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Recursive relations in MadGraph
Yoshitaro Takaesu (Sokendai, KEK)
November 2, 2016 1Y. Takaesu - Recursive relations in MG
What is the Recursive Relation
November 2, 2016 Y. Takaesu - Recursive relations in MG 2
Off-shell R.R. for gluons in fixed color-order
Why do we use R.R. ?
November 2, 2016 Y. Takaesu - Recursive relations in MG 3
MG5 is Fantastic!
November 2, 2016 Y. Takaesu - Recursive relations in MG 4
from Johan’s talk
More Efficient than MG4
BUT still not satisfied!
November 2, 2016 Y. Takaesu - Recursive relations in MG 5
Because
For some processes, Generated HELAS codes
cannot be
compiled and calculated...
Multi-parton QCD processes
Especially for
Why codes for
November 2, 2016 Y. Takaesu - Recursive relations in MG 6
cannot be evaluated?
# of diagrams (Function Calls)
because of
November 2, 2016 Y. Takaesu - Recursive relations in MG 7
AMPs cannot be compiled
7,000
QCD processes with
November 2, 2016 Y. Takaesu - Recursive relations in MG 8
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?
November 2, 2016 Y. Takaesu - Recursive relations in MG 9
from Johan’s talk
November 2, 2016 Y. Takaesu - Recursive relations in MG 10
Recursive relation for gluonic subamp.
Reduce the # of diagrams (AMPs)
We added n-point off-shell R.R. subroutines to HELAS Library
November 2, 2016 Y. Takaesu - Recursive relations in MG 11
GLUON4_0.f, GLUON4_1.f, …
GLUON5_0.f, GLUON5_1.f, …...
November 2, 2016 Y. Takaesu - Recursive relations in MG 12
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
November 2, 2016 Y. Takaesu - Recursive relations in MG 13
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. .
November 2, 2016 Y. Takaesu - Recursive relations in MG 14
Future works
November 2, 2016 Y. Takaesu - Recursive relations in MG 15
• Apply to processes with quarks,
qg > q ng, qq > qq ng
• Phase space integration and event generation
November 2, 2016 Y. Takaesu - Recursive relations in MG 16