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use fancy enumeration feature of cref instead of and

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hiro98 2020-05-13 11:05:10 +02:00
parent e3ff9bd183
commit 7394c322b7
2 changed files with 16 additions and 14 deletions
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22
latex/tex/monte-carlo/sampling.tex
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@ -203,7 +203,7 @@ the distribution \(f\) is required.
and weighting distribution.}
\end{figure}
\subsection{Observables}
\subsection{Observables}%
\label{sec:obs}
Having obtained a sample of a distribution, distributions of other
@ -223,9 +223,10 @@ probability that
A^{-1}\qty[\int_{0}^{\gamma^{-1}(z')}f(x')\dd{x'},
\int_{0}^{\gamma^{-1}(z')+\partial_z(\gamma^{-1})(z')\dd{z'}}f(x')\dd{x'}]\]
which is
\(A^{-1}\cdot f(\gamma^{-1}(z'))\cdot (\partial_z\gamma^{-1})(z')\dd{z'}\). That
is the same result, as if the distribution had been transformed by
multiplying the appropriate Jacobian.
\(A^{-1}\cdot f(\gamma^{-1}(z'))\cdot
(\partial_z\gamma^{-1})(z')\dd{z'}\). That is the same result, as if
the distribution had been transformed by multiplying the appropriate
Jacobian.
Using the distribution \cref{eq:distcos} for the variable
\(\cos\theta\) and choosing the polar angle \(\varphi\) uniformly
@ -273,15 +274,16 @@ in \cref{sec:simpdiphotriv}.
include histograms generated by \sherpa\ and \rivet.}
\end{figure}
Where \cref{fig:histeta} shows clear resemblance
of \cref{fig:xs-int-eta}, the sharp peak in \cref{fig:histpt} around
Where \cref{fig:histeta} shows clear resemblance of
\cref{fig:xs-int-eta}, the sharp peak in \cref{fig:histpt} around
\(\pt=\SI{100}{\giga\electronvolt}\) seems surprising. When
transforming the differential cross section to \(\pt\) it can be seen
in \cref{fig:diff-xs-pt} that there really is a singularity at
\(\pt =\abs{\vb{p}}\). Furthermore the histograms \cref{fig:histeta}
and \cref{fig:histpt} are consistent with their \rivet-generated
counterparts and are therefore considered valid.
\(\pt =\abs{\vb{p}}\). This singularity will vanish once considering a
more realistic process (see \cref{chap:pdf}). Furthermore the
histograms \cref{fig:histeta,fig:histpt} are consistent
with their \rivet-generated counterparts and are therefore considered
valid.
%%% Local Variables:
%%% mode: latex

8
latex/tex/qqgammagamma/calculation.tex
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@ -164,10 +164,10 @@ The crucial step here was to sum over \(\mu\) and utilizing
_{\mu }=-2\gamma ^{\sigma }\gamma ^{\rho }\gamma ^{\nu }\).
After multiplying out the terms in \cref{eq:averagedm} and applying
the \cref{eq:gii} and \cref{eq:gij} there results (after rather
technical simplifications) the averaged matrix element
of \cref{eq:averagedm_final}. It is noteworthy that the mixing terms
After multiplying out the terms in \cref{eq:averagedm} and plugging in
\cref{eq:gii,eq:gij} there results (after rather technical
simplifications) the averaged matrix element of
\cref{eq:averagedm_final}. It is noteworthy that the mixing terms
cancel out, in other terms: \(\Gamma_{12} + \Gamma_{21} = 0\). The
result can also be expressed in terms of the pseudo-rapidity
\(\eta \equiv -\ln[\tan(\frac{\theta}{2})]\).