Slide 1 of 5

Taday’s lecture

† NLL corrections

† Inclusive mode for highest multiplicity sample

† Simplified MLM

Literature:

S. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP (2001) 063

S. Höche, F, Krauss, N. Lavesson, L. Lönnblad, M. Mangano, A. Schälicke, S. Schumann,

hep-ph/o602031

Various details (improvements) about CKKW and MLM

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Slide 2 of 5

Quark-antiquark pair production

F H4LIQ2, t m32, m4

2M = Dq IQ2 tMµDq IQ2 tMDq Imè12 tM

Dq Imè12 tMµDg Im32 tMDg Im42 tM

µDq Im42 tMµDq Im42 tM = ADq IQ2 tME2 µDg Im32 tMµDf Im42 tM

m32

m42

R4IQ2, tM = 2‡t

Q2

dm32 ‡

t

m32

dm42 Gq IQ2, m3

2M Gf Im42M F IQ2, t m32, m4

2M

Df Im42 tM = ADq Im42 tME2 ëDg Im42 tMwhere

where Gf Im2M =1m2

as Im2M2 p

Nf

3

Algorithm:

1. "Gluonic" vetoed parton shower in the direction pØ

q + pØ

q

evolves from mg2 (gluon was born) to mq q2 (pair was born),

so that mg2 > mq q2

2. Two quark vetoed parton showers in the directions

pØ

q and pØ

q evolve from mq q2 to t.

Simplified algorithm:

1. Two quark vetoed parton showers in the direction pØ

q and pØ

q

evolve from mg2 to t.

It corresponds to the replacement CA to 2CF in the coherent part,

but overall contribution is NLL

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Slide 3 of 5

Highest multiplicity sample

¤ Common problem is that jets above resolution scale tini are produced by ME-generator.

Thus number of jets at tini is always smaller than Nmax – maximal parton multiplicity

¤ The solution for CKKW (for highest multiplicity sample n = Nmax):

1. Generate n-parton event by ME-generator with kT2 > tini

2. For the construction of Sudakov factor use mn2 (minimal nodal value of kT2) instead of tini

3. Run PS with veto kT2 > mn2

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Slide 4 of 5

MLM-like algorithm

1. Obtain n-parton event by an ME-generator IkT2 > tini)

2. Run kT -clustering algorithm to find nodal

values 9m22 = Q2, m32..,mn2}

3. Reweight the event:

w = as Im32M .. as Imn2M ë Aas Itini2 MEn-2 F IQ2, tini m32, .. mn

2M

4. For each final state paton find the node

where the parton was born mborn2 .

5. Generate n vetoed parton showers in

the directions of the primary partons,

so that the inital condition for each PS is mborn2

1. Obtain n-parton event by an ME-generator IkT2 > tini)

2. Run kT -clustering algorithm to find nodal

values 9m22 = Q2, m32..,mn2}

3. Reweight the event: w = as Im32M .. as Imn2M ë @as HtiniLDn-2

4. For each final state paton find the node

where the parton was born mborn2 .

5. Generate n parton showers in

the directions of the primary partons,

so that the inital condition for each PS is mborn2

6. Run kT -clustering algorithm to find all jets

at the resolution scale tini

7. If all the jets match primary partons then accept

the event, else reject everything and go to step 1.

CKKW MLM-like

¤ Each event generated by ME with reweighting yields

a showered events

¤ Some events generated by ME are rejected that is equivalent

to the CKKW reweighting snH0L Ø sn

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Slide 5 of 5

MLM-like algorithm

Matched, accepted Mismatched, rejected

Mismatched, but can be acepted

for highest multiplicity sample

jet found

¤ MLM doesn't use analytic Sudakov factors nor vetoed PS.

(rejection probability is Sudakov factor calculated by MC-integration)

¤ ME-generator can produce sample with another (relaxed ?) separation

among partons (like DR jj > Rmin). Then one can use simple jet cone

algorithm with cone size Rmin to find jets.

¤ «If the distance between the parton and the jet centroid is smaller

than Rmin, the parton and the jet match»

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