet particle level 19 %

Jet em scale -5.8 %

Jet hadronic calibration 21%

Example Cone jet R=0.7

Imbalance between photon and quarks, particles, EM jets and Had jets


P 28

+jet or Z0+jet in-situ processes

Which useful information can be extracted from these processes ?

Pro’s and Z0 are “electromagnetic objects”, calibrated at a well-known

scale the selection of the jet can be independent of the jet finding

algorithm, jet fragmentation, etc... by selecting simply the highest ET jet in the opposite hemisphere to the or Z0

comparative jet algorithm studies can be done: difference in calibration between different jet algorithms, relative efficiencies, etc.

+jet with pT>20 GeV: ~ 10k events in 1 minute but identification efficiency & trigger!

can be used to calibrate calorimeter region with dead material, uniformity scans, monitoring, etc.


P 29

Con’s or Z0 is not an unbiased estimator of the back-to-back parton

because of ISR and FSR Difficulty for absolute energy scale : this applies particularly in the low

pT range up to ~ 40 GeV the background to the or Z0 may bring an additional bias

The background will be more severe for ’s that for Z0

the pT range covered with good statistics may be limited The effect of the trigger has also to be considered (standard menu or

downscaled)

+jet or Z0+jet in-situ processes

W-mass determination


P 31

W-mass determination


P 32

Measurement by comparing MC

Relevant quantities Hadronic recoil U PT of the muon

I.e. for correct transverse mass MT the PT of the recoil U is needed

Straightforward MC method: Construct MC ‘template’ for MT by

taking into account: Initial State Radiation Angular distributions Recoil model Detector resolution

Fit template to data to extract MW

Not the best method! Heavily rely on details of event

generation, Monte Carlo simulation.

Can one be a bit clever and reduce dependency on MC?

W

ν

Hadronic recoil

up anti-downUPEE T

missTT


P 33

MW by comparison to Z data

Use data from process Z Factor 10 lower cross section, but

with abundant Z production no problem

Substitute one muon by a neutrino Z-decays have almost identical

topology

Calculate MT(Z) from remaining muon and recoil Use the precise knowledge of MZ

Transform MT(Z) distribution to MT(W) distribution and extract MW/MZ. Take difference of production

mechanism into account

Reduce MC dependency MC only needed to predict effect

of topology difference (small effect)

Determination of a ratio and MZ to determine MW

Z

Hadronic recoil

up anti-down


P 34

Analysis

To compare W and Z samples: Use technique to create MT

templates for arbitrary mass and width:

Use both muons to reconstruct Z Boosts muons into Z rest frame Set Z mass to arbitrary new value

MX, and width ΓX. Consider one muon to be a

neutrino Calculate outgoing 4 vectors Boost back into LAB frame Calculate MT

X from recoil and remaining muon

Compare many MTX templates

with the observed, measured MT

W distribution, to extract MW as MX.


P 35

Analysis and worries..

Now MW can be determined from fit to templates MT(W) Very small uncertainties With 106 events uncertainty

~10 MeV (stat)

Test method on fully simulated events

Use MC to assess Final State Radiation effects Neutrino does not radiate Muon does radiate

Completely different use of the MC!

Top physics


P 37

Top studies

Top physics at LHC Top one of ‘easiest’ bread and butter

Cross section 830±100 pb

Used as calibration tool What variations in predictions of t-tbar

– which generator to use? Underlying event parameterization Background estimation from MC

Tuning b-tagging at startup Jet energy scale

Try to be as independent from MC as possible.

Semi-leptonic top channel

detector tools involved:

Lepton reconstruction

Missing ET

Jets + calibration

B-tagging


P 38

Lepton + jet: reconstruct top

Hadronic side W from jet pair with closest invariant mass to MW

Require |MW-Mjj|<20 GeV

Assign a b-jet to the W to reconstruct Mtop

Kinematic fit Using remaining l+b-jet, the leptonic part is

reconstructed |mlb -<mjjb>| < 35 GeV Kinematic fit to the tt hypothesis,

using MW constraints

j1

j2

b-jet

tW-mass Selection efficiency 5-10%


P 39

High Pt sample

The high pT selected sample deserves independent analysis: Hemisphere separation (bckgnd reduction, much less combinatorial) Higher probability for jet overlapping

Use all clusters in a large cone R=[0.8-1.2] around the reconstructed top- direction Less prone to QCD, FSR,

calibration UE can be subtracted

j1

j2

b-jet

t

Statistics seems OK but what about syst?

R

Mtop Mtop


P 40

Underlying event evolution

It is not only minimum bias event!

The underlying event is everything except the two outgoing hard scattered jets.

In a hard scattering process, the underlying event has a hard component (initial + final-state radiation and particles from the outgoing hard scattered partons) and a soft component (beam-beam remnants).

ljet

CDF analysis:• charged particles: pt>0.5 GeV and |η|<1

• cone jet finder:

7.022 R

UE is defined as the Transverse Region


P 41

LHC predictions: UE

Tra

nsv

erse

< N

chg >

Pt (leading jet in GeV) Tevatron

x 4

x 5

LHC

x 3


P 42

Top-quark production UE

Charged particle density in pseudorapidity: Tevatron and LHC predictions.

Widly different predictions!


P 43

Jimmy UE: Cells & Jets

Herwig vs Jimmy LO t-tbar

At jet-level effectreduced

10 GeV

Cell multiplicity

Cluster multiplicity

Jet multiplicity


P 44

Reconstruct the top

Top peak for various reconstruction methods Difference in mass can be as large

as 5 GeV

Really need data to check data on UE Study effect better with data itself!!


P 45

Background events

Top physics background Mistags or fake tags Non-W (QCD) W+jets, Wbbar, Wccbar Wc WW,WZ,ZZ Z tt Single top

~ 150 pb-1 W+4jet background Not completely trivial to generate

Can we observe the top without b-tagging?

Largest background is W+4 jet.

This background cannot be simulated by Pythia or Herwig shower process. Dedicated generator needed: e.g. AlpGen. Large uncertainties in rate

Ultimately, get this rate from data itself. For example, measure Z+4 jets rate in data, and determine ratio (Z+4 jets)/(W+4 jets) from MC

W+4 extra light jets

Jet: Pt>10, ||<2.5, R>0.4

No lepton cuts


P 46

Non btag: top sample

Signal plus background at initial phase of LHC

Most important background for top: W+4 jets Leptonic decay of W, with 4 extra ‘light’ jets

With extreme simple selection and reconstruction the top-peak should be visible at LHC

L = 150 pb-1

(2/3 days low lumi)

Selection: Isolated lepton with PT>20 GeV

Exactly 4 jets (R=0.4) with PT>40 GeV

Reconstruction: Select 3 jets with maximal

resulting PT


P 47

Extraction of top signal

Fit to signal and background Gaussian signal 4th order polynomal Chebechev background

Extract

cross section

and Mtop?

150 pb-1


P 48 Can we see the W? (4 jets sample)

Select the 2 jets with highest resulting PT W peak visible in signal No peak in background Better ideas well possible!

E.g. utilizing 2 body decay in top rest frame.

Select 2 jets with invariant mass closest to Mw (80.4 GeV) Large peak in background Enormous bias Not useable!

150 pb-1


P 49

Fit to W mass

Fit signal and background also possible for W-mass Not easy to converge fit

150 pb-1 mean σ(stat)

in peak 3.0% 5%

Mtop 167.0 0.8

Mw 77.8 0.7

With W sample we can check the jet energy scales


P 50

Jet Energy scale / MC dependence

Variation of the jet energy scale to infer systematics Bjet scale: 0.92 – 0.96 – 1.00 – 1.04

– 1.08 Light scale:0.94 – 0.98 – 1.00 – 1.02 – 1.04

(1) (2) (3) (4) (5)

1) Analysis with jet energyscaled

2) All with MC@NLO, Herwigand Pythia;

3) Redo analysis with doubled W+4jet background (stat indep)

Top mass

155

160

165

170

175

180

0 5 10 15 20 25

Scale variations

To

p m

ass

Raw Top Mass

Scaled Top Mass

Determine Mtop and σ(top)

‘Raw’, i.e. no correction for jet scale

‘Corrected’, i.e. apply percentage difference of W-peak to the reconstructed top

Dependence on top mass reduced by scaling with W:

Rms Raw: 6.2 GeV

Rms Scaled: 1.2 GeV

Top mass rescaled using W constraint

‘Raw’ Top mass


P 51

Some results… (still no b-tag)

To summarize: We can ‘easily’ observe top mass peak

Sideband subtraction: limited sensitivity to background

From this sample we see the W-mass peak Rescale the jet energies

Select pure top sample Use to obtain b-tagging efficiencies


P 52

Lower luminosity?

Go down to 30 pb-1 Both W and T peaks already

observable First check of jet energy scale

30 pb-1 mean σ(stat)

in peak 0.8% 17%

Mtop 170.0 3.2

Mw 78.3 1.030 pb-1

P 53

Use exclusive b-decays with high mass products (J/) Higher correlation with Mtop Clean reconstruction (background free) BR(ttqqb+J/) 5 10-5 ~ 30% 103 ev./100 fb-1

(need high lumi)

Top mass from J/

Different systematics (almost no sensitivity to FSR)

Uncertainty on the b-quark fragmentation function becomes the dominant error

M(J/+l) Mtop

M(J/+l)

MlJ/

Purely leptonic determination


P 54

Non-W (QCD-multijet) background

Not possible to realistically generate this background Crucially depends on the detector capability to minimize

mis-identification and increase e/ separation This background has to be obtained from data itself

E.g. method developed by CDF during run-1:

Rely now on e/ separation of 10-5

Use missing ET vs lepton isolation to define 4 regions:

A. Low lepton quality and small missing ET

Mostly non-W events (i.e. QCD background)

B. High lepton quality and small missing ET

Reduction QCD background by lepton quality cuts

C. Low lepton quality and high missing ET

W enriched sample with a fraction of QCD background

D. High lepton quality and high missing ET

W enriched sample, fraction of QCD estimated by (B·C)/(A·D)


P 55

Detector scenarios: b-tagging

Precise alignment of ID can be reached only after few months of data taking. Most precise alignment using tracks from data

Top events to evaluate b-tagging efficiencies from data Select a pure t-tbar sample with tight kinematical cuts

Count the number of events with at least 1 tagged jet Compare 0 vs 1 vs 2 b-tagged jets in top events Can expect the b-tagging efficiency different in data from MC


P 56

Top in physics arena:

Inputs to the top analysis

Estimate of the single electron trigger efficiency Can be done by using the Z

triggered as single electron How much time is needed to arrive

to a reasonable evaluation of this efficiency?

Estimate of the initial lepton identification efficiency

Estimate of the integrated luminosity At the beginning the precision on L

should be around 10-20%. The ultimate precision should be <

5% Eventually:

B-tagging efficiency Jet scales

What top events can provide

Top candidates enriched samples A “pure” one, obtained with quite

tight selection criteria A “loose” one: a more “background

enriched” sample, to be used as control sample for background calculations etc…

Estimate of a light jet energy scale correction Assume 10% for light and b-quark

jets, look at effect on Mtop and stop Assume that at the very beginning

only the EM scale is known (means: do not put any weight on the hadronic scale)

Output: provide the MW peak to rescale the light jets

Estimate of the b-tagging efficiency


P 57

One slide on supersymmetry

Impressive result to get MSUSY

How well do we know the MC predictions?

Herwig parton shower

Matrix element MC(GeV) )(jet p E M4

1iiT

missTeff

signalEvents for 10 fb-1

background

Study of Z+jet events from data will asses the validity of the MC prediction

Testbeam


P 59

Testbeam analysis

We have data to test/tune simulation Example: Atlas testbeam

Slice of the Atlas detector at fixed value of η~0 Useful for trigger/DAQ tests Calibration of the detector

Calorimeter calibrations ID alignment Muon r-t and alignment

Full Geant4 simulation available for the testbeam setup Check of the ‘computing model’


P 60


P 61

Tracking

Data for tracking – to

compare to MC

9 GeV e/

B=0

Pixel+SCT+TRT


P 62

Muons: Sagitta measurements

• Create r-z and phi track-segments, perform pattern recognition

• Segments fit on each muon station

• Combination of inner and outer,compare with middle station

• Misalignment affects mean value and width

• Multiple scattering affects width

Sagitta definition at the TB:

Sagitta

Outer

Middle

Innerstation


P 63

Comparisons with G4 simulation

Real data/G4 sim reconstruction comparison can provide important feedback to the G4 validation effort

First tests: generate muons in the testbeam setup (only muon detectors activated for now) at beam energies measured in data• Track reconstruction• Compare fit residuals and sagitta resolution

Data=61m

G4 =57 m

MDT fit residuals


P 64

Comparisons with G4 simulation

G4Data

Athena 8.7.0

DataG4

Athena 8.8.0

- Difference G4-Data 1/p: material problem(effect corresponding to ~ 3 cm aluminumequivalent).- Detailed check of materials associated to GeoModel volumes-problem was found in RPC

DED

RPC internal structure

After fixing the problem

Sagitta width Sagitta width


P 65

Summary / conclusions

Use all the tools available to test the simulation prediction by using data Masses of W and Z, top Constraints

Using the simulation, the game can be prepared now


P 66

Backup slides


P 67 Calorimetry: LAr-Tile correlation

Use noise of the calorimeter

Correlations between EM and hadron calorimeter

e

Internal consistency checks useful tools to understand sub-detector

S()/N 7

Barrel middle compartment

Test-beam data


P 68

To summarize:

We can ‘easily’ observe top mass peak

Sideband subtraction: limited sensitivity to background

From this sample we see the W-mass peak

Rescale the jet energies

Select pure top sample

Use to obtain b-tagging efficiencies


P 69

Material Study

Attempt to recreate ATLAS inner detector material distribution at = 1.6 (DC-2)

Proposed Actual

Pixel / SCT 15% X0 / 12.5mm Al 12% X0 / 10mm Al

SCT / TRT 20% X0 / 16.7mm Al 24% X0 / 20mm Al

Some simulations with the added material have now been examined. Analysis of actual data not done yet (pending improvements in

alignment)


P 70

Simulation

CTB-G4Sim modified to add new material. Reconstruction in e-gamma rec of 1000 single electron events @

45GeV Effect of increased brem clearly visible in E/p distribution with added

material.

Without added Material With added Material


P 71

Different jet finder with + jet

Measured pT distribution compared to MC and to photon PT

Understanding jet-splitting, underlying event, etc

Documents

How not to use the Monte Carlo Stan Bentvelsen Nordic LHC workshop