Interference processes: [LIxtree=QCD] and [treextree] left/right syntax

[oliviermattelaer]

Summary

Two processes on one line, of which only the interference 2 Re(A_left A_right^*) is computed:

generate g g > h > t t~ [LIxtree=QCD] g g > t t~      # loop-induced x tree
generate g g > h > t t~ [LIxtree=QCD]                 # right-hand side implied
generate p p > z > e+ e- [treextree] p p > a > e+ e-  # tree x tree
output madevent

This automates the recipe of the wiki page LoopInducedTimesTree (special model with UVtree copies of the vertices, a BKGQCD order, five source patches) without exposing any of it to the user.

Syntax

• The keyword is case-insensitive ([LIxtree=QCD], [lixtree=QCD], [TreeXTree]).
• Each side takes its own s-channel requirements, exclusions and amplitude orders. In the first example the > h > requirement applies to the loops only.
• Squared-order constraints constrain the interference: they go between ] and the right-hand process, and are refused on the right-hand process.
• Both sides must have the same external legs in the same order. The right-hand legs may be wider multiparticles.
• Without a right-hand process, LIxtree interferes with the tree-level process of the same legs, with the orders a plain generate would choose.
• help generate documents it.

Implementation

• A hidden coupling order INTERF (hierarchy 0, added to the model in memory, never printed) tags the right-hand amplitudes. INTERF^2==1, also as a split order, keeps the left x right products only, in the generated code too.
• LIxtree: the right-hand trees are generated per subprocess and stored as loop_UVCT_diagrams with UVCT_orders={INTERF:1} and a unit coupling. The ref_orders of a Born-less loop process now include the UVCT amplitudes; without that MadLoop stops at initialisation ("Could not find squared orders"). A subprocess whose loops are all discarded is dropped together with its trees.
• treextree: the right-hand diagrams are appended after the left-hand generation, and the squared-order filter acts on the union. HELAS copies the tag onto the amplitude orders, on a copy because those dicts are shared with the model interactions. Crossing reuse is off for these processes.
• treextree output: madevent, standalone_fortran, and, since PR Interference in mg7: madevent helicity convention, IDWTUP -4, signed-weight fixes #244 (madmatrix split orders on CPU and GPU, signed weights in madspace), mg7 and the C++ standalone. The other formats have no squared split orders and would return |L+R|^2, so they are refused before anything is written. LIxtree needs a loop backend: madevent and standalone_fortran only.

Run card and systematics

• Interference processes get the existing interference defaults (dynamical_scale_choice = 3, systematics off by default). Before this, the detection relied on ^2 appearing in the printed process.
• config_nqcd.inc: one power of alpha_s for every channel, half the QCD order of the left x right products. For QCD u d > u d against its electroweak counterpart this is 1, where the channels would have given 2 or 0.
• systematics.py: the summary printed no scale variation and wrong-signed percentages for a negative total cross section. This affects any interference sample. The file has diverged from mg5 3.7.3, so the same fix is needed there separately.

Validation

tests/acceptance_tests/test_loop_induced_x_tree.py, at fixed phase-space points:

Quantity	Result	Reference	Agreement
g g > h > t t~ interference	-2.3256785052943e-04	wiki recipe, independent tree construction	10 digits
loop squared	8.1044796923476e-05	[sqrvirt=QCD]	10 digits
tree squared (helicity filter off)	0.59262610090352	tree-level g g > t t~	10 digits
u u~ Z x photon	1.2397455147009e-03	|Z+a|^2 - |Z|^2 - |a|^2	10 digits

madevent:

Sample	This PR	Reference
g g > h > t t~, mH = 500 GeV, wH = 30 GeV, 13 TeV	-0.957 ± 0.008 pb	-0.965 ± 0.002 pb (wiki recipe)
p p > e+ e-, mll > 200 GeV	0.0598 ± 0.0028 pb	0.0629 ± 0.0048 pb (three squared samples)

Tests

• New unit tests: interface/test_interference_syntax.py (17), loop/test_loop_induced_x_tree.py (7), core/test_tree_interference.py (6).
• Full unit suite before merging main: 2448/2449, the failure being a guard on decay-chain amplitudes, since fixed. After merging main: core, interface, madspin and loop suites and the two acceptance tests pass.

Notes

• In the standalone check of a LIxtree process, the loop-squared and tree-squared lines are diagnostics. They are complete only with HelicityFilterLevel 0, since MadLoop filters helicities on the selected interference. The interference itself is exact either way.
• check refuses interference processes and points to output standalone_fortran.