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65 lines
3.4 KiB
65 lines
3.4 KiB
\midheading{Higgs production, ($m_t=\infty$), processes 111--121}
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\label{subsec:h}
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This process is calculable at leading LO,
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at next-to-leading order NLO, and at next-to-next-to-leading order NNLO.
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These processes represent the production of a Standard Model Higgs
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boson that decays either into a bottom quark
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pair ({\tt nproc=111}), a pair of tau's ({\tt nproc=112}),
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a $W^+W^-$
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pair that further decays leptonically ({\tt nproc=113})
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a $W^+W^-$ pair where the $W^-$ decays hadronically ({\tt nproc=114,115})
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or a $ZZ$ pair ({\tt nproc=116-118}) . In addition, the loop-level decays of the Higgs
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into a pair of photons ({\tt nproc=119}) and the $Z\gamma$ decay are included
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({\tt nproc=120,121}).
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For the case of $W^+W^-$ process {\tt nproc=115} gives the contribution
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of radiation from the hadronically decaying $W^-$.
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Process {\tt 114} may be run at NLO with the option {\tt todk},
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including radiation in the decay of the hadronically decaying $W^-$.~\footnote{
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We have not included the case of a hadronically decaying $W^+$; it can
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be obtained from processes {\tt nproc=114,115} by performing the
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substitutions $\nu \to e^-$ and $e^+ \to \bar{\nu}$.}
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For the case of a $ZZ$ decay,
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the subsequent decays can either be into a pair of muons and a pair of electrons
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({\tt nproc=116)}, a pair of muons and neutrinos ({\tt nproc=117}) or
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a pair of muons and a pair of bottom quarks ({\tt nproc=118}).
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At LO the relevant diagram
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is the coupling of two gluons to the Higgs via a top quark loop.
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This calculation is performed in the limit of infinite top quark mass, so that
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the top quark loop is replaced by an effective operator. This corresponds
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to the effective Lagrangian,
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\begin{equation}
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\mathcal{L} = \frac{1}{12\pi v} \, G^a_{\mu\nu} G^{\mu\nu}_a H \;,
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\label{eq:HeffL}
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\end{equation}
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where $v$ is the Higgs vacuum expectation value and $G^a_{\mu\nu}$ the
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gluon field strength tensor.
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The calculation may be performed at NLO, although radiation from the
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bottom quarks in the decay of processes {\tt 111} and {\tt 118} is not yet included.
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%At the end of the output the program will also display the cross section rescaled
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%by the constant factor,
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%\begin{equation}
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%\frac{\sigma_{\rm LO}(gg \to H, \mbox{finite}~m_t)}{\sigma_{\rm LO}(gg \to H, m_t \to \infty)} \;.
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%\label{eqn:hrescale}
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%\end{equation}
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%For the LO calculation this gives the exact result when retaining a finite value for $m_t$,
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%but this is only an approximation at NLO. The output histograms are not rescaled in this way.
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When {\tt removebr} is true in processes {\tt 111,112,113,118},
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the Higgs boson does not decay.
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Process {\tt 119} implements the decay of the Higgs boson into two photons
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via loops of top quarks and $W$-bosons.
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The decay is implemented using the formula Eq.(11.12) from ref.~\cite{Ellis:1991qj}.
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When {\tt removebr} is true in process {\tt 119} the Higgs boson does not decay.
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Processes {\tt 120} and {\tt 121} implement the decay of the Higgs boson into an lepton-antilepton
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pair and a photon. As usual the production of a charged lepton-antilepton pair is mediated by a
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$Z/\gamma^*$ (process {\tt 120}) and the production of three types of neutrinos
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$\sum \nu \bar{\nu}$ by a $Z$-boson (process {\tt 121}). These processes are implemented
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using a generalization of the formula of \cite{Djouadi:1996yq}. (Generalization to take into
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account off-shell $Z$-boson and adjustment of the sign of $C_2$ in their Eq.(4)).
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