# Presentation: 431504

## Progress on VirColA Parton Shower MC based on Antenna Formalism

- W. Giele (Fermilab), D. Kosower (Saclay), P. Skands (Fermilab)

## QCD at High Energies

- Progress on VirCol

## QCD at High Energies

- LO
- NLO
- NNLO
- ...

- DGLAP
- BFKL

- LL
- NLL
- NNLL
- ...

- Diffraction
- Rapidity Gaps

- Hadronisation
- Hadron Decays

- Underlying Event
- Beam Remnants

- Parton Showers
- ME/PS Matching

- Flavour Physics

- EW/BSM/Higgs (+ Jets)
- EW/BSM/Higgs precision

**Event**** ****Generators**

- Progress on VirCol

## QCD at High Energies

- LO
- NLO
- NNLO
- ...

- DGLAP
- BFKL

- LL
- NLL
- NNLL
- ...

- Diffraction
- Rapidity Gaps

- Hadronisation
- Hadron Decays

- Underlying Event
- Beam Remnants

- Parton Showers
- ME/PS Matching

- Flavour Physics

- EW/BSM/Higgs (+ Jets)
- EW/BSM/Higgs precision

**Event**** ****Generators**

- Progress on VirCol

## Hard & Soft

_**Matrix Elements (Fixed Order):**_
- Fixed order in -> Exact interference, helicity, loops, ...
- At present can do 2->5/6 (less with loops)
- Perturbative expansion better at higher energy (asymptotic freedom)
- Multiple soft emissions important for full event structure = exclusive observables
- Widely separated scales -> big logs / big truncation errors.
- Phase space for soft emissions increases at high energies

- Progress on VirCol

## Hard & Soft

_**Matrix Elements (Fixed Order):**_
- Fixed order in -> Exact interference, helicity, loops, ...
- At present can do 2->5/6 (less with loops)
- Perturbative expansion better at higher energy (asymptotic freedom)
- Multiple soft emissions important for full event structure = exclusive observables
- Widely separated scales -> big logs / big truncation errors.
- Phase space for soft emissions increases at high energies

_**Parton Showers:**_
- Derived in universal limit of QCD  depend on universal parameters
- Exponentiate infinite O() ideal for widely separated scales (logs resummed)
- Arbitrary number of partons in final state match to hadronisation descriptions
- Derived in _limit_ (collinear) of QCD approx. for wide-angle / hard emissions.** **

- Progress on VirCol

## Hard & Soft

_**Matrix Elements (Fixed Order):**_
- Fixed order in -> Exact interference, helicity, loops, ...
- At present can do 2->5/6 (less with loops)
- Perturbative expansion better at higher energy (asymptotic freedom)
- Multiple soft emissions important for full event structure = exclusive observables
- Widely separated scales -> big logs / big truncation errors.
- Phase space for soft emissions increases at high energies

_**Parton Showers:**_
- Derived in universal limit of QCD  depend on universal parameters
- Exponentiate infinite O() ideal for widely separated scales (logs resummed)
- Arbitrary number of partons in final state match to hadronisation descriptions
- Derived in _limit_ (collinear) of QCD approx. for wide-angle / hard emissions.** **

- Marriage desireable!!

- Progress on VirCol

## Possible Ceremonies

- Merging (old) (HERWIG, PYTHIA, ARIADNE)
- Correct ‘hardest’ jet in parton shower to X+jet rate from ME. Hard to generalise.
- Tree-level ME/PS matching (ARIADNE, SHERPA, PATRIOT)
- Improve tree-level X+j, X+2j, X+3j, ... by Sudakov reweighting and parton showers. LO normalisation.
- NLO matching (MC@NLO)
- Match X (NLO) & X+jet (LO) to parton shower. Only 1 extra jet correct, not Lorentz invariant, hardwired to HERWIG + formalism somewhat cumbersome.
- + new ideas ... (Kramer+Soper, Nagy, Collins et al, VirCol, ...)

- Progress on VirCol

## Vircol – Basic SKETCH

- Perturbative expansion for some observable J, 			dm=0dm	;	dm= dm|M|2(J-J(k1,k2,...,km))
- Assume we know some Matrix Elements                                                	d0 , d1 , ... dn  	(w or w/o loops)
- And we have some approximation Tn n+1 , so that                     	dn+1 ~ Tn n+1 dn 	(~ parton shower)
- A ‘best guess’ cross section 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.
- We will now reorder this series in a useful way ...

- Progress on VirCol

## Reordering example: hgg

- Assume we know ME for 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 _modified_ ggg matrix element.
- Double counting avoided since singularities/shower subtracted in dggg .

- Use 1=Sn-Tnn+1Sn+1

- Progress on VirCol

## What IS THE Difference?

- 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 FS _remains_ n-jet above cutoff)  gets rid of double counting when mixed with other ME’s (Sudakov wt dampens singularity).
- Apply PS with no emissions above cutoff.

- VirCol 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  Leading Logs resummed.
- + full NLO: divergent part already there = unitarity of shower assumption  just include extra finite contribution in d0:		d= d0(0) + d1(0) + sing[d0(1)] + F(1) + ...
- + now NNLO/NLL possible  talks by Gehrmann, Gehrmann-De Ridder

- Progress on VirCol

## The ANTENNA Shower

- So far, we have written a C++ code that (for the moment) generates a pure gluon cascade ordered in:
- 	yR = 4sa1s1b/s2a1b = 4p2T;ARIADNE/sa1b
- ...with the antenna / subtraction function:
- 	|A(a,ba,1,b)|2 =
- 	2(sa1b(sa1+s1b)+sab2 )2/(sa1s1b(sa1bsab+sa1s1b)sa1b)
- 	 “usual” collinear limit, but different outside.
- This gives  an analytical Sudakov integral 				= [Mathematica output] .
- (No Matrix Elements yet ... but work in progress).

- Progress on VirCol

## The ANTENNA Shower

- So far, we have written a C++ code that (for the moment) generates a pure gluon cascade ordered in:
- 	yR = 4sa1s1b/s2a1b = 4p2T;ARIADNE/sa1b
- ...with the antenna / subtraction function:
- 	|A(a,ba,1,b)|2 =
- 	2(sa1b(sa1+s1b)+sab2 )2/(sa1s1b(sa1bsab+sa1s1b)sa1b)
- 	 “usual” collinear limit, but different outside.
- This gives  an analytical Sudakov integral 				= [Mathematica output] .
- (No Matrix Elements yet ... but work in progress).

- y1b

- ya1

- Collinear
- Soft

- Progress on VirCol

## Resolution & sharing

- Sudakov  yR for next branch  select phase space point along iso-yR contour:
- Rewrite Antenna function in terms of y2=yR ; =(sa1+s1b)/y :
- Partial-fraction singular structure + overestimate numerators  generate uniform R and solve for R:

- Progress on VirCol

## Resolution & sharing

- Sudakov  yR for next branch  select phase space point along iso-yR contour:
- Rewrite Antenna function in terms of y2=yR ; =(sa1+s1b)/y :
- Partial-fraction singular structure + overestimate numerators  generate uniform R and solve for R:

- Progress on VirCol

## Resolution & sharing

- Q1: Where’s the soft singularity?

- Progress on VirCol

## Resolution & sharing

- Q1: Where’s the soft singularity?

-  A1: Sudakov suppressed, (sum of ordered branching probs  unordered probability)

- Progress on VirCol

## Resolution & sharing

- Q1: Where’s the soft singularity?
- Q2: Is that a ‘dead region’ ?

- Progress on VirCol

## Resolution & sharing

- Q1: Where’s the soft singularity?
- Q2: Is that a ‘dead region’ ?

-  A2: Yes, it is cut out by ‘unresolution criterion’, i.e. that neighbour dipoles remain resolved after branching.
- Due to Hgg in colour singlet state! (pathological)
- Eventually, could be filled by Matrix Elements and/or by changing evolution var.

- Progress on VirCol

## Preliminary Results

- Thrust and 3-jet rate, compared to Q2-ordered and pT2-ordered PYTHIA showers.

- Preliminary: matrix elements should be added and parton-level matched to hadronisation models eventually + all showers only include gluons here...

- Progress on VirCol

## Conclusion & Outlook

- Construction of VIRCOL shower monte carlo:
-          gluons shower MC (based on LO, done!)
-          gluons shower MC (based on NLO)
-          parton shower MC (LO/NLO(/NNLO))
-          parton shower MC (NLL + NLO/NNLO)
- Hadron collider shower MC’s
- Higher order Sudakov factor calculations(this will reduce a lot of implicit and explicit uncertainties: e.g. renormalization scale, choice of subtraction function,...)

- Progress on VirCol