NLO+PS polarisation: put the MC-counterterm azimuth in the me_frame

[oliviermattelaer]

Polarised cross-sections at NLO were validated at fixed order only. This makes the
NLO+PS (MC@NLO) path frame-consistent as well, and adds a test with a verified
negative control.

The bug

get_mbar (Template/NLO/SubProcesses/montecarlocounter.f) took borntilde from a
boosted sborn_frame but built the azimuthal phase entirely in the partonic c.m. —
azifact from unboosted emission spinors, cphi_mother=±1 from the mother lying on
the beam axis. borntilde is the ±gluon-helicity interference, so the mother's
little-group phase enters it, and that phase only cancels against the one in
azifact if both are computed in the same frame. fks_singular.f had already solved
this at fixed order with azifact_me_frame.

Nothing blocked NLO+PS: no guard distinguishes fixed order from event generation,
and generate_events ran end to end on the unfixed code. The failure was silent.

Measured on p p > z{0} j [QCD], me_frame=[3]: the ISR phase error was a constant
37.4°, 63.4° and 156.6° on three collinear scans, flat down to 1-y = 1e-10. It never
converged. After the fix it falls off like sqrt(1-y) (10.07° → 0.97° → 0.097° →
0.0003°).

The change

Three routines in boost_to_frame.f — me_frame_born_boost, azifact_from_spinors,
azifact_mc_frame — and if (me_boosted) … else <legacy verbatim> endif at both
get_mbar sites, plus the same edit in montecarlocounter_alt.f (dead code, but
leaving the two copies inconsistent is a trap). The R_y(pi) flip is skipped when a
frame is requested: it only put a j_fks=2 mother back on +z, and for a one-leg
frame it would also flip the polarisation axis of the leg at rest — harmless for {0},
but it would swap {+}/{-}.

The collinear branch is now taken only at exactly 1-y <= 0. At any kt>0 the spinor
route is exact and the kperp route is an approximation, so there is no case for
preferring the approximation.

Validation

generate_events aMC@NLO --parton -f, 1000 events, iseed=33, nn23lo1, fixed scales
91.188, ptj 30, etaj 4.0, me_frame=[3] (FRAME_ID = 8 read back from
Source/run_card.inc):

	before	after
total	2.172e+03 ± 8.3e+00 pb	2.189e+03 ± 8.2e+00 pb
absolute	4.837e+03 ± 1.2e+01 pb	4.378e+03 ± 9.8e+00 pb
ratio	2.2273	1.9999

The total must not move and does not (1.4 sigma) — the MC counterterm cancels between
the S and H event. The absolute cross-section must move and does, by 30 sigma: it
measures how local the subtraction is, which is what the azimuth controls. Repeated on
a fresh pair with iseed=7717: 2.2220 → 2.0060, totals agreeing at 0.02 sigma.

me_frame=[3,4] on p p > z{0} z{0} j [QCD]: 3.134e-01 ± 2.2e-03 pb, agreeing with
the fixed-order value at 1.3 sigma, 20/20 poles in all 12 P dirs.

No frame requested stays bit-identical. Two copies of one output dir differing only
in the changed files: res_0/1/2.txt and the 2.1 MB events.lhe.gz compare byte for
byte.

Test

test_polarised_nlo_ps_me_frame, wired in as acceptancetest_106 (the workflow
invokes tests by explicit name, so an unwired test never runs). It passes on the
branch, and with montecarlocounter.f alone reverted it fails on the intended
assertion — AssertionError: 2.22732091828047 not less than 2.15 — reproduced
independently by the reviewer.

Caveats, stated rather than omitted

• The PYTHIA8 handoff is unexercised here. The local MG5aMC_PY8_interface was
  built against v3.5.15 and its C++ link fails on arm64, strictly after events.lhe
  is written. Everything this PR touches is upstream of the handover, but no showered
  polarised event was produced on this machine.
• test_MC is vacuous upstream and passed on the broken code — it is not evidence
  for this change. test_soft_col_limits.f assigns the same xmcsubt_wrap result to
  both sides of the comparison, so checkres2 sees a ratio of exactly 1 and returns
  PASS unconditionally. Two further breaks in the same area (the split-order sub-check
  comparing one ME under two jacobians, and ilim=0 aborting on MCcntcalled) are
  recorded in the M5 doc. All three are pre-existing on main and are being handled
  separately.

[oliviermattelaer]

On hold — do not merge yet.

Review of a follow-up branch found a pre-existing MadLoop-core bug that this PR can reach. IMPROVE_PS_POINT_PRECISION overwrites the last external leg's three-momentum with the momentum-conservation residual (madgraph/iolibs/template_files/loop/improve_ps.inc:707-714), unconditionally. If the me_frame leg held at rest is that last leg, the exact zero becomes ~1e-14, vxxxxx takes its pp.eq.rZero branch on rounding noise, and the longitudinal polarisation axis is built along that noise.

Measured on g g > z{0} z{0} [noborn=QCD], where me_frame=[3] and [4] must agree pointwise: 0.02543 pb versus 0.03211 pb, +26%, 34 sigma. Restoring the exact zero inside the shared quad routine closes it to 0.06 sigma. An LO control on the same final state gives bit-identical [3] and [4], so the split is purely the MadLoop artefact.

This PR is reachable in principle — any run_card NLO mode whose polarised massive particle is the last Born leg, e.g. p p > j z{0} [QCD] with me_frame=[4]. Both acceptance tests here happen to dodge it ([3,4] leaves no leg at rest; [3] has the jet last), so CI is green and the hole is invisible.

Held on Olivier's call until the improve_ps fix lands on its own branch with its own MadLoop validation. Nothing is wrong with the code in this PR.