Polarised cross-sections at fixed-order NLO (me_frame), and a live LO bug it uncovered

.github/workflows/acceptancetest.yml

@@ -1389,3 +1389,24 @@ jobs:
             cd $GITHUB_WORKSPACE
             ./tests/test_manager.py test_density_mode_vs_standalone_LI1 -pA -t0 -l INFO
 
+
+
+  acceptancetest_105:
+    # The type of runner that the job will run on
+    runs-on: ubuntu-24.04
+    if: github.event_name == 'push' || github.event.pull_request.head.repo.fork == true
+
+    # Steps represent a sequence of tasks that will be executed as part of the job
+    steps:
+      # Checks-out your repository under $GITHUB_WORKSPACE, so your job can access it
+      - uses: actions/checkout@v4
+      - uses: ./.github/actions/checkout_mg5
+      - uses: ./.github/actions/restore_all
+
+      # Polarised fixed-order NLO evaluated in a chosen rest frame. Asserts on
+      # check_poles, which is the only check sensitive to the frame handling of
+      # the Born against the virtual.
+      - name: test one of the test test_polarised_nlo_me_frame
+        run: |
+            cd $GITHUB_WORKSPACE
+            ./tests/test_manager.py test_polarised_nlo_me_frame -pA -t0 -l INFO

Template/LO/SubProcesses/genps.f

@@ -1771,7 +1771,8 @@ subroutine boost_to_frame(P1, frame_id, P2)
 
       integer ids(nexternal)
       integer i,j
-      logical trivial_boost 
+      integer nsel, isel
+      logical trivial_boost
 
 c     uncompress
       call mapid(frame_id, ids)
@@ -1807,12 +1808,41 @@ subroutine boost_to_frame(P1, frame_id, P2)
             enddo
          endif
       enddo
-      do j=1,3	
+      do j=1,3
           Pboost(j) = -1 * Pboost(j)
-      enddo	    
+      enddo
       do i=1, nexternal
          call boostx(p1(0,i), pboost, p2(0,i))
-      enddo   
+      enddo
+
+c     A frame built from a single leg puts that leg at rest, and there the
+c     boost has to be exactly right rather than right to rounding. HELAS
+c     changes convention at exactly zero: vxxxxx builds the polarisation
+c     vectors of a massive vector along the z axis when pp.eq.0d0 and along
+c     the momentum direction otherwise. boostx only reaches p=0 up to the
+c     rounding of lf (it forms p(i)+q(i)*lf with lf=1 up to the rounding of
+c     (q(0)-m)+p(0)), so the residual is a few 1d-14 with a noise direction,
+c     and whether it rounds to zero varies event by event. Every event that
+c     misses zero gets its longitudinal polarisation vector pointed along
+c     rounding noise instead of along z.
+c     This was found through the NLO port, where it breaks the FKS
+c     subtraction outright: see docs/nlo_polarisation_boost_plan.md, M2, and
+c     the same fix in Template/NLO/SubProcesses/boost_to_frame.f.
+c     Only a one-leg selection needs this: with two or more selected legs it
+c     is their sum that is at rest, no single leg sits on the branch point.
+      nsel = 0
+      isel = 0
+      do i=1, nexternal
+         if (ids(i).eq.1) then
+            nsel = nsel + 1
+            isel = i
+         endif
+      enddo
+      if (nsel.eq.1) then
+         p2(1,isel) = 0d0
+         p2(2,isel) = 0d0
+         p2(3,isel) = 0d0
+      endif
       return
       end
 

Template/NLO/Cards/run_card.dat

@@ -66,6 +66,7 @@
  %(lpp2)s   = lpp2    ! beam 2 type (0 = no PDF)
  %(ebeam1)s   = ebeam1  ! beam 1 energy in GeV
  %(ebeam2)s   = ebeam2  ! beam 2 energy in GeV
+$frame
 #***********************************************************************
 # PDF choice: this automatically fixes also alpha_s(MZ) and its evol.  *
 # pdlabel: lhapdf = LHAPDF (installation needed) [1412.7420]           *

Template/NLO/Source/run.inc

@@ -50,8 +50,16 @@ c
       double precision    ebeam(2), xbk(2),q2fact(2)
       common/to_collider/ ebeam   , xbk   ,q2fact,   lpp
 c
+c     Rest frame in which the matrix-elements are evaluated (polarization).
+c     Bit n of frame_id is set for each leg n listed in me_frame; see
+c     mapid() and boost_to_me_frame() in boost_to_frame.f. The default
+c     me_frame=[1,2] gives frame_id=6, which means "no boost".
+c
+      integer frame_id
+      common/to_frame_me/frame_id
+c
 c     BW treatment
-c      
+c
       double precision bwcutoff
       common/to_bwcutoff/ bwcutoff
 c

Template/NLO/SubProcesses/add_write_info.f

@@ -275,7 +275,7 @@ subroutine add_write_info(p_born,pp,ybst_til_tolab,iconfig,Hevents
       if (colour_connections(1,1).lt.0) then
          ! colour not yet set: Get color flow that is consistent with
          ! iconfig from Born
-         call sborn(p_born,wgt1)
+         call sborn_frame(p_born,wgt1)
          sumborn=0.d0
          do i=1,max_bcol
             if (icolamp(i,iBornGraph,1)) then