Matching of Matrix Elements and Parton Showers CKKW matching in e + - - PowerPoint PPT Presentation

Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure

Matching of Matrix Elements and Parton Showers Lecture 2: Matching in e+e− collisions

Johan Alwall

Theoretical Physics, SLAC HELAS/MadGraph Workshop, KEK, 18-27 Oct 2006

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure

Why Matching?

1

Why Matching?

2

Present matching approaches

3

CKKW matching in e+e− collisions

4

The MLM procedure

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure

Why Matching?

Matrix element and Parton shower approaches complementary. Want to combine them without double-counting!

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches The Pythia approach The Herwig approach CKKW matching in e+e− collisions The MLM procedure

Present matching approaches

1

Why Matching?

2

Present matching approaches The Pythia approach The Herwig approach

3

CKKW matching in e+e− collisions

4

The MLM procedure

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches The Pythia approach The Herwig approach CKKW matching in e+e− collisions The MLM procedure

The Pythia approach

Pythia uses a virtuality-ordered shower, similar to the descriptions presented last

• lecture. In the Pythia shower, the first emission is corrected such that its

kinematical distribution corresponds to the matrix element expression for a number of simple processes (1 → 2 or 2 → 1-processes). The procedure is as follows:

1

Choose a starting scale for the (forward final-state or backward initial-state) showering corresponding to the total amount of available energy in the event s.

2

With the kinematics of the Pythia parton shower, this choice of starting scale ensures that the first radiation will over-populate the whole phase-space (above the cut-off).

3

The produced radiation is then kept with a probability dσME/dσPS

4

If the radiation is rejected, the shower evolution is continued from the rejected t value onwards (the veto algoritm)

Examples of ME-improved processes in Pythia

Final-state: Z 0 → q¯ q, t → bW +, h → q¯ q, ... Initial-state: q¯ q → Z, W +, γ∗ and gg → h (in heavy top limit)

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches The Pythia approach The Herwig approach CKKW matching in e+e− collisions The MLM procedure

The Herwig approach

The Herwig shower uses the branching angle as evolution variable. This corresponds to explicitly taking into account the coherence effects, due to interference between soft gluon emissions from different legs, giving strict angular ordering (towards smaller emission angles), while it is not ordered in kT

• r virtuality.

In Pythia, coherence effects are taken into account “post-facto” by vetoing increasing angles in the emission.

In Herwig, this gives rise to “dead cones”, where there is no emission at all from the parton showers. The matrix element corrections of Herwig is applied to the dead cones, and to all emissions which are found to be the “hardest so far”, since there the first emission does not necessarily have the highest kT .

Examples of ME-improved processes in Herwig

Some e+e− processes, DIS, top decay, Drell-Yan, gg → h (in heavy top limit)

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

CKKW matching in e+e− collisions

1

Why Matching?

2

Present matching approaches

3

CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations

4

The MLM procedure

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

CKKW matching in e+e− collisions

Previous methods for matching ME and PS are restricted to certain processes (or classes of processes) and only allowed the matching of the first emission (or a fixed number of emissions). The CKKW (Catani-Krauss-Kuhn-Webber) algorithm for ME-PS matching in e+e− collisions is constructed to allow corrections of (in principle) any number

• f emissions.

The method is constructed to use matrix elements to describe the distribution

• f particle with a phase-space separation yij > ycut (using some jet separation

measure y), and parton showers to describe particles with a smaller separation then ycut. For e+e−, the procedure uses the infrared-safe Durham (or kT ) jet measure: yij = 2 min “ E 2

i , E 2 j

” (1 − cos θij)/E 2

cm

The procedure ensures that the matrix elements behave as parton showers close to the cut-off, while the parton shower is vetoed above the cut-off in such a way that there is no dependence on the chosen cut-off value to NLL order = ⇒ smooth passage between regions described by parton showers and matrix elements

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Overview of the CKKW procedure

The procedure to generate configurations in e+e− → n jets at a c.m. energy Q0 = ECM and jet resolution yini can be summarized as follows:

1

Select the jet multiplicity n and parton identities i with probability P(n, i) = σn,i Pk=N

k,j

σk,j where σn,i is the tree-level e+e− → n-jet cross section with the strong coupling calculated as αs(dini) (dini = Q0√yini)

2

Pick parton momenta according to the n-parton matrix elements squared |Mn,i|2, still using fixed αs(dini), with jet resolution cut-off yini

3

Cluster the event to find the parton-shower history corresponding to the event and the splitting node resolution values dj = Q0√yj for each jet (j > 2)

4

For each strong node (vertex) dk, apply a coupling-constant weight of αs(dk)/αs(dini) < 1.

5

For each quark or gluon line running between two nodes dj > dk (where dk can be the cut-off scale dini), apply a Sudakov weight factor ∆i(dj)/∆i(dk) < 1.

6

Accept or reject the configuration according to the combined weight.

7

If the configuration is accepted, perform parton showers starting from the generation scale of the parton, but vetoed above yini

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Clustering the n-jet event

1

Find the two partons with smallest jet separation yij

2

If partons allowed to cluster by QCD splitting rules: combine partons to new particle (e.g. q¯ q → g, qg → q)

3

Iterate 1-2 until 2 → 2 process reached (e+e− → q¯ q) With the choice of the Durham jet measure, the jet separations di = √yiQ0 at each branching corresponds closely to the kT of that branching, and is therefore suitable to use as argument for αs in the branching.

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Sudakov reweighting

You have already seen (in the first lecture) that the argument for αs in each parton emission should be the relative kT of the splitting partons, motivating the αs reweighting. But why do we need the Sudakov reweighting? The probability for a parton generated at a scale di not to radiate above the scale dini is given by the Sudakov ∆(di, dini). If we define a jet as a shower of particles with y < yini, that parton will give rise to exactly one jet. So, in order to find the cross-section where each outgoing parton gives rise to exactly one jet, we must weight each event by the product of Sudakovs ensuring that no leg radiates above the scale dini. In the example to the right, the combined Sudakov weight is ∆q(d3, dini) ∆q(d3, dini) ∆q(d2, dini) ∆q(d2, dini)× × ∆g(d2, dini) ∆g(d1, dini) ∆q(d1, dini)∆q(d1, dini) = = [∆q(d3, dini)]2 ∆g(d2, dini) ∆g(d1, dini) ∆q(d1, dini)∆q(d1, dini) Note that the quark Sudakovs always end up going all the way to dini.

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Vetoed parton showers

What remains after αs and Sudakov reweighting of the multi-jet event is to generate the parton showers below the cut-off yini. Naively one could think that one just has to generate the showers with starting scale dini = Q√yini. However, this would give a deficit of radiation close to the cutoff, due to a more restricted available angular region (remember angular

• rdering!): for a d1 < dini

∆q(Q0, dini)∆q(dini, d1) = ∆q(Q0, d1) We therefore need to allow the showers to evolve from the highest scale Q0, but veto any radiation with y > yini – the radiation is forbidden but the scale and angles are reset as if the radiation had occurred.

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

For a quark generated at the scale Q, the probability for no radiation between Q and d1 < dini is the sum of probabilities for 0, 1, 2, ... vetoed branchings above dini: ∆q(Q, d1)+ Z Q

dini

dq Γq(q, Q) ∆q(Q, d1) ∆q(q, d1) ∆q(q, d1) + Z Q

dini

dq Γq(q, Q) Z q

d1

dq′ Γq(q′, Q) ∆q(Q, d1) ∆q(q, d1) ∆q(q, d1) ∆q(q′, d1) ∆q(q′, d1) + · · · = ∆q(Q, d1) exp Z Q

dini

dq Γq(Q, q) ! = ∆q(Q, d1)/∆q(Q, dini) The factor 1/∆q(Q, dini) is cancelled by the Sudakov weight ∆q(Q, dini) given to the quark line. So we end up with the correct probability ∆q(Q, d1) that there are no emissions along the line between Q and d1. We also see that The veto procedure × Sudakov suppression × αs reweighting removes the dependence on yini (to NLO accuracy)

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Starting scales for the vetoed showers

To get the correct cancellation of the yini dependence between Sudakov suppression and the vetoed showers, the starting scale for the vetoed shower of each parton line must be the same as the scale of the total Sudakov suppression for that line (see slide 11). For quarks created in the hard scattering, it is the scale of the hard

• scattering. Note that quarks always survive all the way down to yini

For gluons created from quarks, which don’t split further, it’s the scale at the node of creation For g → gg splitting, the harder of the gluons is considered to have the scale of the mother gluon, while the softer of the gluons has the scale of the g → gg node For g → q¯ q (the only subtlety): This branching only contributes at NLL

• level. If we use the mother gluon scale for both the quark and the

anti-quark this intruduces only a small error of relative order 1/N2

c (since

we approximate the color factor CA by 2CF ).

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Example of shower generation and starting scales

1

Showering from the quark and anti-quark originating from the photon vertex is started from the scale d3 = √s

2

Showering from the quark and anti-quark coming from the gluon splitting has the starting scale d2 of the node where the gluon is generated.

3

A further gluon coming e.g. from the lower quark leg would shower starting from the scale of the node where the gluon is generated.

4

All showering is vetoed above the scale dini.

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Highest multiplicity treatment

It was later realized that there is a problem in the procedure: Say that the highest multiplicity generated by matrix elements is N. If we then look at the jet rate for N → N + 1 jets after showering and matching, it will be cut-off at yini, since no radiation is allowed from the N-jet sample above he scale yini. This gives a deficit of radiation as compared to if we would have included also the N + 1-parton matrix element. This can be easily remedied in the following way: If the event belongs to a sample with multiplicity < N, perform Sudakov reweighting and veto the PS radiation as usual If the event belongs to the highest multiplicity sample, replace dini by the smallest clustering scale (Q1 in the example to the right). Veto the PS radiation only above the same smallest clustering scale, and allow all radiation below this scale We then let the parton shower mimic the contributions from all higher multiplicity matrix elements.

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Results of CKKW matching (Sherpa)

The authors of the CKKW paper implemented the matching using the parton shower generator APACIC++, with the modification that: The initial probability for choosing the different jet multiplicities are modified by multiplying the argument of αs by factors κi, different for the different jet multiplicities The parton shower is of Pythia kind: leading log virtuality-ordered with angular ordering imposed, rather than NLL The PS veto is however in kT (as in the recipie) Note that the following figures are made after hadronization, giving a considerable smearing of jet quantities

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Results of CKKW matching (Sherpa)– 1

10

• 3

10

• 2

10

• 1

1 10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Delphi 91 GeV APACIC++ v.1.1 Pythia 6.1 Ariadne 4.08 Herwig 6.1 1-Thrust 1/N dN/dT 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1-Thrust MC/Data 10

• 2

10

• 1

1 10 0.1 0.2 0.3 0.4 0.5 0.6 Delphi 91 GeV APACIC++ v.1.1 Pythia 6.1 Ariadne 4.08 Herwig 6.1 Major 1/N dN/dM 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 Major MC/Data 10

• 1

1 10 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Delphi 91 GeV APACIC++ v.1.1 Pythia 6.1 Ariadne 4.08 Herwig 6.1 Minor 1/N dN/dm 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Minor MC/Data

• Fig. 1: Thrust, Major and Minor at LEP I

– Sherpa compared to PS generators

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Results of CKKW matching (Sherpa)– 2

10

• 3

10

• 2

10

• 1

1 10 10 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Delphi 91 GeV APACIC++ v.1.1 Pythia 6.1 Ariadne 4.08 Herwig 6.1 Differential 3→2 1/N dN/dy 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Differential 3→2 MC/Data 10

• 3

10

• 2

10

• 1

1 10 10 2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Delphi 91 GeV APACIC++ v.1.1 Pythia 6.1 Ariadne 4.08 Herwig 6.1 Differential 4→3 1/N dN/dy 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Differential 4→3 MC/Data 10

• 2

10

• 1

1 10 10 2 10 3 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Delphi 91 GeV APACIC++ v.1.1 Pythia 6.1 Ariadne 4.08 Herwig 6.1 Differential 5→4 1/N dN/dy 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Differential 5→4 MC/Data

• Fig. 2: Differential jet rates (3 → 2, 4 → 3, 5 → 4) at LEP I

– Sherpa compared to PS generators

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Results of CKKW matching (Sherpa)– 3

log(y)

• 2

10

• 1

10 1 SHERPA1

3 → 2

Y

Hadron level

log(y)

• 4.5
• 4
• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5
• 0.2

0.2

log(y)

• 2

10

• 1

10 1 SHERPA1

5 → 4

Y

Hadron level

hadrons →

• e

+

e 2 jet ME 3 jet ME 4 jet ME 5 jet ME

log(y)

• 5 -4.5
• 4 -3.5
• 3 -2.5
• 2 -1.5
• 1 -0.5
• 0.5

0.5

• Fig. 3: Differential jet rates (2 → 3, 4 → 5) at LEP I

– Sherpa with two different yini (solid lines: 10−2.5, dashed lines: 10−2.0)

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Difficulties with practical implementations– 1

In practical implementations of the CKKW procedure, there are a few difficulties which one must bear in mind: The procedure assumes NLL parton densities – however, all parton shower implementations are at improved LL level. Therefore the Sudakovs used must be adapted to the actual parton shower, which is non-trivial since the parton showers don’t always have an analytic formulation. The CKKW procedure (as far as I’ve understood) uses the Durham kT as evolution variable – the different shower implementations use virtuality or θE (except Ariadne, which uses dipole showers, and the new kT -ordered shower of Pythia). This means that the vetoed showers are non-trivial to accomplish, since one cannot just make a cut in the evolution variable. At least in the Pythia shower (both old and new!), subsequent branchings will change the kT of a given emission – so the shower should need to be developed completely before performing the veto.

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions Overview of the CKKW procedure Clustering the n-jet event Sudakov reweighting Vetoed parton showers Highest multiplicity treatment Results of CKKW matching (Sherpa) Difficulties with practical implementations The MLM procedure

Difficulties with practical implementations– 2

Also the kT ordered showers (Ariadne and the new Pythia shower) are not trivial to use: For Ariadne, the showering is done from dipoles, i.e. using 2 → 3 branchings rather than 1 → 2 branchings as in the original CKKW formulation For Pythia, the evolution variable is not the Durham kT , but closer to the LUCLUS measure d2

ij = 1

2 (|pi| |pj|−pi ·pj) 4 |pi| |pj| (|pi| + |pj|)2 = 4 |pi|2 |pj|2 sin2(θij/2) (|pi| + |pj|)2 ≈ |pi × pj| |pi + pj| Although the same for small kT , does make a significant difference for larger kT . = ⇒ Need to modify the Sudakovs to incorporate these differences

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

The MLM procedure

1

Why Matching?

2

Present matching approaches

3

CKKW matching in e+e− collisions

4

The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

The MLM procedure

One problem discussed in the last slides is that the Sudakov form factor must describe the actual probability that there is no radiation in the parton shower used. Another difficulty is to make an efficient veto in the parton shower Michelangelo L. Mangano (author of AlpGen) suggested a very simple solution the the two problems: Use the parton shower itself to generate the Sudakov suppression AND the vetoed shower in “one go”

1

Begin by picking a subprocess and momenta in the same way as in the CKKW algorithm

2

Cluster the event

3

Perform αs reweighting

4

Perform showering, using s as starting scale

5

Perform a jet algorithm on the showered particles (before hadronization!)

6

Match matrix-element outgoing partons with the jets such that each ME parton corresponds to exactly one reconstructed jet

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

Jet-parton matching

Collinear double-log double counting Event matched, Njet = Npart = 3 – Keep event Not matched, Njet = Npart = 3 but Nmatched = 2 – throw away Soft single-log double counting Event matched, but Njet > Npart – Keep for highest-multiplicity sample only Solid lines = ME partons Broken lines = PS partons

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

MLM versus CKKW matching

Formally, the MLM matching should give exactly the same result as CKKW for the same parton showers: The events are still suppressed by exactly the same Sudakovs as in the CKKW, since they are discarded if there is radiation above the scale dini The probability for no radiation above the scale d1 < dini is simply ∆(Q0, dini), as wanted. The advantage with the MLM method is its simplicity: There is no need to implement vetoing into presently existing parton shower generators (where the parton showers are optimized to work with the hadronization routines) It is not necessary to find an analytical form for the Sudakov form factor used in practice by the parton shower The main advantage of the CKKW method is in efficiency: In the CKKW procedure it’s possible to include the Sudakov reweighting in the generation procedure, meaning that no events at all need to be discarded after generation In the MLM procedure, the Sudakov suppression method means that events must necessarily be discarded after being fully showered, making generation less efficient (lose 30% − 70% of the events, depending on cutoff scale)

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

Difficulties in MLM matching using Pythia

The Pythia authors have been kind enough to provide a routine that allows the vetoing of events after the parton shower but before decays, hadronization and underlying event addition, which makes it suitable for MLM matching. This routine works however (do far) only for the “old” virtuality-ordered shower, and not for the new kT -ordered shower. Therefore mathing is done with the old shower. There are certain problems one must keep in mind when matching to the Pythia parton showers (and probably also with Herwig showers): In the Pythia shower the kT of the showering partons is shifted. Therefore it is necessary to generate the hard events with a more generous cut (e.g. lower in the jet measure d) than is used in the vetoing after parton showers In order to get the correct Sudakov suppressions, the final state showering

• f different partons should start at different scales. This is not

implemented in the old showers (but it is in the new showers) Note that it is possible to study the effects of changing the cutoff scale without rerunning MadEvent, as long as the cutoff scale after the parton showers is larger than the cutoff in the ME generation. More about MLM matching next lecture!

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

To be continued.... (next time: Hadronic collisions!)

Tutorial 2

Note! Before today’s tutorial, you will need to download a new version of the Pythia-PGS library from the Roma server (brand new fixes implemented!) http://madgraph.roma2.infn.it/Downloads/downloads.html During the tutorial, I will ask you to look closer at matching of matrix elements and parton showers at e+e− colliders

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Lecture 2: Matching in e+e− collisions Why Matching? Present matching approaches CKKW matching in e+e− collisions The MLM procedure Jet-parton matching MLM versus CKKW matching Difficulties in MLM matching using Pythia

Bibliography

• S. Catani, F. Krauss, R. Kuhn and B. R. Webber, “QCD matrix elements

+ parton showers,” JHEP 0111, 063 (2001) [arXiv:hep-ph/0109231].

• A. Schalicke and F. Krauss, “Implementing the ME+PS merging

algorithm,” JHEP 0507, 018 (2005) [arXiv:hep-ph/0503281]. M.L. Mangano, “Merging multijet matrix elements and shower evolution in hadronic collisions,” http://cern.ch/∼mlm/talks/lund-alpgen.pdf

• S. Hoche, F. Krauss, N. Lavesson, L. Lonnblad, M. Mangano, A. Schalicke

and S. Schumann, “Matching parton showers and matrix elements,” arXiv:hep-ph/0602031.

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