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75 lines
4.1 KiB
75 lines
4.1 KiB
\midheading{$H \to ZZ \to e^- e^+ \mu^- \mu^+$ production, ($m_t=$~finite), processes 128-133}
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These processes represent the production of a Higgs boson that decays to $Z Z$,
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with subsequent decay into charged leptons. For process {\tt 128}, the exact form of the triangle
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loop coupling a Higgs boson to two gluons is included, with both top and bottom quarks
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circulating in the loop. This is to be contrasted with process {\tt 116} in which only the
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top quark contribution is included in the effective coupling approach.
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Process {\tt 129} includes only the effect of the interference of the
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Higgs and $gg \to ZZ$ amplitudes.
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The calculation is available at LO only. LO corresponds to $O(\alpha_s^2)$ in this case.
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The calculation of loops containing the third quark generation
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includes the effect of both the top quark mass and the bottom quark, while the first two
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generations are considered massless. For numerical stability, a small cut on the
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transverse momentum of the $Z$ bosons is applied: $p_T(Z)>0.05$~GeV.
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This typically removes less than $0.1$\% of the cross section. The
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values of these cutoffs can be changed by editing \verb|src/ZZ/getggZZamps.f| and recompiling.
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Process {\tt 130} includes all $gg$-initiated diagrams that have a Higgs boson in the $s$-channel,
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namely the square of the $s$-channel Higgs boson production and the interference with the diagrams
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that do not contain a Higgs boson, (i.e. $gg \to Z/\gamma^*+Z/\gamma^* \to e^- e^+ \mu^- \mu^+$),
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i.e.~$|M_H|^2+2 |M_H^* M_{ZZ}|$.
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Process {\tt 131} calculates the full result for this process from $gg$-intitiated diagrams.
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This includes diagrams that have a Higgs boson in the $s$-channel, the continuum $ Z/\gamma^*+Z/\gamma^*$
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diagrams described above and their interference, i.e.~$|M_H+M_{ZZ}|^2$.
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Process {\tt 132} gives the result for the square of the box diagrams alone, i.e. the process
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$gg \to Z/\gamma^*+Z/\gamma^* \to e^- e^+ \mu^- \mu^+$, i.e.~$|M_{ZZ}|^2$.
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Process {\tt 133} calculates the interference for the $qg$ initiated process.
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For those processes that include contributions from the Higgs boson, the form
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of the Higgs propagator may be changed by editing the file
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{\tt src/Need/sethparams.f}. If the logical variable {\tt CPscheme} is
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changed from the default value {\tt .false.} to {\tt .true.} then the
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Higgs propagator is computed using the ``bar-scheme'' that is
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implemented in the HTO code of G. Passarino~\cite{Goria:2011wa,Passarino:2010qk}.
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The value of the Higgs boson width has been computed with v1.1 of the
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HTO code, for Higgs masses in the interval $50 < m_H< 1500$~GeV. These
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values are tabulated, in $0.5$~GeV increments, in the file
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{\tt Bin/hto\_output.dat}. The widths for other masses in this range
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are obtained by linear interpolation.
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% \bottomheading{Specifying other final states}
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% \label{specifyingZdecays}
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% As described above, these processes refer to a final state
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% $e^- e^+ \mu^- \mu^+$. It is however possible to specify a final state
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% that corresponds to a different set of $Z$ boson decays. This is achieved
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% by altering the value of {\tt NPROC} in the input file by appending a
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% period, followed by two 2-character strings that identify each of the decays.
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% Possible values for the strings, and the corresponding decays, are
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% shown in the table below.
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% \begin{center}
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% \begin{tabular}{ll}
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% string & $Z$ decay \\
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% \hline
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% {\tt el,EL} & $(e^-,e^+)$ \\
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% {\tt mu,MU,ml,ML} & $(\mu^-,\mu^+)$ \\
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% {\tt tl,TL} & $(\tau^-,\tau^+)$ \\
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% {\tt nu,NU,nl,NL} & $(\nu,\bar\nu) \times 3$ \\
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% {\tt bq,BQ} & $(b,\bar b)$ \\
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% \end{tabular}
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% \end{center}
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% Note that, for the case of neutrino decays, the sum over three flavours of
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% neutrino is performed. The labelling of the particles in the output is best
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% understood by example. Setting {\tt nproc=132.ELNU} corresponds to the
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% process $gg \to Z/\gamma^*+Z/\gamma^* \to e^-(p_3) e^+(p_4) \nu(p_5) \bar\nu(p_6)$.
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% Note that the default process corresponds to the string {\tt ELMU} so that,
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% for instance {\tt nproc=132.ELMU} is entirely equivalent to
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% {\tt nproc=132}.
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% The effect of changing the lepton flavour is only seen in the output
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% of LHE events, where the correct mass is then used when producing the
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% event record.
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