169 f(-p1) + f(-p2) t(e-(p3) + ν(p4) + b(p5)) + q(p6)

,full t-channel mb=0

169.1 Single-top-quark production and decay at NNLO, process 1650

This calculation is based on ref. [1]. This process constitutes the real correction needed for the complete NNLO order calculation. In other words it is the plus-one-jet process evaluated at NLO.

169.2 Off-shell single top production in SM and SMEFT, processes 164,169

The processes 164 and 169 represent off-shell single-top-quark and anti-top-quark production, respectively. The calculations are performed in the complex-mass scheme. Both the SM and contributions from the SMEFT can be calculated. For more details on this calculation, please refer to ref. [2].

Dynamical double deep inelastic scattering scales can be consistently used at NLO by setting dynamicscale to ‘DDIS’ and scale=facscale to 1d0. In this way the momentum transfer along the W-boson Q2 is used as the scale for the light-quark-line corrections μ2 = Q2, and μ2 = Q2 + mt2 for the heavy-quark-line corrections. These scales are also consistently used for the non-resonant contributions, with QCD corrections on the ud-quark line, and separate QCD corrections on the bottom-quark line.

The new block ‘Single top SMEFT, nproc=164,169’ in the input file governs the inclusion of SMEFT operators and corresponding orders. The scale of new physics Λ can be separately set, and has a default value of 1000 GeV. The flag enable 1/lambda4 enables the 1Λ4 contributions, where operators Q33φud,Q33dW,Q33dG and Q4R can contribute for the first time. For the non-Hermitian operators we allow complex Wilson coefficients. We also have a flag to disable the pure SM contribution, leaving only contributions from SMEFT operators either interfered with the SM amplitudes or as squared contributions at 1Λ4. This can be used to directly and quickly extract kinematical distributions and the magnitudes of pure SMEFT contributions.

To allow for easier comparisons with previous anomalous couplings results, and possibly estimate further higher order effects, we allow for an anomalous couplings mode at LO by enabling the corresponding flag. The relations between our operators and the anomalous couplings are

δV L = C(3,33) φq   2
Λ2, where V L = 1 + δV L ,
V R = C33 φud*m2t
 Λ2 ,
gL = -4mW--mt
  Λ2 C33 dW ,
gR = -4mW-2mt
  Λ C33 uW*,

where mW is the W-boson mass, and mW = 1
2gWv has been used to derive this equivalence. Note that the minus sign for gL and gR is different from the literature. See also the publication  [2] for more information.

For comparisons with on-shell results one needs to add up the contributions from processes 161 at NLO and from the virt and real contributions from 162, see above.

The analysis/plotting routine is contained in the file ‘src/User/nplotter_ktopanom.f’, where all observables presented in this study are implemented, and the W-boson/neutrino reconstruction is implemented and can be switched on or off.

169.3 Plotter

nplotter_ktopanom.f is the default plotting routine.

169.4 Example input and output file(s)

input169.ini process169.out


[1]    J. Campbell, T. Neumann and Z. Sullivan, Single-top-quark production in the t-channel at NNLO, JHEP 02 (2021) 040 [2012.01574].

[2]    T. Neumann and Z.E. Sullivan, Off-Shell Single-Top-Quark Production in the Standard Model Effective Field Theory, JHEP 06 (2019) 022 [1903.11023].