A particular supergraph may be loaded by calling ltd.CrossSection(), which takes two yaml files as input. The first file is the squared topologies file, which cn be found in the Rust_inputs folder. The second file is the hyperparameters.yaml file.
For example, to load the first supergraph in the LU_epem_a_ddx_NLO example we call:
cross_section = ltd.CrossSection("LU_epem_a_ddx_NLO/Rust_inputs/SG_QG0.yaml", "hyperparameters.yaml")
There are several ways to evaluate the integrand. evaluate_integrand() evaluates the integrand in the -dimensional hypercube parameterization, where is the number of loops of the supergraph. The argument of evaluate_integrand() is an array containing numbers in the range .
For example, to evaluate the first supergraph in the LU_epem_a_ddx_NLO example at
we call:
cross_section.evaluate_integrand([0.1, 0.2, 0.3, 0.4, 0.5, 0.6])
cross_section.evaluate_integrand can also be used as input to your own integrator of choice.
It is also possible to evaluate the integrand at a particular cut using evaluate_cut(loop_momenta, cut_index, scaling). Unlike evaluate_integrand(), this evaluation is done in momentum space. The argument loop_momenta is a double array containing the components of each spatial momenta. cut_index tells the function which cut to consider, and scaling is the rescaling required to put the relevant momenta on the cut. This scaling may be found using get_scaling.
For example, to evaluate the first supergraph in the LU_epem_a_ddx_NLO example at
the second cut:
loop_momenta = [[2,1,2],[4,2,8]] # just take some random values, not important in this example.
scaling = cross_section.get_scaling(loop_momenta, 1)[1][0] #take the positive solution
result = cross_section.evaluate_cut(loop_momenta, 1, scaling)
The function get_scaling(loop_momenta, cut_index) computes the scaling in order to put the relevant momenta on the cut. get_scaling returns both the positive and negative solution, and the jacobian associated to the rescaling. This Jacobian is however already included in evaluate_cut.
The function parameterize(x, loop_index, e_cm_squared) can be used to compute the spatial momenta from the value in the
-dimensional hypercube.
TODO