# Presentation: 119270

## Antenna Showers and Color Annealing

- Workshop on collider physics, Argonne, May 2006

- Fermi National Accelerator Laboratory

- Peter Skands
- Theoretical Physics Dept

- with W. Giele, D. Kosower, M. Sandhoff, T. Sjöstrand, D. Wicke

## Overview

-  Road to High Precision:
- Solve _more of QCD_, control it _more exactly_
- Large pT: Matching with QCD antennae. The VINCIA code
- Medium pT: Three new infinite families of parton showers
- Small pT: Colour Annealing in PYTHIA 6.4. First results

- Quest for unification

- High Precision at Hadron Colliders:

- 

## QCD at High-Energy Colliders

## Collider Energy Scales

- Non-Perturbative
- hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton, kaon/pion, ...

- Soft Jets + Jet Structure
- Multiple collinear/soft emissions (initial and final state brems radiation), Underlying Event (multiple perturbative 22 interactions + ... ?), semi-hard separate brems jets

- Resonance Masses ...

- Hard Jet Tail
- High-pT wide-angle jets

-  & Widths

- + “UNPHYSICAL” SCALES:
-  QF , QR : Factorisation & Renormalisation

- s

- This has an S matrix expressible as a series in gi, ln(Q1/Q2), ln(x), m-1, fπ-1 , ...
**To do precision physics**:
- Need to compute and/or control all large terms
-  EVENT GENERATORS

**Inclusive**

**Exclusive**

- Hadron Decays

## High-pT phenomenology

- High-pT phenomenology

- _The signal_
- Large cross sections for coloured BSM resonances
- E.g. monojet signature for ED _relies_ on hard QCD radiation
- Cascade decays  _Many-body_ final states
- _Backgrounds_
- _Also_ large cross sections for top, nZ/W, *other* resonances (?), ...
- With jets
- _Theory:_
- Fixed-order perturbation theory
- Asymptotic freedom  improved convergence at high pT
- Phase space increases

- _Resonances & Hard Jets:_
- SM and BSM Resonance Production, Hard Jet Tail (esp. ISR), Successive (cascade) resonance decays

- Problem 1: Many legs is hard  E.g. successive factorization of res. decays
- Problem 2: Many loops is hard  Get a personal physician for Frank
- Problem 3: Only good for inclusive observables  Match to resummation

## Medium-pT phenomenology

- Problem 1: Need to get both soft and hard emissions “right”  ME/PS Matching
- Problem 2: Underlying Event not well understood  what does it look like at LHC?

- Medium-pT phenomenology

- Extra Jets
- In signal
- = extra noise / confusion
- Combinatorics, vetos
- In backgrounds
- Irreducible backgrounds
- Some fraction  _fakes_!
- Heavy flavour
- Jet energy scale
- Jet broadening
- Underlying activity
- Theory
- Fixed Order with explicit jets
- Parton Showers / Resummation
- Models of Underlying Event

- _Minijets & Jet Structure:_
- Semi-hard separate brems jets (esp. ISR),
- jet broadening (FSR), gcc/bb, multiple perturbative 22 interactions      (underlying event), ... ?

## Low-pT phenomenology

- Measurements at LEP 
- Fragmentation models (HERWIG, PYTHIA) “tuned”
- Strangeness and baryon production rates well measured
- Colour reconnections ruled out in WW (to ~ 10%)
- Measurements at hadron colliders
- Different vacuum, colour in initial state  “colour promiscuity”?
- Underlying Event and Beam Remnants
- Intrinsic kT
- Lots of min-bias. Fragmentation tails  fakes!

- Example Problem:
- What is the non-perturbative
- uncertainty on the top mass?

## Large pT: Matching with QCD antennae. The VINCIA code

## Fixed Order + Resummation

- X=Anything (e.g. ttbar)
- PS=Parton Shower

- [ + FEHiP: NNLO (no PS) for pp hhγγ + jets ]

## New Approaches – Why Bother?

- MC@NLO:
- Used to think it was impossible! Giant step towards precision QCD 
- But complicated  tough to implement new processes  (just ask Carlo)
- “Only” gets first jet right (rest is PS) 
- Hardwired to HERWIG 
- CKKW & MLM:
- Best approach when multiple hard jets important.
- Retains LO normalization 
- Dependence on matching scale 
- CKKW@NLO: Nagy & Soper  ...
- MC with SCET: Bauer & Schwartz  ...

- Not easy to control theoretical error on exponentiated part (also goes for ARIADNE, HERWIG, PYTHIA, ...) 

## Perturbative expansion for some observable J, 			dm=0dm	;	dm= dm|M|2(J-J(k1,k2,...,km))
Assume 
We calculate some Matrix Elements d0 , d1 , ... dn  (w or w/o loops) 
And we have some approximation dn+1 ~ Tn n+1 dn (~ parton shower)
A ‘best guess’ cross section for J is then: 				dd0 + d1 + ... + dn (1 + Tn n+1 + Tn n+1Tn+1n+2 + ... )	            	dd0 + d1 + ... + dn Sn	; Sn= 1 + Tn n+1 Sn+1
For this to make sense, the Tn n+1 have to at least contain the correct singularities (in order to correctly sum up all logarithmically enhanced terms), but they are otherwise arbitrary. 
Now reorder this series in a useful way ...

- Assume
- We calculate some Matrix Elements d0 , d1 , ... dn  (w or w/o loops)
- And we have some approximation dn+1 ~ Tn n+1 dn (~ parton shower)
- A ‘best guess’ cross section for J is then: 				dd0 + d1 + ... + dn (1 + Tn n+1 + Tn n+1Tn+1n+2 + ... )	            	dd0 + d1 + ... + dn Sn	; Sn= 1 + Tn n+1 Sn+1
- For this to make sense, the Tn n+1 have to at least contain the correct singularities (in order to correctly sum up all logarithmically enhanced terms), but they are otherwise arbitrary.
- Now reorder this series in a useful way ...

- VINCIA – Basic Sketch

## Assume we know Hgg and Hggg. Then reorder:

d~ dgg + dggg Sggg					  	= Sggdgg + Sggg (dggg – Tgggggdgg)			= Sggdgg + Sggg dggg		(generalises to n gluons) 
I.e shower off gg and subtracted ggg matrix element. 
 	Double counting avoided since singularities (shower) 	subtracted in dggg .
The shower kernels, Tgg, are precisely the singular subtraction terms used in HO perturbative calculations. As a basis we use Gehrman-Glover antennae:

- d~ dgg + dggg Sggg					  	= Sggdgg + Sggg (dggg – Tgggggdgg)			= Sggdgg + Sggg dggg		(generalises to n gluons)
- I.e shower off gg and subtracted ggg matrix element.
-  	Double counting avoided since singularities (shower) 	subtracted in dggg .
- The shower kernels, Tgg, are precisely the singular subtraction terms used in HO perturbative calculations. As a _basis_ we use Gehrman-Glover antennae:

- Use 1=Sn-Tnn+1Sn+1

- Reordering Example: “H” gluons

-  Gehrmann-De Ridder, Gehrmann, Glover PLB612(2005)49

## CKKW (& friends) in a nutshell:
Generate a n-jet Final State from n-jet (singular) ME
Construct a “fake” PS history
Apply Sudakov weights on each “line” in history  from inclusive n-jet ME to exclusive n-jet (i.e. probability that n-jet remains n-jet above cutoff)  gets rid of double counting when mixed with other ME’s.
Apply PS with no emissions above cutoff

- Generate a n-jet Final State from n-jet (singular) ME
- Construct a “fake” PS history
- Apply Sudakov weights on each “line” in history  from _inclusive_ n-jet ME to _exclusive_ n-jet (i.e. probability that n-jet **remains** n-jet above cutoff)  gets rid of double counting when mixed with other ME’s.
- Apply PS with no emissions above cutoff

- _VINCIA in a nutshell:_
- Subtract PS singularities from n-jet ME (antenna subtraction)
- Generate a n-jet Final State from the subtracted (finite) ME.
- Apply PS with same antenna function  Leading Logs resummed
- + full NLO: divergent part already there  just include extra finite contribution in d= d0(0) + d1(0) + sing[d0(1)] + F(1) + ...
- + NNLO/NLL possible?
- + Easy to vary shower assumption
-  _first parton shower with ‘error band’!_ (novelty in itself)

- What is the Difference?

-  Gehrmann-De Ridder, Gehrmann, Glover JHEP09(2005)056

## Medium pT: Three new infinite families of parton showers

## Parton Showers: the basicsEssentially: a simple approximation  infinite perturbative orders

- Today, basically 2 (dual) approaches:
- Parton Showers (12, e.g. HERWIG, PYTHIA)
- and Dipole Showers (23, e.g. ARIADNE, VINCIA)

**Formally correct in **collinear** limit p****T(i) ****<< p****T(i-1)****,**** **but (very) approximate for hard emissions (we return to this)
- Depends on various phenomenological params (color screening cutoff, renorm. scale choice, ...)  compare to data ** ****‘best’ choice ~  `tune'**

## C++ code running: gluon cascade
Dipole shower with 3 different ordering variables:

- 			 ~ p2T;PYTHIA

- C++ code running: _gluon cascade_
- Dipole shower with 3 different ordering variables:

- RI(m12,m23) 	= 4 s12s23/s
- 			= p2T;ARIADNE

- RII(m12,m23) 	= 2 min(s12,s23)
- 			~ m2PYTHIA

- The VINCIA code

**VI**rtual **N**umerical **C**ollider with **I**nterfering **A**ntennae

- m23

- m12

**PS**

- Illustration with quarks, sorry

- 1

- 3

- 2

## The VINCIA code

- an infinite family of antenna  functions, all with correct collinear and soft behaviour:
- Using rescaled invariants:
- Our antenna function (a.k.a. radiation function, a.k.a. subtraction function) is:

- The VINCIA code

- Illustration with quarks, sorry

- 1

- 3

- 2

**VI**rtual **N**umerical **C**ollider with **I**nterfering **A**ntennae

- Changes to Gehrman-Glover:
-  ordinary DGLAP limit
-  First parton shower with systematic possibility for variation 		  (+ note: variation absorbed by matching!)

## The VINCIA code

-  Sudakov Factor contains integral over PS:

- The VINCIA code

**VI**rtual **N**umerical **C**ollider with **I**nterfering **A**ntennae

- Compact analytical solutions for types I and II (here without Cmn pieces)

## VINCIA – First Branching

- Starting scale Q = 20 GeV
- Stopping scale Qhad = 1 GeV
- ~ 1st order expansion in perturbation theory
- Axes: yab = m2ab / m2dipole

- Type I ~ pT2
- More collinear

- Type II ~ m2
- More soft

## Type I Sudakov (~ pT evolution) with C00 = -1,0,1

- VINCIA – Matching – kT jet rates

- _Matched: 2-jet + 3-jet ME_ + PS
- ~ matched Parton Shower_ _

- _2-jet only – no matching_
- ~ standard Parton Shower

## Construction of VINCIA shower MC
gluon shower MC 
based on LO, done! 
based on NLO, done! (but ‘trivial’ so far)
‘They’re just fooling around with it’ [T. Becher]
Including initial-state radiation ...
Including quarks ...
 Hadron collider shower MC
Higher orders: NNLO, NLL ?

- gluon shower MC
- based on LO, done!
- based on NLO, done! (but ‘trivial’ so far)
- ‘They’re just fooling around with it’ [T. Becher]
- Including initial-state radiation ...
- Including quarks ...
-  Hadron collider shower MC
- Higher orders: NNLO, NLL ?

- Outlook – VINCIA

- writeup in progress...

## Small pT: Colour Annealing in PYTHIA 6.4. First results

## Min-bias collisions at the Tevatron
Well described by Rick Field’s “Tune A” of PYTHIA
Theoretical framework is from 1987. I made some improvements.
Wanted to use “Tune A” as initial reference target
But it kept on being different ...

- Well described by Rick Field’s “Tune A” of PYTHIA
- Theoretical framework is from 1987. I made some improvements.
- Wanted to use “Tune A” as initial reference target
- But it kept on being different ...

- Motivation

- Multiplicity distribution OK (plus a lot of other things), but <pT>(Nch) never came out right  _something must be wrong or missing?_

## Multiplicity in string fragmentation ~ log(mstring)
More strings  more hadrons, but average pT stays same
Flat <pT>(Nch) spectrum ~ ‘uncorrellated’ underlying event
But if MPI interactions correlated in colour 

each scattering does not produce an independent string, 
average pT  not flat
Central point: multiplicity vs pT correllation probes color correllations! 
What’s so special about Tune A? 
It and all other realistic ‘tunes’ made turn out to have to go to the very most extreme end of the parameter range, with 100% correllation in final state. 

- Multiplicity in string fragmentation ~ log(mstring)
- More strings  more hadrons, but _average_ pT stays same
- Flat <pT>(Nch) spectrum ~ ‘uncorrellated’ underlying event
- But if MPI interactions correlated in colour
- each scattering does not produce an independent string,
- average pT  not flat
- Central point: multiplicity vs pT correllation probes color correllations!
- What’s so special about Tune A?
- It and all other realistic ‘tunes’ made turn out to have to go to the very most extreme end of the parameter range, with 100% correllation in final state.

- Sjöstrand & v Zijl  : Phys.Rev.D36:2019,1987  “Old” Pythia model

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

Prompted by CDF data and Rick Field’s ‘Tune A’ to reconsider. What do we know?
More prominent in hadron-hadron collisions? 
What is <pT>(Nch) telling us?
Top mass? 
Implications for LHC?

Problem: existing models only for e+e- WW

- Searched for at LEP
- Major source of W mass uncertainty
- Most aggressive scenarios excluded
- But effect still largely uncertain ~ 10%
- Prompted by CDF data and Rick Field’s ‘Tune A’ to reconsider. What do we know?
- More prominent in hadron-hadron collisions?
- What is <pT>(Nch) telling us?
- Top mass?
- Implications for LHC?
- Problem: existing models only for e+e- WW

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

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

## 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:

String formation for interacting string pieces determined by annealing-like minimization of  ‘Lambda measure’ (~string length~log(m)~N)

 good enough for order-of-magnitude

- At hadronisation time, each string piece has a probability to interact with the vacuum / other strings:
- String formation for interacting string pieces determined by annealing-like minimization of  ‘Lambda measure’ (~string length~log(m)~N)
-  good enough for order-of-magnitude

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

- Color Annealing

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

- First Results

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

-  Investigating effect on DØ top mass with D. Wicke (U. Wuppertal)

## Conclusions – Underlying Event

- Ever-present yet poorly understood part of QCD. How ‘good’ are current physical models?
- What’s the relation between min-bias and underlying events? Are there color reconnections? Are they more prolific in hadron collisions? Are there other collective phenomena? Does this influence top mass etc?
- New generation of models address more detailed questions: correllations, baryon flow, ... more?
- Energy Extrapolation largest uncertainty for LHC! RHIC pp collisions vital?  energy scaling
- Increasing interest, both among theorists and experimenters.

## Coming Soon!

- Recommended Reading:
- “Les Houches Guidebook to Monte Carlo Generators for hadron collider physics”: hep-ph/0403045
- “QCD (&) Event Generators” (DIS’05 minireview): hep-ph/0507129
- “QCD radiation in the production of high s-hat final states”: hep-ph/0511306
- “Colour Annealing – A Toy Model of Colour Reconnections”: in Les Houches ‘05 SMH proceedings