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57 lines
2.9 KiB
57 lines
2.9 KiB
\midheading{Off-shell single top production in SM and SMEFT, processes 164,169}
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\label{subsec:offstop}
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The processes 164 and 169 represent off-shell single-top-quark and anti-top-quark production, respectively.
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The calculations are performed in the complex-mass scheme.
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Both the SM and contributions from the SMEFT can be calculated.
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For more details on this calculation, please refer to ref.~\cite{Neumann:2019kvk}.
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Dynamical double deep inelastic scattering scales can be
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consistently used at NLO by setting \texttt{dynamicscale} to `DDIS'
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and \texttt{scale}$=$\texttt{facscale} to 1d0. In this way the
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momentum transfer along the $W$-boson $Q^2$ is used as the scale for
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the light-quark-line corrections $\mu^2=Q^2$, and $\mu^2=Q^2+m_t^2$ for
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the heavy-quark-line corrections. These scales are also consistently
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used for the non-resonant contributions, with QCD corrections on the
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$ud$-quark line, and separate QCD corrections on the bottom-quark
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line.
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The new block `Single top SMEFT, nproc=164,169' in the input
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file governs the inclusion of SMEFT operators and corresponding
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orders. The scale of new physics $\Lambda$ can be separately set, and
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has a default value of $1000$~GeV. The flag \texttt{enable
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1/lambda4} enables the $1/\Lambda^4$ contributions, where operators
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$\Qtwo, \Qfour, \Qseven$ and $\Qnine$ can contribute for the first
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time. For the non-Hermitian operators we allow complex Wilson
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coefficients. We also have a flag to disable the pure SM
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contribution, leaving only contributions from SMEFT operators
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either interfered with the SM amplitudes or as squared
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contributions at $1/\Lambda^4$. This can be used to directly and
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quickly extract kinematical distributions and the magnitudes of
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pure SMEFT contributions.
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To allow for easier comparisons with previous anomalous couplings
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results, and possibly estimate further higher order effects, we allow
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for an anomalous couplings mode at LO by enabling the corresponding
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flag. The relations between our operators and the anomalous couplings
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are
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\begin{align*}
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\delta V_L &= \Cone \frac{m_t^2}{\Lambda^2} ,\,\text{where } V_L = 1 + \delta V_L\,,\\
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V_R &= \Ctwo{}^* \frac{m_t^2}{\Lambda^2}\,, \\
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g_L &= -4\frac{m_W m_t}{\Lambda^2} \cdot \Cfour\,, \\
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g_R &= -4 \frac{m_W m_t}{\Lambda^2} \cdot \Cthree{}^*\,,
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\end{align*}
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where $m_W$ is the $W$-boson mass, and $m_W = \frac{1}{2} g_W v$ has
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been used to derive this equivalence. Note that the minus sign for
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$g_L$ and $g_R$ is different from the literature. See also the publication~~\cite{Neumann:2019kvk} for more information.
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For comparisons with on-shell results one needs to add up the contributions
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from processes 161 at NLO and from the virt and real contributions from 162, see above.
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The analysis/plotting routine is contained in the file
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`\texttt{src/User/nplotter\_ktopanom.f}', where all observables
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presented in this study are implemented, and the $W$-boson/neutrino
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reconstruction is implemented and can be switched on or off.
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