Standard Model with internal polarization selectionΒΆ

Recola 1.4.2 supports the selection of internal polarizations which is based on [BMP18], [BMP19] and has been used with Recola in [DP20], [DP21b] and [DP21a]. Examples of how to use this feature are given below:

program main_rcl
  use recola
  use outgoing_momenta_rcl, only: set_outgoing_momenta_rcl
  implicit none

  integer, parameter :: dp = kind (23d0) ! double precision
  real (dp)          :: p7(0:3,1:7),s, A2M(2), A2P(2), A20(2), A2(2),A20aux(2)

  call set_output_file_rcl('*')

  ! to select polarizations of massive particles use the subroutine:
  ! set_internal_projection_rcl(npr,v,p)
  ! npr: process number
  ! v  : particle binary id
  ! p  : polarisation state: -1, 0, +1

  ! External particle are identified by binaries, i.e. in this example
  ! 1 (u), 2 (u~), e+(4), nu_e(8), mu-(16), nu_mu~(32), g(64)

  call define_process_rcl(1, 'u u~ > e+ nu_e mu- nu_mu~ g', 'LO')
  call set_internal_projection_rcl(1, 12, -1) ! 12 refers to e+ (4) + nu_e (8)
  !call set_internal_projection_rcl(1, 48, -1) ! 48 refers to mu- (16) + nu_mu~ (32)

  call define_process_rcl(2, 'u u~ > e+ nu_e mu- nu_mu~ g', 'LO')
  call set_internal_projection_rcl(2, 12, +1)

  call define_process_rcl(3, 'u u~ > e+ nu_e mu- nu_mu~ g', 'LO')
  call set_internal_projection_rcl(3, 12, 0) ! transverse direction

  call define_process_rcl(4, 'u u~ > e+ nu_e mu- nu_mu~ g', 'LO')
  call set_internal_projection_rcl(4, 12, 2) ! auxiliary pol. See Eq. (2.3) in 1710.09339

  call define_process_rcl(5, 'u u~ > e+ nu_e mu- nu_mu~ g', 'LO')
  call set_internal_projection_rcl(5, 12, 3) ! coherent sum of left- and right-handed polarization vector.

  call define_process_rcl(6, 'u u~ > e+ nu_e mu- nu_mu~ g', 'LO')

  ! works in the same way in combination with selecting resonances
  call define_process_rcl(7, 'u u~ > W+ (e+ nu_e) W- (mu- nu_mu~) g', 'LO')

  s = 1000d0/2
  p7(:,1) = [s,0d0,0d0, s]
  p7(:,2) = [s,0d0,0d0,-s]
  call generate_processes_rcl

  ! I generate a rambo psp for demonstration.
  call set_outgoing_momenta_rcl(1, p7(:,1:2), p7)
  call compute_process_rcl(1,p7,'LO',A2M)
  write(*,*) "A2M(1):", A2M(1)
  call compute_process_rcl(2,p7,'LO',A2P)
  write(*,*) "A2P(1):", A2P(1)
  call compute_process_rcl(3,p7,'LO',A20)
  write(*,*) "A20(1):", A20(1)
  call compute_process_rcl(4,p7,'LO',A20aux)
  write(*,*) "A2x(1):", A20aux(1)

  ! note that off-shell, these amplitudes are gauge-depenent and an on-shell
  ! projection is required. In this case also the sum of polarisations,
  ! neglecting interferences should yield a good approximation.
  !write(*,*) "A2M(1) + A2P(1) + A20(1):", A2M(1) + A2P(1) + A20(1) + A20aux(1)
  call compute_process_rcl(5,p7,'LO',A2)
  write(*,*) "A2(1):", A2(1)
  call compute_process_rcl(6,p7,'LO',A2)
  write(*,*) "A2(1):", A2(1)

  call reset_recola_rcl

end program main_rcl
program main_rcl

  use recola

  implicit none

  integer, parameter :: dp = kind (23d0) ! double precision
  real (dp)          :: pr(0:3,1:9),s

  call set_output_file_rcl('*')

  call set_delta_uv_rcl(7d0)
  call set_delta_ir_rcl(13d0, 77d0)
  call set_mu_uv_rcl(100d0)
  call set_mu_ir_rcl(17d0)
  call set_print_level_squared_amplitude_rcl (1)
  call set_dynamic_settings_rcl(1)
  call set_pole_mass_h_rcl(125.9d0,0d0)
  call set_pole_mass_top_rcl(173.34d0,1.5d0)

  call set_alphas_rcl(1d0,200d0,5)
  call use_gfermi_scheme_rcl(a=7.5581257818126456D-03)
  call set_resonant_particle_rcl('t')

  call define_process_rcl(1,'g g -> t(e+ nu_e b) t~(mu- nu_mu~ b~) H','LO')

  call define_process_rcl(2,'g g -> t(e+ nu_e b) t~(mu- nu_mu~ b~) H','LO')
  call set_internal_projection_rcl(2, 4+8+16, -1)  ! t[-]
  call set_internal_projection_rcl(2, 32+64+128, +1) ! t~[+]

  call define_process_rcl(3,'g g -> t(e+ nu_e b) t~(mu- nu_mu~ b~) H','LO')
  call set_internal_projection_rcl(3, 4+8+16, -1)  ! t[-]

  call define_process_rcl(4,'g g -> t(e+ nu_e b) t~(mu- nu_mu~ b~) H','LO')
  call set_internal_projection_rcl(4, 32+64+128, +1) ! t~[+]

  call define_process_rcl(5,'g g -> t(e+ nu_e b) t~(mu- nu_mu~ b~) H','LO')
  call set_internal_projection_rcl(5, 4+8+16, +1) ! t[+]
  call set_internal_projection_rcl(5, 32+64+128, -1) ! t~[-]

  call generate_processes_rcl

  ! in this PSP the internal tops are on-shell.
  s = 1000d0/2
  pr(:,1)=[1658.6042064580165d0, 0.0000000000000000d0, 0.0000000000000000d0, 1658.6042064580165d0]
  pr(:,2)=[93.167391792675502d0, 0.0000000000000000d0, 0.0000000000000000d0,-93.167391792675502d0]
  pr(:,3)=[290.23203995788782d0,0.21869328541838526d0, 87.165794239673843d0, 276.83336776106086d0]
  pr(:,4)=[250.51659532810453d0, 51.628356024538881d0, 122.57366359199837d0, 212.29407524145455d0]
  pr(:,5)=[82.153984919510563d0,-33.946760734409288d0, 60.085139806118882d0, 44.572083732703945d0]
  pr(:,6)=[96.964294188537764d0,-29.489914748098268d0,-2.2283141261186357d0, 92.344214176019378d0]
  pr(:,7)=[281.86645248355819d0,-62.627197237084872d0,-139.32428266727388d0, 236.88662997548596d0]
  pr(:,8)=[431.94277986559786d0, 1.4436286863595815d0,-93.060576824025731d0, 421.79640830075340d0]
  pr(:,9)=[318.09545150749534d0, 72.773194723275566d0,-35.211424020372817d0, 280.71003547786290d0]

  call compute_process_rcl(1,pr,'LO')
  call compute_process_rcl(2,pr,'LO')
  call compute_process_rcl(3,pr,'LO')
  call compute_process_rcl(4,pr,'LO')
  call compute_process_rcl(5,pr,'LO')

end program main_rcl


Alessandro Ballestrero, Ezio Maina, and Giovanni Pelliccioli. $W$ boson polarization in vector boson scattering at the LHC. JHEP, 03:170, 2018. arXiv:1710.09339, doi:10.1007/JHEP03(2018)170.


Alessandro Ballestrero, Ezio Maina, and Giovanni Pelliccioli. Polarized vector boson scattering in the fully leptonic WZ and ZZ channels at the LHC. JHEP, 09:087, 2019. arXiv:1907.04722, doi:10.1007/JHEP09(2019)087.


Ansgar Denner and Giovanni Pelliccioli. Polarized electroweak bosons in $\bf \text W^+\text W^-$ production at the LHC including NLO QCD effects. JHEP, 09:164, 2020. arXiv:2006.14867, doi:10.1007/JHEP09(2020)164.


Ansgar Denner and Giovanni Pelliccioli. NLO EW and QCD corrections to polarized ZZ production in the four-charged-lepton channel at the LHC. JHEP, 10:097, 2021. arXiv:2107.06579, doi:10.1007/JHEP10(2021)097.


Ansgar Denner and Giovanni Pelliccioli. NLO QCD predictions for doubly-polarized WZ production at the LHC. Phys. Lett. B, 814:136107, 2021. arXiv:2010.07149, doi:10.1016/j.physletb.2021.136107.