# "The two-loop helicity amplitudes for qqb' -> V1V2 -> 4 leptons"
# T. Gehrmann, A. von Manteuffel, L. Tancredi
#
# This file defines our integral families in Reduze2 format.
# Please see the file "kinematics.yaml" for the kinematics definition.
integralfamilies:
- name: "PL1"
loop_momenta: [k1, k2]
propagators:
- [ "k1", 0 ]
- [ "k2", 0 ]
- [ "k1-k2", 0 ]
- [ "k1-p1", 0 ]
- [ "k2-p1", 0 ]
- [ "k1-p1-p2", 0 ]
- [ "k2-p1-p2", 0 ]
- [ "k1-p1-p2+p3", 0 ]
- [ "k2-p1-p2+p3", 0 ]
permutation_symmetries:
# k1 -> k2, k2 -> k1
- [ [ 1, 2 ], [ 4, 5 ], [ 6, 7 ], [8, 9] ]
# the different virtualities p3^2 != p4^2 break the following symmetry:
# k1 -> -k1+p1+p2, k2 -> -k2+p1+p2 --- p1<->p2, p3<->p4
# - [ [ 1, 6 ], [ 2, 7 ] ]
- name: "PL2"
loop_momenta: [k1, k2]
propagators:
- [ "k1", 0 ]
- [ "k2", 0 ]
- [ "k1-k2", 0 ]
- [ "k1-p1", 0 ]
- [ "k2-p1", 0 ]
- [ "k1-p1+p3", 0 ]
- [ "k2-p1+p3", 0 ]
- [ "k1-p1-p2+p3", 0 ]
- [ "k2-p1-p2+p3", 0 ]
permutation_symmetries:
# k1 -> k2, k2 -> k1
- [ [ 1, 2 ], [ 4, 5 ], [ 6, 7 ], [8, 9] ]
- name: "NPL"
loop_momenta: [k1, k2]
propagators:
- [ "k1", 0]
- [ "k2", 0]
- [ "k1-k2", 0]
- [ "k1-p1", 0]
- [ "k2-p1", 0]
- [ "k1-p1-p2", 0]
- [ "k1-k2-p3", 0]
- [ "k2-p1-p2+p3", 0]
- [ "k1-k2-p1-p2", 0]
# Some Feynman diagram require the x34 crossed version of NPL for matching.
# In the current version, Reduze2 doesn't support crossings of external legs
# with different masses. It is straight-forward to stick with reductions
# for the above 3 families and apply the crossing x34 with another program.
# Alternatively one can also include another family by hand, which is
# convenient to determine the shifts of loop momenta for Feynman graphs
# to sectors.
# - name: "NPLx34"
# loop_momenta: [k1, k2]
# propagators:
# - [ "k1", 0]
# - [ "k2", 0]
# - [ "k1-k2", 0]
# - [ "k1-p1", 0]
# - [ "k2-p1", 0]
# - [ "k1-p1-p2", 0]
# - [ "k1-k2-p4", 0]
# - [ "k2-p1-p2+p4", 0]
# - [ "k1-k2-p1-p2", 0]