# Presentation: 646240

## Towards Improved Event Generators

- Peter Skands
- Fermilab / Particle Physics Division / Theoretical Physics
- In collaboration with W. Giele (FNAL), D. Kosower (CEA/Saclay),             T. Sjöstrand (CERN & Lund U), D. Wicke (DØ, Wuppertal)

## Overview

- Parton Showers
- QCD & Event Generators
- Antenna Showers: the VINCIA code
- Matching
- LL shower + tree-level matching (through to αs2)
- E.g. [X](0) , [X + jet](0) , [X + 2 jets](0) + shower (~ CKKW, but different)
- LL shower + 1-loop matching (through to αs)
- E.g. [X](0,1) , [X + jet](0) + shower (~ MC@NLO, but different)
- A sketch of further developments
- The rest is strings
- The theory of hadron collisions: the underlying event, and colour
- Non-perturbative QCD effects and the top mass at the Tevatron

- Towards Improved Event Generators

- Peter Skands

## Main Tool
Approximate by truncation of perturbative series at fixed coupling order

Example:

- Main Tool
- Approximate by truncation of perturbative series at fixed coupling order
- Example:

- QuantumChromoDynamics

- Reality is more complicated

- Towards Improved Event Generators

- Peter Skands

## Traditional Event Generators

- Basic aim: improve lowest order perturbation theory by including leading corrections  exclusive event samples
**sequential resonance decays**
**bremsstrahlung **
**underlying event**
**hadronization**
**hadron (and ****τ****) decays**

- E.g. PYTHIA
- 2006: first publication of PYTHIA manual
- JHEP **0605:026,2006**
- (FERMILAB-PUB-06-052-CD-T)

- Towards Improved Event Generators

- Peter Skands

## The Bottom Line 

- The S matrix is expressible as a series in gi, gin/tm, gin/xm, gin/mm, gin/fπm , ...
**To do precision physics**:
- _Solve more of QCD_
- Combine approximations which work in different regions: matching
- _Control it_
- Good to have comprehensive understanding of uncertainties
- Even better to have a way to systematically improve
- _Non-perturbative effects_
- don’t care whether we know how to calculate them

- FO

- DGLAP

- BFKL

- HQET

- χPT

- Towards Improved Event Generators

- Peter Skands

## A Problem

- The best of both worlds? We want:
- A description which accurately predicts hard additional jets
- + jet structure and the effects of multiple soft emissions
- How to do it?
- Compute emission rates by parton showering?
- Misses relevant terms for hard jets, rates only correct for strongly ordered emissions pT1  >> pT2 >> pT3 ...
- (common misconception that showers are soft, but that need not be the case. They can err on *either side* of the right answer.)
- Unknown contributions from higher logarithmic orders
- Compute emission rates with matrix elements?
- Misses relevant terms for soft/collinear emissions, rates only correct for well-separated individual partons
- Quickly becomes intractable beyond one loop and a handfull of legs
- Unknown contributions from higher fixed orders

- Towards Improved Event Generators

- Peter Skands

## Example: tops, gluinos, and squarks plus jets

- T. Plehn, D. Rainwater, PS -PLB645(2007)217 + hep-ph/0511306

- Towards Improved Event Generators

- Peter Skands

## Double Counting

- Combine different multiplicites  *inclusive *sample?
- In practice – Combine
- [X]ME + showering
- [X + 1 jet]ME + showering
- ...
-  Double Counting:
- [X]ME + showering produces some X + jet configurations
- The result is X + jet in the shower approximation
- If we now add the *complete* [X + jet]ME *as well*
- the total rate of X+jet  is now _approximate + exact_ ~ double !!
- some configurations are generated *twice*.
- and the total inclusive cross section is also not well defined
- When going to X, X+j, X+2j, X+3j, etc, this problem gets worse

****

- Towards Improved Event Generators

- Peter Skands

## Matching

- Matching of up to one hard additional jet
- PYTHIA-style (reweight shower: ME = w*PS)
- HERWIG-style (add separate events from ME: weight = ME-PS)
- MC@NLO-style (ME-PS subtraction similar to HERWIG, but NLO)
- Matching of generic (multijet) topologies (at tree level)
- ALPGEN-style (MLM)
- SHERPA-style (CKKW)
- ARIADNE-style (Lönnblad-CKKW)
- PATRIOT-style (Mrenna & Richardson)
- Brand new approaches (still in the oven)
- Refinements of MC@NLO (Nason)
- CKKW-style at NLO (Nagy, Soper)
- SCET approach (based on SCET – Bauer, Schwarz)
- VINCIA (based on QCD antennae – Giele, Kosower, PS)

- Towards Improved Event Generators

- Peter Skands

## MC@NLO

- Nason’s approach:
- Generate 1st shower emission separately  easier matching
- Avoid negative weights + explicit study of ZZ production

- Frixione, Nason, Webber, JHEP 0206(2002)029 and 0308(2003)007

- JHEP 0411(2004)040

- JHEP 0608(2006)077

- MC@NLO in comparison
- Superior precision for total cross section
- Equivalent to tree-level matching for event shapes (differences higher order)
- Inferior to multi-jet matching for multijet topologies
- So far has been using HERWIG parton shower  complicated subtractions

- Towards Improved Event Generators

- Peter Skands

## VINCIA

- _VINCIA Dipole shower_
- C++ code for gluon showers
- Standalone since ~ half a year
- Plug-in to PYTHIA 8 (C++ PYTHIA) since ~ last week
- Most results presented here use the plug-in version
- So far:
- 2 different shower evolution variables:
- pT-ordering (~ ARIADNE, PYTHIA 8)
- Virtuality-ordering (~ PYTHIA 6, SHERPA)
- For each: an infinite family of antenna  functions
- shower functions = leading singularities plus arbitrary polynomials (up to 2nd order in sij)
- Shower cutoff contour: independent of evolution variable
-  IR factorization “universal”  less wriggle room for non-pert physics?
- Phase space mappings: 3 choices implemented
- ARIADNE angle, Emitter + Recoiler, or “DK1” (+ ultimately smooth interpolation?)

- Dipoles – a dual description of QCD

- 1

- 3

- 2

- VIRTUAL NUMERICAL COLLIDER WITH INTERACTING ANTENNAE

- Giele, Kosower, PS : in progress

- Towards Improved Event Generators

- Peter Skands

## Expanding the Shower

- Start from Sudakov factor
- = No-branching probability: (n or more  n and only n)
- Decompose inclusive cross section
- Simple example (sufficient for matching through NLO):

**NB: simplified notation! **
- Differentials are over entire respective phase spaces
- Sums run over all possible branchings of all antennae

- Towards Improved Event Generators

- Peter Skands

## Matching at NLO: tree part

- NLO real radiation term from parton shower
- Add extra tree-level X + jet (at this point arbitrary)
- Correction term is given by matching to fixed order:
-  variations (or dead regions) in |a|2 canceled by matching at this order
- (If |a| too hard, correction can become negative  constraint on |a|)
- Subtraction can be automated from ordinary tree-level ME’s
- + no dependence on unphysical cut or preclustering scheme (cf. CKKW)
- - not a complete order: normalization changes (by integral of correction), but still LO

**NB: simplified notation! **
- Differentials are over entire respective phase spaces
- Sums run over all possible branchings of all antennae
- Twiddles = finite (subtracted) ME corrections
- Untwiddled = divergent (unsubtracted) MEs

- Towards Improved Event Generators

- Peter Skands

## Matching at NLO: loop part

- NLO virtual correction term from parton shower
- Add extra finite correction (at this point arbitrary)
- Have to be slightly more careful with matching condition (include unresolved real radiation) but otherwise same as before:
- Probably more difficult to fully automate, but |a|2 not shower-specific
- Currently using Gehrmann-Glover (global) antenna functions
- Will include also Kosower’s (sector) antenna functions

- Tree-level matching just corresponds to using zero

-  (This time, too small |a|  correction negative)

- Towards Improved Event Generators

- Peter Skands

## Matching at NNLO: tree part

- Adding more tree-level MEs is straightforward
- Example: second emission term from NLO matched parton shower
- X+2 jet tree-level ME correction term and matching equation

**Matching equation looks identical to 2 slides ago ******
- If all indices had been shown: sub-leading colour structures not derivable by nested 23 branchings do not get subtracted

- Towards Improved Event Generators

- Peter Skands

## Matching at NNLO: tree part, with 24

- Sketch only!
- But from matching point of view at least, no problem to include 24
- Second emission term from NLO matched parton shower with 24
- (For subleading colour structures, only *|b|**2* term enters)
- Correction term and matching equation
- (Again, for subleading colour structures, only *|b|**2* term is non-zero)
- So far showing just for fun (and illustration)
- Fine that matching seems to be ok with it, but ...
- Need complete NLL shower formalism to resum 24 consistently
- If possible, would open the door to MC@NNLO

- Towards Improved Event Generators

- Peter Skands

## Under the Rug

- The simplified notation allowed to skip over a few issues we want to understand slightly better, many of them related
- Start and re-start scales for the shower away from the collinear limit
- Evolution variable: global vs local definitions
- How the arbitrariness in the choice of phase space mapping is canceled by matching
- How the arbitrariness in the choice of evolution variable is canceled by matching
- Constructing an exactly invertible shower (sector antenna functions)
- Matching in the presence of a running renormalization scale
- Dependence on the infrared factorization (hadronization cutoff)
- Degree of automation and integration with existing packages
- To what extent negative weights (oversubtraction) may be an issue
- None of these are showstoppers as far as we can tell

- Towards Improved Event Generators

- Peter Skands

## Under the Rug 2

- We are now concentrating on completing the shower part for Higgs decays to gluons, so no detailed pheno studies yet
- The aim is to get a standalone paper on the shower out faster, accompanied by the shower plug-in for PYTHIA 8
- We will then follow up with a writeup on the matching
- I will just show an example based on tree-level matching for Hgg

- Towards Improved Event Generators

- Peter Skands

## Checks: Analytic vs Numerical vs Splines

- Calculational methods
- Analytic integration over resolved region (as defined by evolution variable) – obtained by hand, used for speed and cross checks
- Numeric: antenna function integrated directly (by nested adaptive gaussian quadrature)  can put in any function you like
- In both cases, the generator constructs a set of natural cubic splines of the given Sudakov (divided into 3 regions linearly in QR – coarse, fine, ultrafine)
- Test example
- Precision target: 10-6
- ggggg Sudakov factor (with nominal αs = unity)

- ggggg: Δ(s,Q2)
-  Analytic
-  Splined

- pT-ordered Sudakov factor
- (= no-branching probability)

- Numeric / Analytic
- Spline (3x1000 points) / Analytic

- Ratios

- Spline off by a few per mille at scales corresponding to less than a per mille of all dipoles  global precision ok ~ 10-6

- VINCIA 0.010
- (Pythia8 plug-in version)

- Towards Improved Event Generators

- Peter Skands

## Why Splines?

- Example: mH = 120 GeV
- Hgg + shower
- Shower start: 120 GeV. Cutoff = 1 GeV
- Speed (2.33 GHz, g++ on cygwin)
- Tradeoff: small downpayment at initialization  huge interest later &v.v.
- (If you have analytic integrals, that’s great, but must be hand-made)
- Aim to eventually handle any function & region  numeric more general

|  | Initialization 
(PYTHIA 8 + VINCIA) | 1 event |
| --- | --- | --- |
| Analytic, no splines | 2s | (< 10-3s ?) |
| Analytic + splines | 2s | < 10-3s |
| Numeric, no splines | 2s | 6s |
| Numeric + splines | 50s | < 10-3s |

- Numerically integrate the antenna function (= branching probability) over the resolved 2D branching phase space for *every single Sudakov trial evaluation*

- Have to do it only once for each spline point during initialization

- Towards Improved Event Generators

- Peter Skands

## VINCIA Example: H  gg  ggg

- 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

- y12

- y23

- y23

- y23

- y23

- 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

_**Outlook:**_
- Immediate Future:
- Paper about gluon shower
- Include quarks  Z decays
- Matching
- Then:
- Initial State Radiation
- Hadron collider applications

- Towards Improved Event Generators

- Peter Skands

## Non-Perturbative Effects

- The Underlying Event and Colour
- String Interactions and the Top Mass at the Tevatron

## Domain of fixed order and parton shower calculations: hard partonic scattering, and bremsstrahlung associated with it.

But hadrons are not elementary 
+ QCD diverges at low pT 
 multiple perturbative parton-parton collisions should occur

Normally omitted in explicit perturbative expansions

+ Remnants from the incoming beams
+ additional (non-perturbative / collective) phenomena?
Bose-Einstein Correlations
Non-perturbative gluon exchanges / colour reconnections ?
String-string interactions / collective multi-string effects ?
Interactions with “background” vacuum / with remnants / with active medium?

- But hadrons are not elementary
- + QCD diverges at low pT
-  multiple _perturbative_ parton-parton collisions should occur
- Normally omitted in explicit perturbative expansions
- + Remnants from the incoming beams
- + additional (non-perturbative / collective) phenomena?
- Bose-Einstein Correlations
- Non-perturbative gluon exchanges / colour reconnections ?
- String-string interactions / collective multi-string effects ?
- Interactions with “background” vacuum / with remnants / with active medium?

- e.g. 44, 3 3, 32

- Additional Sources of Particle Production

- Towards Improved Event Generators

- Peter Skands

## Classic Example: Number of tracks

- UA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias events

- Simple physics models ~ Poisson
- Can ‘tune’ to get _average_ right, but much too small _fluctuations_
-   inadequate physics model

- Morale (will return to the models later):
- It is not possible to ‘tune’ anything better than the underlying physics model allows
- Failure of a physically motivated model usually points to more physics

- Towards Improved Event Generators

- Peter Skands

## Multiple Interactions  Balancing Minijets

- Look for additional balancing jet pairs “under” the hard interaction.
- Several studies performed, most recently by Rick Field at CDF  ‘lumpiness’ in the underlying event.

-  (Run I)

- angle between 2 ‘best-balancing’ pairs

- CDF, PRD 56 (1997) 3811

- Towards Improved Event Generators

- Peter Skands

## Basic Physics

- Sjöstrand and van Zijl (1987):
- First serious model for the underlying event
- Based on resummation of _perturbative_ QCD 22 scatterings at successively smaller scales  multiple parton-parton interactions
- Dependence on impact parameter crucial to explain Nch distributions.
- Peripheral collisions  little matter overlap  few interactions. Central collisions  many
- Nch Poissonian for each impact parameter convolution with impact parameter profile  wider than Poissonian!
- Colour correlations also essential
- Determine between which partons hadronizing strings form (each string  log(mstring) hadrons)
- Important ambiguity: what determines how strings form *between* the different interactions?

- UA5
**N****ch**
- 540 GeV

- Towards Improved Event Generators

- Peter Skands

## Underlying Event and Colour

- In PYTHIA (up to 6.2), some “theoretically sensible” default values for the colour correlation parameters had been chosen
- Rick Field (CDF) noted that the default model produced too soft charged-particle spectra.

- (The same is seen at RHIC:)
- For ‘Tune A’ etc, Rick noted that <pT> increased when he increased the colour correlation parameters
- Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations
- Tune A, and hence its more extreme colour correlations are now the default in PYTHIA (will return to this ...)

- M. Heinz (STAR), nucl-ex/0606020; nucl-ex/0607033

**STAR**
**pp @ 200GeV**

- Towards Improved Event Generators

- Peter Skands

## Correlation: <pT> vs Nch

- Both RHIC and Rick find the average hadron is harder in high-multiplicity events than in low-multiplicity ones
- If high multiplicity is interpreted as ~ large UE, this raises the question:
- Why do ‘active’ collisions produce harder hadrons?
- If I just stack independent collisions on top of each other, the prediciton would be ~ flat
- How do the hadrons from a central collision ‘know’ it was central? Do they talk to each other?
- What do they talk about? And how?

**Tevatron Run II**
- Pythia 6.2 Min-bias
*<p**T**>(N**ch**)*

- Tune A

- old default

- Central
- Large UE

- Peripheral
- Small UE

- Non-perturbative <pT> component in string fragmentation (LEP value)

- Not only more (charged particles), but each one is harder

*Diffractive?*

- Towards Improved Event Generators

- Peter Skands

## The ‘Intermediate’ Model

- Meanwhile in Lund: Sjöstrand and PS (2003):
- Further developments on the multiple-interactions idea
- First serious attempt at constructing multi-parton densitities
- If sea quark kicked out, “companion” antiquark introduced in remnant (distribution derived from gluon PDF and gluon splitting kernel)
- If valence quark kicked out, remaining valence content reduced
- Introduction of “string junctions” to represent beam baryon number
- Detailed hadronization model for junction fragmentation  can address baryon number flow separately from valence quarks

- Sjöstrand & PS  : Nucl.Phys.B659(2003)243, JHEP03(2004)053

- Towards Improved Event Generators

- Peter Skands

## The ‘New’ Model

- Sjöstrand and PS (2005):
- ‘Interleaved’ evolution of multiple interactions and parton showers

- Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129

- multiparton
- PDFs derived
- from sum rules

- Beam remnants
- Fermi motion /
- primordial kT

- Fixed order
- matrix elements

- pT-ordered
- parton shower
- (matched to ME
- for W/Z/H/G + jet)

- perturbative
- “intertwining”?

- NB: Tune A still default since more thoroughly tested. To use new models, see e.g. PYTUNE (Pythia6.408+)

- Towards Improved Event Generators

- Peter Skands

## Hooking it Up

- But the old ambiguity remained.
- How are the interaction initiators (and thereby their final states) correlated in colour?
- Fundamentally a non-perturbative question, so hard to give definite answers
- Simple-minded guess
- There are many partons in the proton. Only a few interact  to first approximation their colour correlations should just be random
- But random connections produced the usual flat <pT>(Nch) behaviour
- Clearly, the new model and showers did not change the fact that *some* non-trivial colour correlations appear to be necessary
- We also tried deliberately optimizing the correlations between the initiators to give the most highly correlated final states
- This did lead to a small rise in the <pT>(Nch) distribution, but too little
- One place left to look
- Could there be some non-trivial physics at work in the final state itself?

- Towards Improved Event Generators

- Peter Skands

## The (QCD) Landscape

- D. B. Leinweber, hep-lat/0004025

- Structure of a high-energy collision
- In reality, this all happens on top of each other
- (only possible exception: long-lived colour singlet)

- Towards Improved Event Generators

- Peter Skands

## Searched for at LEP 
Major source of W mass uncertainty
Most aggressive scenarios excluded
But effect still largely uncertain  Preconnect ~ 10%

Prompted by CDF data and Rick Field’s studies to reconsider. 	         	What do we know?
Non-trivial initial QCD vacuum
A lot more colour flowing around, not least in the UE
String-string interactions? String coalescence? 
Collective hadronization effects?
More prominent in hadron-hadron collisions?
What is <pT>(Nch) telling us?
What (else) is RHIC, Tevatron telling us? 
Implications for Top mass? Implications for LHC?

**toy model for all final states: colour annealing**

- Searched for at LEP
- Major source of W mass uncertainty
- Most aggressive scenarios excluded
- But effect still largely uncertain  Preconnect ~ 10%
- Prompted by CDF data and Rick Field’s studies to reconsider. 	         	What do we know?
- Non-trivial initial QCD vacuum
- A lot more colour flowing around, not least in the UE
- String-string interactions? String coalescence?
- Collective hadronization effects?
- More prominent in hadron-hadron collisions?
- What is <pT>(Nch) telling us?
- What (else) is RHIC, Tevatron telling us?
*Implications for Top mass? Implications for LHC?*

**OPAL**, Phys.Lett.B453(1999)153 & **OPAL**, hep-ex0508062

- Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more ...

- Color Reconnections

- Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120

- Towards Improved Event Generators

- Peter Skands

## Colour Annealing

- Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120

- Toy model of (non-perturbative) color reconnections, applicable to any final state
- at hadronisation time, each string piece has a probability to interact with the vacuum / other strings:
- 				Preconnect = 1 – (1-χ)n
- χ = strength parameter: fundamental reconnection probability (free parameter)
- n = # of multiple interactions in current event ( ~ counts # of possible interactions)
- For the interacting string pieces:
- New string topology determined by annealing-like minimization of  ‘Lambda measure’
- Similar to area law for fundamental strings: Lambda ~ potential energy ~ string length ~ log(m) ~ N
-  good enough for order-of-magnitude

- Towards Improved Event Generators

- Peter Skands

## A First Study

- Using Tevatron min-bias as constraint
- Those were the distributions that started it all
- High-multiplicity tail should be somewhat similar to top  less extrapolation required
- Why not use LEP? Again, since the extrapolation might not be valid.
- No UE in ee, no beam remnants, less strings, no ‘bags’ in initial state.
- The comparison would still be interesting and should be included in a future study
- As a baseline, all models were tuned to describe Nch and <pT>(Nch)

- No CR

- Field’s Tunes & new models

- Improved Description of Min-Bias
- Effect _Still_ largely uncertain
- Worthwhile to look at top etc

- Tevatron Run II min-bias

- PYTHIA 6.408

- PYTHIA 6.408

- Towards Improved Event Generators

- Peter Skands

## Event Generation Selection
For each model 100k inclusive events were generated
Jets are reconstructed using both
Cone (ΔR = 0.5, pT > 15 GeV)
kT (dcut = 150 GeV2)
Exactly 4 reconstructed Jets
Technical simplifications:
Generator semileptonic events.
Unique assignment to MC truth by ΔR possible.
Reconstruct mass on correct assignment only: 
m2 = (pbjet + pqjet + pqbarjet)2

- For each model 100k inclusive events were generated
- Jets are reconstructed using *both*
- Cone (Δ*R *= 0*.*5, *p**T** > *15 GeV)
- kT (*d*cut = 150 GeV2)
- Exactly 4 reconstructed Jets
- Technical simplifications:
- Generator semileptonic events.
- Unique assignment to MC truth by Δ*R *possible.
- Reconstruct mass on correct assignment only:
*m**2* = (*p**b*jet + *p**qjet* + *p**qbarjet*)2

- Top Mass Estimator

- D. Wicke (DØ)

- Used for paper

- Towards Improved Event Generators

- Peter Skands

## Top Mass Estimator

- Also considered +/- 30 GeV

- Also considered Gaussian + p1, and flat

- D. Wicke (DØ)

- Towards Improved Event Generators

- Peter Skands

## Top Mass Estimator

- D. Wicke (DØ)

- Towards Improved Event Generators

- Peter Skands

## Top Mass Estimator

- D. Wicke (DØ)

- Towards Improved Event Generators

- Peter Skands

## Preliminary Conclusions

- Delta(mtop) ~ 1 GeV from parton shower
- To some extent already accounted for by HERWIG – PYTHIA, should still be investigated
- Match to hard matrix elements for top + jets + further constrain shower parameters

- Delta(mtop) ~ 0.5 GeV from infrared effects
- Early days. May be under- or overestimated. Models are crude, mostly useful for reconnaissance and order-of-magnitude
- Pole mass does have infrared sensitivity. Can we figure out some different observable which is more stable?
- It may be difficult to derive one from first principles, given the complicated environment, but proposals could still be tested on models
- Infrared physics ~ universal?  use complimentary samples to constrain it. Already used a few min-bias distributions, but more could be included
- As a last resort, take top production itself and do simultaneous fit?

- A few weeks ago: D. Wicke + PS, **hep-ph/0703081**

- Towards Improved Event Generators

- Peter Skands