# Presentation: 123929

## Monte Carlo Event Generators

- Peter Skands

- for HEP Studies

-  Physics Studies at the Interaction Point
- This talk is meant to give an update on HEP event generators, with special focus on *μ**+**μ**-**** HEP*

- Physics at the IP

- = Primary Vertex

- Event Generator Status

- Peter Skands

## The Event Generator Position

- Collider

- Detector

- Reconstruction Framework

- Detailed Simulations prerequisite for:
-  Serious physics studies
-  Detector design studies
-  Design reports ...

- Event Generator Status

- Peter Skands

## The Monte Carlo Method

- Hard Part
- Hundreds of GeV  Ecm

- Parton
- Showers
- Multi-GeV

- Hadron Decays

- Hadronization
- ~ 1 GeV ~ 10-15 m

- σhard process, *P*res

*P*ISR,* P*FSR

*P*hadronization

*P*decays

- Event Generator Status

- Peter Skands

## Starting observation: photon forward brems singularity is process-independent. Fundamental property of gauge theory  also applies to gluon brems. 
Leading contributions to both QED (photon radiation) & QCD (quark, gluon radiation) can be worked out to all orders once and for all
 exponentiated (Altarelli-Parisi) integration kernels

Iterative (Markov chain) formulation = parton shower
can be used to generate the forward singular (“collinear”) parts of QED and QCD corrections to any process to infinite order in the coupling
ordered in a measure of resolution  a series of successive factorizations the lower end of which can be matched to a hadronization description at some fixed low hadronization scale

Limitations
misses interference terms relevant in the deep non-singular region
kinematic ambiguities and double counting between fixed order part and resummed part

- Leading contributions to both QED (photon radiation) & QCD (quark, gluon radiation) can be worked out to _all orders_ once and for all
-  exponentiated (Altarelli-Parisi) integration kernels
- Iterative (Markov chain) formulation = parton shower
- can be used to generate the forward singular (“collinear”) parts of QED and QCD corrections to any process to infinite order in the coupling
- ordered in a measure of resolution  a series of successive factorizations the lower end of which can be matched to a hadronization description at some fixed low hadronization scale
- Limitations
- misses interference terms relevant in the deep non-singular region
- kinematic ambiguities and double counting between fixed order part and resummed part

- Bremsstrahlung: Parton Showers

- Event Generator Status

- Peter Skands

## Pre-LEP Event Generators

*“**Seated on a tripod above a crack in the earth, she went into a trance by the stupefying vapors rising from the earth and by chewing laurel leaves. From the incoherent babbling which the priestess spoke in her ecstasy, the temple priests formulated the oracle.”*

- There was a certain amount of voodoo involved
- Still, an impressive amount of data could be accounted for
- We now have much better voodoo

- The Pythia

- ARIADNE, HERWIG, and PYTHIA

- T. Sjöstrand, S. Mrenna, PS, JHEP 05 (2006) 026

- Event Generator Status

- Peter Skands

## Developments since LEP

- Hard Bremsstrahlung (additional jets, e.g. Z3,4,5 jets)
- Parton shower approximation breaks down  large uncertainties
- Lots of progress in last ~ 5 years: “matching” to matrix elements
- Jet Broadening (soft/collinear parton bremsstrahlung)
- New generation of theoretical models
- Improved parton showers implemented in both general-purpose generators (HERWIG(++) and PYTHIA)
- + work here at Fermilab: VINCIA – a next-generation “antenna” shower
- The Final Femtometer – Hadronization
- With short-distance parts better under control  non-perturbative side has less wiggle room  also here improved possibility for studies
- Current studies at hadron colliders  feed back to lepton collider physics

- Event Generator Status

- Peter Skands

## VINCIA

- _VINCIA Dipole shower_
- C++ code for gluon showers – running
- Can evolve in either of 2 different shower evolution variables:
- pT-ordering (~ ARIADNE)
- Virtuality-ordering (~ Pythia 6.2 & SHERPA)
- For each evolution type, an infinite family of radiation  functions implemented, all with correct collinear and soft behaviour               (= “antenna functions”)

- First parton shower with systematic possibility of variation of shower variable and shower functon  control uncertainties
- To any fixed order, these variations can be absorbed by  a new type of matching to matrix elements

- Dipoles – a dual description of QCD

- 1

- 3

- 2

- virtual numerical collider with integrated antennae

- Giele, Kosower, PS : in progress

- Event Generator Status

- Peter Skands

## VINCIA Example: H  gg  ggg

- VINCIA 0.008
**Unmatched**
- “soft” |A|2

- VINCIA 0.008
**Unmatched**
- “hard” |A|2

- VINCIA 0.008
**Matched**
- “soft” |A|2

- VINCIA 0.008
**Matched**
- “hard” |A|2

- Expect public code and long writeup before summer

- Giele, Kosower, PS : in progress

- y12

- y23

- y23

- y23

- y23

- Later: plug-in for Pythia 8 ?

- Next: Quarks and leptons  lepton colliders

- y12

- First Branching ~ first order in perturbation theory
- Unmatched shower varied from “soft” to “hard” : soft shower has “radiation hole”. Filled in by matching.

- radiation hole in high-pT region

- Event Generator Status

- Peter Skands

## The Move to C++ (from F77)

**HERWIG++: complete reimplementation**
- Improved parton shower and decay algorithms
- Eventually to include “CKKW”-style matching ?
- B.R. Webber; S. Gieseke, D. Grellscheid, A. Ribon, P. Richardson, M. Seymour, P. Stephens, . . .
**SHERPA: complete implementation, has CKKW matching**
- ME generator + wrappers to / adaptations of PYTHIA, HERWIG
- F. Krauss; T. Fischer, T. Gleisberg, S. Hoeche, T. Laubrich, A. Schaelicke, S. Schumann, C. Semmling, J. Winter
**PYTHIA 8: selective reimplementation**
- Improved PS and UE, limited number of hard subprocesses
- Many obsolete features not carried over  simpler, less parameters
- T. Sjöstrand, S. Mrenna, P. Skands

- Event Generator Status

- Peter Skands

## PYTHIA for the Muon Collider

- Instructive Examples

## Z’ Radiative Return

- Event listing (summary)
-     I particle/jet KS     KF  orig    p_x      p_y      p_z       E        m
-     1 !mu+!        21     -13    0    0.000    0.000  750.000  750.000    0.106
-     2 !mu-!        21      13    0    0.000    0.000 -750.000  750.000    0.106
-  ==============================================================================
-     3 !mu+!        21     -13    1    0.000    0.000  750.000  750.000    0.000
-     4 !mu-!        21      13    2    0.000    0.000 -750.000  750.000    0.000
-     5 !mu+!        21     -13    3   35.339   66.868  627.465  632.007    0.000
-     6 !mu-!        21      13    4    0.549    2.140 -388.502  388.509    0.000
-     7 !Z'0!        21      32    0   35.888   69.007  238.963 1020.516  989.090
-     8 !nu_e!       21      12    7 -162.336 -426.971  135.508  476.466    0.000
-     9 !nu_ebar!    21     -12    7  198.224  495.978  103.455  544.050    0.000
-  ==============================================================================
-    10 (Z'0)        11      32    7   35.888   69.007  238.963 1020.516  989.090
-    11 gamma         1      22    3  -35.320  -66.793  108.367  132.107    0.000
-    12 gamma         1      22    4    0.514   -1.099  -16.725   16.769    0.000
-    13 gamma         1      22    4   -1.082   -1.115 -330.605  330.608    0.000
-    14 nu_e          1      12    8 -162.336 -426.971  135.508  476.466    0.000
-    15 nu_ebar       1     -12    9  198.224  495.978  103.455  544.050    0.000
-    16 gamma         1      22    1    0.000    0.000    0.000    0.000    0.000
-    17 gamma         1      22    2    0.000    0.000    0.000    0.000    0.000
-  ==============================================================================
-                    sum:  0.00         0.000    0.000    0.000 1500.000 1500.000

- Z’ with mass 1 TeV, with invisible decays (here neutrinos)
- MC running at 1.5 TeV. Radiative return via photon bremsstrahlung

|  | Beam |
| --- | --- |
|  | Initial State 
(= beam + initial-state radiation) |
|  | Final State
(at Leading Order) |
|  | Final State
(after bremsstrahlung)
 |

- Examples using PYTHIA 6.410
- T. Sjöstrand, S. Mrenna, PS, JHEP 05 (2006) 026
- http://projects.hepforge.org/pythia6/

- Note: also handles full γ/Z0/Z’0 interference for SM channels

- Standard PC 
- ~ 1M evts / hr.

- Event Generator Status

- Peter Skands

## SM Higgs Factory

-  Event listing (summary)
-     I particle/jet KS     KF  orig    p_x      p_y      p_z       E        m
-     1 !mu+!        21     -13    0    0.000    0.000   60.000   60.000    0.106
-     2 !mu-!        21      13    0    0.000    0.000  -60.000   60.000    0.106
-  ==============================================================================
-     3 !mu+!        21     -13    1    0.000    0.000   60.000   60.000    0.000
-     4 !mu-!        21      13    2    0.000    0.000  -60.000   60.000    0.000
-     5 !mu+!        21     -13    3    0.000    0.000   60.000   60.000    0.000
-     6 !mu-!        21      13    4    0.000    0.000  -60.000   60.000    0.000
-     7 !h0!         21      25    0    0.000    0.000    0.000  120.000  120.000
-     8 !b!          21       5    7  -27.886    6.281   52.534   60.000    4.800
-     9 !bbar!       21      -5    7   27.886   -6.281  -52.534   60.000    4.800
-  ==============================================================================
-    10 (h0)         11      25    7    0.000    0.000    0.000  120.000  120.000
-    11 gamma         1      22    1    0.000    0.000    0.000    0.000    0.000
-    12 gamma         1      22    2    0.000    0.000    0.000    0.000    0.000
-    13 (ubar)    A  12      -2    8   -0.243   -0.347    0.397    0.668    0.330
-    14 (g)       I  12      21    8    0.173   -0.630    0.658    0.927    0.000
-    15 (g)       I  12      21    8   -0.887   -0.091    1.462    1.712    0.000
-    16 (b)       V  11       5    8   -9.565   10.722   44.056   46.587    4.800
-    17 (u)       A  12       2    8  -12.758   -3.627   -0.934   13.300    0.330
-    18 (g)       I  12      21    8   -1.441   -0.459    0.931    1.775    0.000
-    19 (g)       I  12      21    9    0.620    0.004   -0.189    0.648    0.000
-    20 (g)       I  12      21    9   -0.081    1.305   -1.532    2.014    0.000
-    21 (g)       I  12      21    9   -0.101    0.355   -0.413    0.554    0.000
-    22 (g)       I  12      21    9    0.773   -0.305   -0.065    0.834    0.000
-    23 (g)       I  12      21    9    0.332    0.059   -0.228    0.407    0.000
-    24 (bbar)    V  11      -5    9   23.177   -6.986  -44.142   50.572    4.800
- ==============================================================================
-    25 (string)     11      92   13  -10.522    9.654   46.573   49.895   10.799
-    26 (omega)      11     223   25   -0.253   -0.461    1.549    1.812    0.778
-    27 (pi0)        11     111   25   -0.480   -0.281    0.321    0.656    0.135
-    28 (pi0)        11     111   25   -1.442    2.077    7.957    8.350    0.135
-    29 (rho-)       11    -213   25   -1.077    1.453    5.978    6.291    0.754
-    30 (B*bar0)     11    -513   25   -7.270    6.866   30.767   32.786    5.325
-    31 (string)     11      92   17   10.522   -9.654  -46.573   70.105   50.416
-    32 (rho0)       11     113   31   -5.421   -1.084   -0.402    5.565    0.492
-    33 (K*+)        11     323   31   -4.307   -1.543    0.409    4.674    0.870
-    34 K-            1    -321   31   -1.770   -0.800   -0.443    2.052    0.494
-    35 p+            1    2212   31   -2.323   -0.381   -0.291    2.551    0.938
-    36 (eta')       11     331   31   -0.351    0.200    0.439    1.128    0.958
-    37 (Deltabar-)  11   -2214   31    1.141    1.009   -1.561    2.513    1.248
-    38 pi+           1     211   31    0.105   -0.415   -1.261    1.339    0.140
-    39 (rho-)       11    -213   31    5.155   -1.570   -8.550   10.137    0.790
-    40 pi+           1     211   31    0.981    0.012   -2.262    2.469    0.140
-    41 (B0)         11     511   31   17.310   -5.083  -32.651   37.676    5.279

|  | Beam |
| --- | --- |
|  | Initial State 
(= beam) |
|  | Final State
(at Leading Order) |
|  | Final State
(after bremsstrahlung)

Legend:
(g): gluon
(u): quark
   A
   I
   I : colour chain
   I
   V
 |
|  | Final State
(after hadronization)

Legend:
(pi0): decayed hadron
K-   : undecayed hadron
(string): hadronizing string |

- Examples using PYTHIA 6.410
- T. Sjöstrand, S. Mrenna, PS, JHEP 05 (2006) 026
- http://projects.hepforge.org/pythia6/

- Standard PC 
- ~ 1M evts / hr.

- Event Generator Status

- Peter Skands

## A0 (from 2HDM)

- A0 (from 2HDM)

- Event listing (summary)
-     I particle/jet KS     KF  orig    p_x      p_y      p_z
-     1 !mu+!        21     -13    0    0.000    0.000  300.000
-     2 !mu-!        21      13    0    0.000    0.000 -300.000
-  ============================================================
-     3 !mu+!        21     -13    1    0.000    0.000  300.000
-     4 !mu-!        21      13    2    0.000    0.000 -300.000
-     5 !mu+!        21     -13    3    0.000    0.000  300.000
-     6 !mu-!        21      13    4    0.000    0.001 -299.999
-     7 !A0!         21      36    0    0.000    0.001    0.001
-     8 !Z0!         21      23    7 -121.255   37.370  250.912
-     9 !h0!         21      25    7  121.255  -37.369 -250.911
-    10 !d!          21       1    8 -124.900   34.235  257.398
-    11 !dbar!       21      -1    8    3.645    3.135   -6.485
-    12 !tau-!       21      15    9  133.239   -9.141 -163.468
-    13 !tau+!       21     -15    9  -11.985  -28.227  -87.444
-  ============================================================
-    14 (A0)         11      36    7    0.000    0.001    0.001
-    15 gamma         1      22    4    0.000   -0.001   -0.001
-    16 (Z0)         11      23    8 -121.255   37.370  250.912
-    17 (h0)         11      25    9  121.255  -37.369 -250.911
-    18 (tau+)       11     -15   13  -11.983  -28.224  -87.433
-    19 (tau-)       11      15   12  131.583   -9.121 -161.287
-    20 gamma         1      22   12    1.655   -0.023   -2.192
-    23 (d)       A  12       1   10  -86.461   23.971  171.287
-    24 (g)       I  12      21   10  -20.973    4.898   39.060
-    25 (g)       I  12      21   10   -4.846    1.556   10.350
-    26 (g)       I  12      21   10   -2.985    1.077    6.514
-    27 (g)       I  12      21   10   -1.208    0.094   11.716
-    28 (g)       I  12      21   10   -1.148    0.894    3.534
-    29 (g)       I  12      21   11   -0.829   -0.584    2.033
-    30 (g)       I  12      21   11   -3.152    1.114    7.427
-    31 (g)       I  12      21   11   -1.286   -0.891    2.165
-    32 (g)       I  12      21   11   -0.322   -0.945    1.215
-    33 (g)       I  12      21   11   -0.390   -0.326   -0.317
-    34 (g)       I  12      21   11    0.284    0.117    0.004
-    35 (g)       I  12      21   11    0.497    2.252   -0.578
-    36 (g)       I  12      21   11    1.241    3.958   -3.508
-    37 (dbar)    V  11      -1   11    0.324    0.184    0.009
-  ============================================================
-    38 nu_taubar     1     -16   18   -8.239  -19.736  -62.376
-    39 (rho+)       11     213   18   -3.745   -8.488  -25.057
-    40 nu_tau        1      16   19    0.376   -0.010   -0.335
-    41 (rho-)       11    -213   19  131.207   -9.111 -160.951
-    42 (string)     11      92   23 -121.255   37.370  250.912
-    43 (omega)      11     223   42  -54.820   14.763  107.817

- H++ (from LR Symmetry)

- Event listing (summary)
-  I particle/jet KS     KF  orig    p_x      p_y      p_z
-     1 !mu+!        21     -13    0    0.000    0.000 1000.000
-     2 !mu-!        21      13    0    0.000    0.000-1000.000
-  ============================================================
-     3 !mu+!        21     -13    1    0.000    0.000 1000.000
-     4 !mu-!        21      13    2    0.000    0.000-1000.000
-     5 !mu+!        21     -13    3    0.097    0.092  991.468
-     6 !mu-!        21      13    4    0.000    0.000 -999.999
-     7 !H_L++!      21 9900041    0  622.421 -441.228  603.501
-     8 !H_L--!      21-9900041    0 -622.324  441.320 -612.033
-     9 !tau+!       21     -15    7  390.204 -216.443  455.416
-    10 !tau+!       21     -15    7  232.217 -224.785  148.085
-    11 !tau-!       21      15    8 -620.412  420.784 -541.234
-    12 !tau-!       21      15    8   -1.912   20.536  -70.799
-  ============================================================
-    13 (H_L++)      11 9900041    7  622.421 -441.228  603.501
-    14 (H_L--)      11-9900041    8 -622.324  441.320 -612.033
-    15 gamma         1      22    3   -0.097   -0.092    8.530
-    16 gamma         1      22    3    0.000    0.000    0.002
-    17 (tau-)       11      15   11 -620.412  420.784 -541.234
-    18 (tau-)       11      15   12   -1.912   20.536  -70.799
-    19 (tau+)       11     -15    9  390.194 -216.438  455.405
-    20 (tau+)       11     -15   10  226.721 -219.279  144.594
-    21 gamma         1      22   10    5.506   -5.511    3.502
-    22 gamma         1      22    1    0.000    0.000    0.000
-    23 gamma         1      22    2    0.000    0.000    0.000
-  ============================================================
-    24 nu_tau        1      16   17 -348.492  235.606 -302.953
-    25 pi-           1    -211   17 -271.921  185.179 -238.281
-    26 nu_tau        1      16   18   -0.933    4.425  -15.491
-    27 pi-           1    -211   18   -0.214    3.391  -10.885
-    28 (rho0)       11     113   18   -0.765   12.720  -44.422
-    29 nu_taubar     1     -16   19  101.142  -55.537  116.914
-    30 pi+           1     211   19  289.052 -160.900  338.491
-    31 nu_e          1      12   20    3.975   -3.877    2.430
-    32 e+            1     -11   20  216.486 -209.065  137.898
-    33 nu_taubar     1     -16   20    6.260   -6.337    4.267
-    34 pi-           1    -211   28   -0.794   12.176  -42.192
-    35 pi+           1     211   28    0.029    0.544   -2.230
-  ============================================================
-                    sum:  0.00         0.000    0.000    0.000

- Examples using PYTHIA 6.410
- T. Sjöstrand, S. Mrenna, PS, JHEP 05 (2006) 026
- http://projects.hepforge.org/pythia6/

- Event Generator Status

- Peter Skands

## Technicolor

-  Event listing (summary)
-  I particle/jet KS     KF  orig    p_x      p_y      p_z       E        m
-     1 !mu+!        21     -13    0    0.000    0.000 1000.000 1000.000    0.106
-     2 !mu-!        21      13    0    0.000    0.000-1000.000 1000.000    0.106
-  ==============================================================================
-     3 !mu+!        21     -13    1    0.000    0.000 1000.000 1000.000    0.000
-     4 !mu-!        21      13    2    0.000    0.000-1000.000 1000.000    0.000
-     5 !mu+!        21     -13    3    0.000    0.000 1000.000 1000.000    0.000
-     6 !mu-!        21      13    4    0.000    0.000-1000.000 1000.000    0.000
-     7 !pi_tc+!     21 3000211    0  330.799 -763.014 -241.681 1000.025  500.022
-     8 !pi_tc-!     21-3000211    0 -330.799  763.014  241.681  999.975  499.920
-     9 !u!          21       2    7  -63.162 -482.381 -111.969  499.218    0.330
-    10 !bbar!       21      -5    7  393.961 -280.633 -129.712  500.808    4.800
-    11 !ubar!       21      -2    8   44.437  520.715  107.332  533.516    0.330
-    12 !b!          21       5    8 -375.236  242.299  134.349  466.459    4.800
-  ==============================================================================
-    13 (pi_tc+)     11 3000211    7  330.799 -763.014 -241.681 1000.025  500.022
-    14 (pi_tc-)     11-3000211    8 -330.799  763.014  241.681  999.975  499.920
-    15 gamma         1      22    1    0.000    0.000    0.000    0.000    0.000
-    16 gamma         1      22    2    0.000    0.000    0.000    0.000    0.000
-    17 (u)       A  12       2    9  -50.238 -373.883  -84.036  386.489    0.330
-    18 (g)       I  12      21    9  -10.115  -94.777  -23.332   98.130    0.000
-    19 (g)       I  12      21    9   -0.365   -1.610   -0.077    1.653    0.000
-    20 (g)       I  12      21    9   -1.459   -5.564    0.547    5.778    0.000
-    21 (g)       I  12      21    9    0.991   -6.413   -5.097    8.252    0.000
-    22 (g)       I  12      21    9    1.065   -1.928   -0.883    2.373    0.000
-    23 (g)       I  12      21   10    0.511   -1.018   -0.464    1.230    0.000
-    24 (g)       I  12      21   10    0.608   -0.218   -0.132    0.659    0.000
-    25 (g)       I  12      21   10    1.588   -0.970   -0.384    1.900    0.000
-    26 (g)       I  12      21   10   13.555  -10.109   -4.320   17.453    0.000
-    27 (bbar)    V  11      -5   10  374.657 -266.523 -123.505  476.108    4.800
-    28 (ubar)    A  12      -2   11   15.212  201.143   42.628  206.173    0.330
-    29 (g)       I  12      21   11   17.753  214.099   42.291  218.957    0.000
-    30 (g)       I  12      21   11    9.279  104.465   21.247  107.007    0.000
-    31 (g)       I  12      21   11    1.138    1.929    0.646    2.331    0.000
-    32 (g)       I  12      21   11   -1.868    0.865    1.543    2.573    0.000
-    33 (g)       I  12      21   12   -1.611    1.425    0.882    2.325    0.000
-    34 (g)       I  12      21   12   -0.409    0.207    0.208    0.504    0.000
-    35 (g)       I  12      21   12   -1.694    1.075    0.416    2.049    0.000
-    36 (b)       V  11       5   12 -368.599  237.806  131.820  458.057    4.800
-  ==============================================================================
-    37 (string)     11      92   17  330.799 -763.014 -241.681 1000.025  500.022
-    38 p+            1    2212   37  -28.471 -214.162  -48.494  221.424    0.938
-    39 (rho+)       11     213   37   -6.754  -52.209  -11.786   53.955    0.925
-    40 pbar-         1   -2212   37  -16.097 -119.073  -27.000  123.156    0.938
-    41 (pi0)        11     111   37   -1.194  -13.408   -2.850   13.760    0.135
-    42 (pi0)        11     111   37   -2.712  -26.468   -6.257   27.333    0.135
-    43 (rho0)       11     113   37   -4.398  -33.030   -7.997   34.277    0.767

- Technicolor Strawman model
-  Lowest-lying bound states of lightest Techni-fermion doublet
-  Can be used for studies of a wide range of non-perturbative New Physics models
- Topcolor, walking Technicolor, extended Technicolor, ...

- Mrenna, Lane
- Phys.Rev.D67:115011,2003

- Examples using PYTHIA 6.410
- T. Sjöstrand, S. Mrenna, PS, JHEP 05 (2006) 026
- http://projects.hepforge.org/pythia6/

- Standard PC 
- ~ 250k evts / hr.

- Event Generator Status

- Peter Skands

## The Generator Outlook

- MC Generators in state of continuous development
- Not much done (yet) specifically for muon colliders, but what’s there is already pretty useful
- As physics studies pick up, interactions likely to foster more developments  more studies  more developments ...
- Get yours today – it’s free

****** ****more precise, more reliable theoretical predictions**

*μ**-*

*μ**+*

- http://projects.hepforge.org/pythia6/

- Event Generator Status

- Peter Skands