This document discusses the use of recursive relations in MadGraph to more efficiently calculate multi-parton QCD processes. Recursive relations reduce the number of amplitude terms that must be calculated by relating higher-point terms to sums of lower-point terms. The author implemented off-shell recursive relation subroutines in the HELAS library to allow MadGraph to calculate processes with 5 or more gluons in the final state. Future work includes applying these techniques to processes with quarks and performing phase space integration and event generation.

1. Recursive relations in
MadGraph
Yoshitaro Takaesu (Sokendai, KEK)
November 2, 2016 1Y. Takaesu - Recursiverelations in MG

2. What is the Recursive Relation
November 2, 2016 Y. Takaesu - Recursiverelations in MG 2
Off-shell R.R. for gluons in fixed color-order

3. Why do we use R.R. ?
November 2, 2016 Y. Takaesu - Recursiverelations in MG 3

4. MG5 is Fantastic!
November 2, 2016 Y. Takaesu - Recursiverelations in MG 4
from Johan’s talk
More Efficient than MG4

5. BUT still not satisfied!
November 2, 2016 Y. Takaesu - Recursiverelations in MG 5
Because
For some processes, GeneratedHELAS codes
cannotbe
compiledand calculated...
Multi-partonQCD processes
Especially for

6. Why codes for
November 2, 2016 Y. Takaesu - Recursiverelations in MG 6
cannot be evaluated?
# of diagrams (Function Calls)
because of

7. November 2, 2016 Y. Takaesu - Recursiverelations in MG 7
AMPs cannot be compiled
7,000
QCD processes with

8. November 2, 2016 Y. Takaesu - Recursiverelations in MG 8
matrix.f gg > ng
Rearrangementof diagrams (AMPs) into JAMPs
takes large amount of compilationtime for many AMPs.
JAMPHELAS
(AMP)

9. How can we go further?
November 2, 2016 Y. Takaesu - Recursiverelations in MG 9
from Johan’s talk

10. November 2, 2016 Y. Takaesu - Recursiverelations in MG 10
Recursive relation
for gluonic subamp.
Reduce the # of diagrams (AMPs)

11. We added n-point off-shell R.R.
subroutines to HELAS Library
November 2, 2016 Y. Takaesu - Recursiverelations in MG 11
GLUON4_0.f, GLUON4_1.f, …
GLUON5_0.f, GLUON5_1.f, …
.
.
.

12. November 2, 2016 Y. Takaesu - Recursiverelations 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

13. November 2, 2016 Y. Takaesu - Recursiverelations in MG 13
Using those off-shell R.R. subroutines,
We calculateJAMPs.
( OK but slow..)

14. Conclusion
• Generated Codes by MG5 for multi-parton
QCD 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 - Recursiverelations in MG 14

15. Future works
November 2, 2016 Y. Takaesu - Recursiverelations in MG 15
• Apply to processes with quarks,
qg > q ng, qq > qq ng
• Phase space integration and event generation

16. November 2, 2016 Y. Takaesu - Recursiverelations in MG 16