ggi october 2007 red, blue, and green things with antennae peter skands cern & fermilab in...

GGI October 2007

Red, Blue, and Green ThingsWith Antennae

Peter Skands

CERN & Fermilab

In collaboration with W. Giele, D. Kosower

Giele, Kosower, PS : hep-ph/0707.3652 ; Sjöstrand, Mrenna, PS : hep-ph/0710.3820)

Peter Skands Red, Blue, and Green Things with Antennae 2

AimsAims► We’d like a simple formalism for parton showers that allows:

1. Extensive analytical control, including systematic uncertainty estimates

2. Combining the virtues of CKKW (Tree-level matching with arbitrarily many partons) with those of MC@NLO (Loop-level matching)

3. To eventually go beyond Leading-NC+Leading-Log?

► Two central ingredients

• A general QCD cascade based on exponentiated antennae a generalized “ARIADNE”

• Extending the ideas of subtraction-based ME/PS matching “MC@NLO” with antennae

• Plus works for more than 1 hard leg Simultaneous matching to several tree- or 1-loop matrix elements


Monte Carlo Basics

High-dimensional problem (phase space)

Monte Carlo integration

+ Formulation of fragmentation as a “Markov Chain”:

1. Parton Showers: iterative application of perturbatively calculable splitting kernels for n n+1 partons ( = resummation of soft/collinear logarithms) Ordered evolution.

2. Hadronization: iteration of X X + hadron, at present according to phenomenological models, based on known properties of QCD, on lattice, and on fits to data.

Principal virtues

1. Stochastic error O(N-1/2) independent of dimension

2. Universally applicable

3. Fully exclusive final states (for better or for worse – cf. the name ‘Pythia’ … )

44 no separate calculation needed for each observable

5. Have become indispensable for experimental studies. Exclusivity possible to calculate a detector response event by event.


►Iterative (Markov chain) formulation = parton shower• Generates leading “soft/collinear” corrections to any

process, to infinite order in the coupling

• The chain is ordered in an “evolution variable”: e.g. parton virtuality, jet-jet angle, transverse momentum, …

a series of successive factorizations the lower end of which can be matched to a hadronization description at some fixed low hadronization scale ~ 1 GeV

BasicsBasics


Improved Event GeneratorsImproved Event Generators► Step 1: A comprehensive look at the uncertainty

• Vary the evolution variable (~ factorization scheme)

• Vary the radiation function (finite terms not fixed)

• Vary the kinematics map (angle around axis perp to 23 plane in CM)

• Vary the renormalization scheme (argument of αs)

• Vary the infrared cutoff contour (hadronization cutoff)

► Step 2: Systematically improve it

• Understand the importance of each and how it is canceled by • Matching to fixed order matrix elements

• Higher logarithms, subleading color, etc, are included

► Step 3: Write a generator

• Make the above explicit (while still tractable) in a Markov Chain context matched parton shower MC algorithm

Subject of this talk


Example: Z decaysExample: Z decays► Dependence on evolution variable


Example: Z decaysExample: Z decays► Dependence on evolution variable

Using

αs(pT),

pThad = 0.5 GeV

αs(mZ) = 0.137

Nf = 2

for all plots

Note: the default Vincia antenna functions reproduce the Z3 parton matrix element;

Pythia8 includes matching to Z3

Beyond the 3rd parton, Pythia’s radiation function is slightly larger, and its kinematics and hadronization cutoff contour are also slightly different


The main sources of uncertaintyThe main sources of uncertainty► Things I can tell you about:

• Non-singular terms in the radiation functions

• The choice of renormalization scale

• (The hadronization cutoff)

► Things I can’t (yet) tell you about

• Effects of sub-leading logarithms

• Effects of sub-leading colours

• Polarization effects


VINCIAVINCIA

► VINCIA shower

• Final-state QCD cascades• At GGI completed (massless) quarks

• Plug-in to PYTHIA 8.1 (C++)

• + working on initial state …

► So far:

• 2 different shower evolution variables:• pT-ordering (~ ARIADNE, PYTHIA 8)

• Mass-ordering (~ PYTHIA 6, SHERPA)

• For each: an infinite family of antenna functions • Laurent series in the branching invariants: singular part fixed by QCD, finite terms arbitrary

• Shower cutoff contour: independent of evolution variable IR factorization “universal”

• Phase space mappings: 2 different choices implemented • Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler

Dipoles – a dual description of QCD

1

3

2

VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE

Giele, Kosower, PS : hep-ph/0707.3652Gustafson, Phys. Lett. B175 (1986) 453

Lönnblad, Comput. Phys. Commun. 71 (1992) 15.


The Pure Shower ChainThe Pure Shower Chain► Shower-improved distribution of an observable:

► Shower Operator, S (as a function of “time” t=1/Q)

► n-parton Sudakov

► Focus on antenna-dipole showersDipole branching phase space

“X + nothing” “X+something”

Giele, Kosower, PS : hep-ph/0707.3652


Dipole-Antenna FunctionsDipole-Antenna Functions► Starting point: “GGG” antenna functions, e.g.,

► Generalize to arbitrary Laurent series (at GGI):

► Can make shower systematically “softer” or “harder”

• Will see later how this variation is explicitly canceled by matching

quantification of uncertainty

quantification of improvement by matching

• (In principle, could also “fake” other showers)

yar = sar / si

si = invariant mass of i’th dipole-antenna

Giele, Kosower, PS : hep-ph/0707.3652

Gehrmann-De Ridder, Gehrmann, Glover, JHEP 09 (2005) 056

Singular parts fixed, finite terms arbitrary


MatchingMatching

Fixed Order (all orders)

Matched shower (including simultaneous tree- and 1-loop matching for any number of legs)

Tree-level “real” matching term for X+k

Loop-level “virtual” matching term for X+k

Pure Shower (all orders)


Tree-level matching to X+1Tree-level matching to X+1► First order real radiation term from parton shower

► Matrix Element (X+1 at LO ; above thad)

Matching Term:

variations in finite terms (or dead regions) in A canceled by matching at this order

• (If A too hard, correction can become negative negative weights)

► 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

Inverse kinematics map = clustering


1-loop matching to X1-loop matching to X► NLO “virtual term” from parton shower (= expanded Sudakov: exp=1 - … )

► Matrix Elements (unresolved real plus genuine virtual)

► Matching condition same as before (almost):

► May be automated ?, anyway: A is not shower-specific• Currently using Gehrmann-Glover (global) antenna functions

• You can choose anything as long as you can write it as a Laurent series

Tree-level matching just corresponds to using zero• (This time, too small A correction negative)


FromFrom to !to !► The unknown finite terms are a major source of uncertainty

• DGLAP has some, GGG have others, ARIADNE has yet others, etc…

• They are arbitrary (and in general process-dependent)

Using αs(MZ)=0.137, μR=1/4mdipole, pThad = 0.5 GeV


Tree-level matching to X+1Tree-level matching to X+1► First order real radiation term from parton shower

► Matrix Element (X+1 at LO ; above thad)

Matching Term:

variations in finite terms (or dead regions) in A canceled by matching at this order

• (If A too hard, correction can become negative negative weights)


Phase Space PopulationPhase Space Population

Soft Standard Hard

Matched Soft Standard Matched Hard

Positive correction Negative correction


FromFrom to !to !► The unknown finite terms are a major source of uncertainty

• DGLAP has some, GGG have others, ARIADNE has yet others, etc…

• They are arbitrary (and in general process-dependent)



Note about “NLO” matchingNote about “NLO” matching► Shower off virtual matching term uncanceled O(α2) contribution

to 3-jet observables (only canceled by 1-loop 3-parton matching)

► While normalization is improved, shapes are not (shape still LO)



What to do next?What to do next?► Go further with tree-level matching

• Demonstrate it beyond first order (include H,Z 4 partons)• May require “true Markov” evolution and/or “sector” antenna functions?

• Automated tree-level matching (w. Rikkert Frederix (MadGraph) + …?)

► Go further with one-loop matching

• Demonstrate it beyond first order (include 1-loop H,Z 3 partons)• Should start to see cancellation of ordering variable and renormalization scale• Should start to see stabilization of shapes as well as normalizations

► Extend the formalism to the initial state

► Extend to massive particles

• Massive antenna functions, phase space, and evolution

► Investigate possibilities for going beyond traditional LL showers:

• Subleading colour, NLL, and polarization


Last SlideLast Slide

Thanks to the organizersThanks to the organizers• A. Brandhuber (Queen Mary University, London), A. Brandhuber (Queen Mary University, London),

• V. Del Duca (INFN, Torino),V. Del Duca (INFN, Torino),

• N. Glover (IPPP, Durham),N. Glover (IPPP, Durham),

• D. Kosower (CEA, Saclay),D. Kosower (CEA, Saclay),

• E. Laenen (Nikhef, Amsterdam), E. Laenen (Nikhef, Amsterdam),

• G. Passarino (University of Torino),G. Passarino (University of Torino),

• W. Spence (Queen Mary University, London),W. Spence (Queen Mary University, London),

• G. Travaglini (Queen Mary University, London),G. Travaglini (Queen Mary University, London),

• D. Zeppenfeld (University of Karlsruhe) D. Zeppenfeld (University of Karlsruhe)

ggi october 2007 red, blue, and green things with antennae peter skands cern & fermilab in...

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