MLM: diagram input, scale floor, merged subprocesses, and no clustering through flavour-forbidden merged graphs (madevent + madspace)

[oliviermattelaer]

Stacked on #157 (claude/mlm-diagram-history), the top of the MLM stack (#72 ← #156 ← #157). Three commits. The samples behind the MG7 paper's MLM figures (Overleaf 1b262a6) come from this branch tip, 03c532a.

46b609b: scale floor, diagram input, merged subprocesses, decays

• Scale floor: min_scale only vetoes under MLM. Every other scale choice clamps the scales into the PDF grid's band instead. A run without beam densities gets no range at all; a decay of a particle under 2 GeV used to come out with zero width.
• Diagram input: under MLM the matrix element goes back to random_diagram_in. Neither backend reads diagram_in, so madmatrix had drawn every event's diagram and colour flow at a fixed random number of 0.5.
• Merged subprocesses: MLM turns merge_subprocesses off, with a warning. Merged, it clustered gluon-initiated matrix elements with a quark beam. p p > e+ e- j at xqcut 20 gives 312.3(6) pb merged against 319.0(7) unmerged.
• Decays: dynamical_scale_choice = mlm on a decay uses the decaying mass as a fixed scale.

317a05f: madevent, no clustering through flavour-forbidden merged graphs

Cherry-pick of #229 (against main). With apply_flavor_grouping, cluster.f filtered candidate graphs with flavor_compatible, but never checked that any graph survived, so the filter had no effect.

Take the q q~ > q' q~' rows of q q~ > q q~. The clustering went through the q–q' t-channel gluon of the merged graph, which does not exist for those flavours, so the αs reweighting of the q' q~' > g clustering was skipped (REWGT = 1).

The fix:

• flavor_filter: works on the event's merged-flavour indices. A g/γ/Z/h may join two merged legs only if they have the same index.
• chcluster: when the clustering is forced onto a channel graph the event's flavours forbid, it now returns zero weight instead of stopping madevent.
• Test: test_mlm_rewgt_auto_match_qq_to_qq compared 32 flavour rows with 8, a factor 3.8 by construction. It now sums every ungrouped P-dir with the same topology. At 50k points it fails at 17σ without the fix and passes at 0.5σ with it.

03c532a: madspace, the same for the C++ clustering

One MLMClustering serves every flavour of a merged subprocess, over the union of its diagrams. The fix:

• Compiler: marks a clustering (TRACE_SAME_FLAVOR, trace bit 16) when it joins two bare external fermions and every diagram left puts a g/γ/Z/h on that line. This is decided per diagram; the union's single line meta would prefer a W.
• Kernel: new instruction inputs flavor_index and leg_flavors (the abs PDG ids of each leg per flavour option, from pid_options). A marked clustering whose legs differ is skipped. If a state offers nothing else, the walk falls back to the best skipped candidate.
• Integrand, per-diagram histories (diagram, madevent): already clustered after the flavour is sampled; they now receive it.
• Integrand, all_diagrams (the default): clusters before sampling, for the flavour prior. When the clustering depends on the flavours, the event is clustered again after sampling and its densities are re-evaluated at the new scales. Nothing changes for an integrand without a flavour-dependent clustering.
• Python: MLMClusteringWithFlavors exposes this, as MLMClusteringAlongDiagram does for the along-diagram path. Two new tests in test_mlm.py.

W + 4 quarks (p p > e+ ve j j, quark-only j, the paper's MLM settings, 5×10⁴ events), flavour grouping on / off, in pb:

clustering_history	before	after
all_diagrams	149.66 / 134.25	134.13 / 134.18
madevent	134.23 / 122.87	123.03 / 122.87
diagram	121.66 / 121.61	unchanged

Validation, on this branch

• madspace: pytest 1667 passed, 11 skipped. The torch-only test_flow.py and test_mlp.py were not run.
• madevent MLM: ./tests/test_manager.py -t0 -p tests/acceptance_tests '.*mlm_rewgt.*': Ran 5 tests, OK.
• madevent A/B, same points, W+2j 4-quark subprocesses: P3_qq_lvlqq 125.7(3.2) → 115.0(2.7), P6_qq_lvlqq 102.7(13.6) → 91.4(11.4). Single channels move by −19% at 6–7σ.
• Paper samples: W±+0,1,2j (mg7 and madevent) and tt̄+0,1,2j (three variants), showered with Pythia8. Every new DJR table is compatible with the previous one (χ²/ndf ≈ 1). W mg7/madevent after the veto is 1.0021. 4-quark events are 1.4% of the W sample, so the effect stays below the statistics of the figures.

For reviewers

• The instruction signature of mlm_clustering_hadronic/_leptonic changes in instruction_set.yaml, so the headers are regenerated. A madspace build rebuilt with the old source hash will refuse to run existing mg7 run directories; regenerate them.
• Only pairs of external legs are checked, as in the Fortran fix. A flavour-forbidden vertex involving an internal line is not caught.
• The madevent A/B and the acceptance tests on main are in Fix MLM clustering through flavour-forbidden merged graphs (apply_flavor_grouping) #229. That PR carries only the Fortran fix; main has no madspace MLM code.