Recursive relations in MadGraph

Yoshitaro Takaesu (Sokendai, KEK)

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What is the Recursive Relation

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Off-shell R.R. for gluons in fixed color-order

Why do we use R.R. ?

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MG5 is Fantastic!

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from Johan’s talk

More Efficient than MG4

BUT still not satisfied!

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Because

For some processes, Generated HELAS codes

cannot be

compiled and calculated...

Multi-parton QCD processes

Especially for

Why codes for

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cannot be evaluated?

# of diagrams (Function Calls)

because of

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AMPs cannot be compiled

7,000

QCD processes with

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matrix.f gg > ng

Rearrangement of diagrams (AMPs) into JAMPstakes large amount of compilation time for many AMPs.

JAMPHELAS(AMP)

How can we go further?

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from Johan’s talk

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Recursive relation for gluonic subamp.

Reduce the # of diagrams (AMPs)

We added n-point off-shell R.R. subroutines to HELAS Library

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GLUON4_0.f, GLUON4_1.f, …

GLUON5_0.f, GLUON5_1.f, …...

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We also forbid gluon propagator between multi-gluon vertices to avoid double counting.

is also made by

For example,

4-point R.R. current

contains

2×(3-point R.R. currents).

Double counting

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Using those off-shell R.R. subroutines, We calculate JAMPs.

( OK but slow..)

Conclusion

• Generated Codes by MG5 for multi-partonQCD process cannot be compiled for more than 5 final states processes.

• Off-shell recursive relations helps us to reduce the # of AMPs and the size of the codes.

• We proposed a way to calculate gg > 5g, 6g, 7g processes by making use of the R.R. .

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Future works

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• Apply to processes with quarks,

qg > q ng, qq > qq ng

• Phase space integration and event generation

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