madspace: always draw the beam orientation before the mapping

[theoheimel]

Stacked on #154 (base is its branch, so merge #154 first or retarget to main).

Summary

• One mirror path. Mirrored flavors always draw the orientation before the phase-space mapping (mirror_beams = true), so boost, cuts and PDFs all see the orientation the event is written with. The post-cut mirror (momenta_mirror_acc, mirror_id_acc, the momenta_me selection) is removed.
• Integrand throws if a flavor is mirrored and the mapping was not built with mirror_beams = true. launch.py sets mirror_beams from has_mirrored_flavors(); asymmetric beams without mirrored flavors only get the y0 boost.
• Removed the cut-invariance machinery (Cuts::non_mirror_invariant_cuts, Cuts::mirror_invariant, Observable::mirror_invariant) and its bindings. Signed cuts (eta, y, phi, pz) with symmetric beams now just work instead of throwing.
• Mapping conditions by name ("permutation_index", "mirror_index") instead of positional indexing, in PhaseSpaceMapping and Integrand.

Fix after merging main

Main's cut-aware rapidity windows assume the beams' frame is the lab frame. With beam_rapidity != 0 that lost ~9% of the cross section (52% accepted vs 81% after the fix) for rambo/propagator modes:

• the x1/x2 window bound is widened by |y0|;
• the decay and t-channel windows now get x1 e^{y0}, x2 e^{-y0} (lab_fractions), with the sign of y0 flipped for mirrored events.

New test test_cut_aware_sampling_loses_nothing_with_asymmetric_beams (with and without mirror_beams); I checked it fails with the mirror sign flipped.

Behavior changes to be aware of

• Symmetric beams with mirrored flavors take the new path: cross sections should agree, but the orientation is a random draw, so odd observables (e.g. ) get statistical noise the old exactly-paired sample did not have. A p p > e+ e- comparison of against main has not been done.
• test_mirror_beams_cuts_the_written_orientation was weakened: cut-aware sampling means the cut and uncut mappings no longer map the same random numbers to the same momenta, so it now checks that accepted points pass the cut as written.
• 2 -> 1 does not use main's x1/x2 window yet (correct, but less efficient with a rapidity cut).

LHE incoming order

Events were written with the incoming particles in the flavor tables' leg order, so mirrored events had particle 1 moving along -z and orderings such as u g never appeared (reported by a collaborator; reproduced on this branch with p p > z j: only g u, with pz(1) < 0 in about half of the events). LHECompleter::complete_event_data now swaps the two incoming records when particle 1 has pz < 0, so particle 1 always comes from beam 1. On the same process both orderings now appear in equal numbers and pz(1) > 0 for every event. The systematics reweighting reads the event buffer and is unaffected. Test: test_first_incoming_particle_moves_along_plus_z. I did not check whether main shows the same ordering.

Testing

• madspace pytest: 1731 passed (torch tests excluded)
• test_mg7_launch.py, test_banner.py: 151 passed
• Acceptance tests (test_check_xsec_processes_mg7.py) not run locally; relying on CI.

[oliviermattelaer]

• cherry-pick done
• test done (results below)
• remerge with main (conflict fixed in 10faf1d)

Merge with main (10faf1d)

Only conflict: mg7/launch.py, build_lhe_meta. Kept this branch's per-beam LHAPDF ids (_lhapdf_id(1), _lhapdf_id(2)) together with main's weight_mode from lhe_weight_info. After the merge madspace was rebuilt; 90 madspace tests, 339 mg7 interface tests and 71 run-card tests pass.

Eta cuts with asymmetric beams and the mirror

Code: lab_fractions() gives the windows the boost from the frame the momenta are generated in to the lab, for both mirror orientations, and the window kernels only read ½ ln(x1/x2), so the rescaled x1, x2 are safe. The window on the rapidity of the partonic system (widened by |y0|) and the colour-ordered ΔR bound (dropped when y0 ≠ 0) are correct but conservative.

Mapping level (no matrix element): 10 topologies (DY, massive t t~, Z g, e e g g, a a and a g a in the t channel, Z j with a composite child, chili) × y0 ∈ {0, 0.28, −1} × mirror on/off:

• every event passing the lab cuts maps back inside the windows (60/60)
• windowed and window-free cut integrals agree within 0.4% (all pulls < 1.7σ at 6M points)

Full mg7 runs with |η| < 2.5, compared with a run without the eta cut where the cut is applied to its events afterwards:

process	beams (GeV)	cut run	no-eta run, cut afterwards	ratio
p p > e+ e-	7000 × 4000	940.08 ± 0.82 pb	939.83 ± 2.09 pb	1.0003 ± 0.0024
p p > e+ e- (after the main merge)	7000 × 4000	939.82 ± 0.58 pb	939.83 ± 2.09 pb	1.0000 ± 0.0023
p p > e+ e-	6500 × 6500	1126.35 ± 0.79 pb	1128.87 ± 2.56 pb	0.9978 ± 0.0024
p p > a a	7000 × 4000	24.974 ± 0.037 pb	24.983 ± 0.064 pb	0.9996 ± 0.0030
p p > a a	6500 × 6500	28.396 ± 0.046 pb	28.383 ± 0.076 pb	1.0005 ± 0.0031
p p > e+ e- j (lepton and jet η cut)	7000 × 4000, 5 seeds	188.70 ± 0.08 pb	188.44 ± 0.16 pb	1.0014 ± 0.0010
p p > e+ e- j (lepton and jet η cut)	6500 × 6500	237.49 ± 0.24 pb	237.13 ± 0.56 pb	1.0015 ± 0.0026

• no written event outside |η| < 2.5 (largest |η| 2.5000)
• the dσ/dη shapes of the cut runs match the cut-afterwards samples, with no dip at the edges
• beams swapped (4000 × 7000): same cross section (DY 940.12 ± 0.81, a a 24.91 ± 0.04, e e j 188.81 ± 0.19 pb) and mirrored η distributions
• without the eta cut ⟨y⟩ of the final state is +0.286, against ½ ln(7/4) = 0.280: the boost goes the right way
• incoming particle 1 never has pz < 0 in the LHE files
• DY 7000 × 4000 agrees with madevent including the asymmetric-beam cut fix (mg5amcnlo PR #416), 939.3 ± 1.5 pb

[oliviermattelaer]

Eta cuts with asymmetric beams and the mirror validated, main merged (details in the comment above).