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\title[MPI in PYTHIA]{{\Huge MPI in PYTHIA}\\
1. Brief overview\\
2. Color reconnection and the top mass}
\author[Torbjörn Sjöstrand]{\Large\bf Torbjörn Sjöstrand\\[-3mm]}
\institute[Lund]{\normalsize Department of Astronomy and Theoretical Physics\\
Lund University\\Sölvegatan 14A, SE-223 62 Lund, Sweden}
\date{\color{red}MPI@LHC 2014, Krakow, 3--7 November 2014}

\begin{document}

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\begin{frame}[plain]

\includegraphics[height=0.25\textheight]{pics/lulogo.pdf}\hspace{5mm}%
\includegraphics[height=0.25\textheight]{pics/vrlogo.png}\hfill%
\includegraphics[height=0.25\textheight]{pics/pylogo.jpg}

\titlepage

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\begin{frame}{1987: the (almost) original PYTHIA model}

\begin{itemize}
\item {\color{red}Seek unified description of hard jets, UE and MB.}
\item {\color{red}Perturbative origin} $\Rightarrow$ $\pT$ d.o.f. essential\\
      {\color{olive}(unlike multi-Pomeron models at the time).} 
\item {\color{red}Screening} $\Rightarrow$ 
      $\d\pTs/\pT^4 \to \d\pTs/(\pTs + \pTo^2)^2$\\ 
      with {\color{red}$\pTo \approx 1.5-2$ GeV} 
      $\Rightarrow$ finite MPI number.
\item {\color{red}$\pT$-ordered generation}, Sudakov/shower style.
\item Hardest MPI standard PDFs, softer modified.
\item Tuneable impact-parameter picture.
\item {\color{red}Colour reconnection} needed.
\end{itemize}
\vspace*{2mm}
Makes use of existing PYTHIA/JETSET components, such as
\begin{itemize}
\item Lund string fragmentation, and
\item initial- and final-state parton showers.
\end{itemize}
\vspace*{2mm}
{\color{olive}TS \& M. van Zijl, Phys.Rev. D36 (1987) 2019} 

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\begin{frame}{1987: the experimental evidence}

\begin{columns}[T]
\begin{column}{0.5\textwidth}
MPI signals included\\[2mm]
\begin{itemize}
\item width of charged multiplicity,
\item forward--backwards correlations, and  
\item {\color{blue}jet pedestal effect:}
\end{itemize}
\includegraphics[width=\textwidth]{pics/maria32.pdf}
\end{column}
\hspace*{-0.1\textwidth}
\begin{column}{0.5\textwidth}
{\color{red}CR signal from $\langle \pT \rangle(n_{\mrm{ch}})$:}
\includegraphics[width=\textwidth]{pics/maria27.pdf}
\end{column}
\end{columns}

\end{frame}

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\begin{frame}{Today: basic generation of MPI}

\begin{itemize}
\item {\color{blue}{\bf Basic ideas remain}: screening, $\pT$-ordered 
generation,\\
all events contain at least one perturbative interaction.}
\item {\color{blue}Still allow for many different impact-parameter profiles.}
\item {\color{red}Screening $\pTo$ energy-dependent for post-HERA PDFs}.
\item {\color{blue}Two $\Rightarrow$ {\color{red}three} basic generation 
possibilities:}
\begin{itemize}
\item[0] {\color{blue}no separate hard interaction $\Rightarrow$ 
minbias events,}
\item[1] {\color{blue}start from fixed hard interaction $\Rightarrow$ 
underlying event, or}
\item[2] {\color{red}select two hard interactions, e.g. $\W^-\W^-$.}
\end{itemize}
\item {\color{red}More sophisticated rescaled PDF's, taking into account
momentum and flavour correlations.}
\item {\color{red}Possible to kick out several valence quarks
($\Rightarrow$ junctions),\\ 
and to have more complicated bream remnants.} 
\item {\color{red}Each MPI associated with its ISR and FSR activity.}
\item {\color{red}MPI machinery also for diffractive events.}
\end{itemize}

\end{frame}

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\begin{frame}{Interleaved evolution}

{\color{blue}
$\bullet$ MPI ordered in $\pT$ from onset.\\[1mm]
$\bullet$ Now also $\pT$-ordered parton showers for ISR and FSR.\\[1mm]
$\Rightarrow$ Allows interleaved evolution for MPI, ISR and FSR:}
\begin{eqnarray*}
  \frac{\d \mathcal{P}}{\d \pT} & \hspace*{-3mm} = \hspace*{-3mm} &
  \left( {\color{blue}\frac{\vphantom{\left(\right)} 
         \d\mathcal{P}_{\mrm{MPI}}}{\d \pT} } +
  \sum   {\color{red}\frac{\vphantom{\left(\right)} 
         \d\mathcal{P}_{\mrm{ISR}}}{\d \pT} } +
  \sum   {\color{olive} \frac{\vphantom{\left(\right)} 
         \d\mathcal{P}_{\mrm{FSR}}}{\d \pT} }
  \right)  \\
  & \hspace*{-3mm} \times \hspace*{-3mm} & 
  \exp \left( - \int_{\pT}^{p_{\perp\mrm{max}}}
  \left( {\color{blue} \frac{\vphantom{\left(\right)}
          \d\mathcal{P}_{\mrm{MPI}}}{\d \pT'} } +
  \sum   {\color{red} \frac{\vphantom{\left(\right)} 
          \d\mathcal{P}_{\mrm{ISR}}}{\d \pT'} } +
  \sum   {\color{olive} \frac{\vphantom{\left(\right)} 
          \d\mathcal{P}_{\mrm{FSR}}}{\d \pT'} }
  \right) \d \pT' \right) 
\end{eqnarray*}
Ordered in decreasing $\pT$ using ``Sudakov'' trick.\\[1mm]
\pause
{\color{red}
Corresponds to increasing ``resolution'' of partonic final state:\\ 
smaller $\pT$ fill in details of basic picture set at larger $\pT$.}\\[1mm]

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\begin{frame}{Rescattering}

\includegraphics[width=\textwidth]{pics/rescattering.pdf}

\end{frame}

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\begin{frame}{An $x$-dependent proton size}

Reasonable to assume that low-$x$ partons are more spread out: 
\[
\rho(r, x) \propto \frac{1}{a^3(x)} \, 
\exp \left( -\frac{r^2}{a^2(x)} \right) ~~~~ \mrm{with} ~~~~
a(x) = a_0 \left( 1 + a_1 \ln \frac{1}{x} \right)
\]
$a_1 \approx 0.15$ tuned to \textbf{rise} of $\sigma_{\mrm{ND}}$\\
$a_0$ tuned to \textbf{value} of $\sigma_{\mrm{ND}}$, given PDF, 
$\pTo$, \ldots\\
\includegraphics[width=0.5\textwidth]{pics/bAvgEik.pdf}%
\includegraphics[width=0.5\textwidth]{pics/hard-bMI.pdf}\\[-1mm]
{\color{red}%
Consequence: collisions at large $x$ will have to happen at small $b$,\\
and hence further large-to-medium-$x$ MPIs are enhanced.}\\
{\color{olive}$a_1 > 0$ not favoured by tunes so far!}

\end{frame}

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\begin{frame}{Colour reconnection}

\begin{columns}[T]
\begin{column}{0.40\textwidth}
{\color{blue}$\langle \pT \rangle(n_{\mrm{ch}})$ effect\\ 
alive and kicking:}\\[1mm]
\includegraphics[width=\textwidth]{pics/ptvsnchRivetAtlas3.pdf}\\[1mm]
{\color{blue}Colour reconnection (CR):\\ 
reduce total string length\\ 
$\Rightarrow$ reduce hadronic multiplicity}
\end{column}
\hspace{-0.08\textwidth}
\begin{column}{0.60\textwidth}
\includegraphics[width=\textwidth]{pics/nhadstr.pdf}\\[1mm]
\hspace*{10mm}{\color{red}String width $\sim$ hadronic width\\[1mm] 
\hspace*{10mm}$\Rightarrow$}
\colorbox{yellow}{\color{red}{Overlap factor $\sim$ 10!}}\\[2mm]
\hspace*{10mm}{\color{red}Larger for hard collisions\\
\hspace*{10mm}(small impact parameter)}
\end{column}
\end{columns}

\end{frame}

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\begin{frame}{A top mass puzzle}

\begin{columns}[T]
\begin{column}{0.50\textwidth}
\vspace*{-5mm}
\[ 
\left. \begin{array}{l} 
\Gamma_{\t} \approx 1.5~\mathrm{GeV}\\
\Gamma_{\W} \approx 2~\mathrm{GeV}\\ 
\Gamma_{\Z} \approx 2.5~\mathrm{GeV}
\end{array} \right\}
{\color{red} \Rightarrow c\tau \approx 0.1~\mathrm{fm} :}
\vspace*{-3mm}
\]
{\color{blue}
p ``pancakes'' have passed,\\
MPI/ISR/FSR for $\pT \geq 2$ GeV,\\
inside hadronization colour fields.}
\end{column}
\hspace{-0.05\textwidth}
\begin{column}{0.50\textwidth}
\vspace*{-3mm}
\includegraphics[width=\textwidth]{pics/topRecon.pdf}
\end{column}
\end{columns}

\includegraphics[width=0.8\textwidth]{pics/spyros1.pdf}
\raisebox{3mm}{\small (S. Argyropoulos)}\\
{\color{olive}1. Great job in reducing the errors.}\\
{\color{blue}2. CR is one of the dominant systematics.}\\
{\color{red}3. Why is the CR uncertainty going down when there are\\
\hspace*{4mm}$\bullet$ no advances in theoretical understanding, and\\
\hspace*{4mm}$\bullet$ no measurements to constrain it?}

\end{frame}

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\begin{frame}{Top mass shift in \textsc{Pythia} 6}

\begin{columns}[T]
\begin{column}{0.40\textwidth}
Studies for the Tevatron.\\[5mm]
{\color{olive}Green bands: old virtuality-ordered showers.}\\[1mm]
{\color{blue}Blue bands: new $\pT$-ordered showers.}\\[1mm]
In total $\pm 1.0$ GeV,\\[1mm] 
whereof {\color{magenta}$\pm 0.7$ GeV perturbative},\\[1mm]
and {\color{red}$\pm 0.5$ GeV nonperturbative}.   
\end{column}
\hspace{-0.08\textwidth}
\begin{column}{0.60\textwidth}
\hspace*{5mm}
Fit $\to$ scaled: Jet Energy Scaling.\\
\includegraphics[width=\textwidth]{pics/wickeShift.pdf}
\end{column}
\end{columns}
{\small\color{olive}(M.Sandhoff and P.Z Skands, FERMILAB-CONF-05-518-T;)\\ 
\mbox{D. Wicke and P.Z. Skands, EPJ C52 (2007) 133, Nuovo Cim. B123 (2008) S1}}

\end{frame}

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\begin{frame}{\textsc{Pythia} 8.1 CR model}

Only one CR model:
\begin{itemize}
\item Starting from lowest-$\pT$ MPI and moving upwards define its 
\[
\mathcal{P}_{\mathrm{rec}}({\color{blue}p_T}) = 
\frac{({\color{red}R_{\mathrm{rec}}}\ p_{T0})^2}%
{({\color{red}R_{\mathrm{rec}}}\ p_{T0})^2+{\color{blue}p_T^2}},
\]
with any higher-$\pT$ MPI. ${\color{red}R_{\mathrm{rec}}}$ one free 
parameter of model.
\item Find colour dipoles of highest-$\pT$ MPI.
\item Consecutively attach each gluon of each lower-$\pT$ MPI to be 
reconnected where it increases the string length $\lambda$ the least.
\item Repeat for lower-$\pT$ MPIs that form separate systems.
\end{itemize}
{\color{red}End result: fewer but bigger systems, with reduced 
total $\lambda$.}\\[2mm]
{\color{blue}Three CR options for top:\\
$\bullet$ no CR at all\\
$\bullet$ late resonance decays: t/W decays after CR\\
$\bullet$ early resonance decays: t/W decays before CR}

\end{frame}

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\begin{frame}{Further \textsc{Pythia} 8.2 CR models}

{\color{olive}
S. Argyropoulos \& TS: arXiv:1407.6653 [hep-ph] $\Rightarrow$ JHEP}\\[2mm]
Basic idea: produce range of models to study how big 
$\Delta m_{\mathrm{top}}$ could be without contradicting data.\\[1mm]
\begin{columns}[T]
\begin{column}{0.45\textwidth}
{\color{red}Top CR as afterburner:\\
toy / {\bf stealth} models\\
$\bullet$ forced random\\
$\bullet$ forced nearest\\
$\bullet$ forced farthest\\
$\bullet$ forced smallest $\Delta \lambda$\\
$\bullet$ smallest $\Delta \lambda$}
\end{column}
\begin{column}{0.45\textwidth}
{\color{blue}Top CR on equal footing:\\
more sophisticated / fragile\\
$\bullet$ swap\\
$\bullet$ move\\
$\bullet$ swap + flip\\
$\bullet$ move + flip\\
so as to reduce $\lambda$}
\end{column}
\end{columns}
\vspace*{3mm}
The $\lambda$ measure of an event is approximated by
\[
\lambda \approx \lambda_{\mathrm{approx}} 
= \sum_{\mathrm{dipoles}} \ln \left( 1 + \frac{m_{ij}^2}{m_0^2} \right)
\]
with $m_0 \approx m_{\mathrm{hadronic}} \approx 1$ GeV.

\end{frame}

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\begin{frame}{Some ways to perform a reconnection}

\hspace*{40mm}swap:\\[-2mm]
\includegraphics[width=\textwidth]{pics/CRswap.pdf}\\
\hspace*{40mm}move:\\[-2mm]
\includegraphics[width=\textwidth]{pics/CRmove.pdf}\\
\hspace*{40mm}flip:\\[-2mm]
\includegraphics[width=\textwidth]{pics/CRflip.pdf}

\end{frame}

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\begin{frame}{Effects on top mass before tuning}

\begin{columns}[T]
\begin{column}{0.65\textwidth}
\includegraphics[width=\textwidth]{pics/mtop_beftune.pdf}\\
\hspace*{7mm}$\Delta m_{\mathrm{top}}$ relative to no CR:\\
\hspace*{7mm}\begin{tabular}{|c|c|c|}
\hline
model & $\Delta m_{\mathrm{top}}$ & $\Delta m_{\mathrm{top}}$\\
      &  [GeV]                  & rescaled \\
\hline 
default (late) & $-0.415$ & $+0.209$ \\
default early  & $+0.381$ & $+0.285$ \\
forced random  & $-6.970$ & $-6.508$ \\
\hline
\end{tabular}
\end{column}
\hspace*{-0.05\textwidth}
\begin{column}{0.35\textwidth}
{\color{white}.}\\[8mm]
{\color{red}
Asymmetric spread:\\[1mm]  
$\Delta m_{\mathrm{top}} < 0$ easy,\\[1mm] 
$\Delta m_{\mathrm{top}} > 0$ difficult.\\[3mm] 
Parton showers already prefer minimal $\lambda$.\\[3mm]
Main effect from jet broadening, some from jet--jet angles.}
\end{column}
\end{columns}

\end{frame}

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\begin{frame}{Effects on top mass after tuning}

No publicly available measurements of UE in top events.\\
{\color{red}$\bullet$ Afterburner models tuned to ATLAS jet shapes in 
$\t\tbar$ events\\
\hspace*{3mm}$\Rightarrow$ high CR strengths disfavoured.}\\
{\color{blue}$\bullet$ Early-decay models tuned to ATLAS minimum bias data\\
\hspace*{3mm}$\Rightarrow$ maximal CR strengths required to (almost) match
$\langle \pT \rangle (n_{\mathrm{ch}})$.}\\[2mm] 
\begin{columns}[T]
\begin{column}{0.4\textwidth}
{\small\begin{tabular}{|c|c|}
\hline
model & $\Delta m_{\mathrm{top}}$\\
      & rescaled \\
\hline 
default (late) & $+0.239$ \\
forced random  & $-0.524$ \\
swap           & $+0.273$ \\
\hline
\end{tabular}}\\[2mm]
$\Delta m_{\mathrm{top}}$ relative to no CR
\end{column}
\hspace*{-0.05\textwidth}
\begin{column}{0.6\textwidth}
\colorbox{yellow}{\color{red}{\boldmath $m_{\mathrm{top}}^{\mathrm{max}} 
- m_{\mathrm{top}}^{\mathrm{min}} \approx 0.80$ GeV}}\\[2mm]
Excluding most extreme (unrealistic) models down to\\[2mm]
\colorbox{yellow}{\color{red}{\boldmath $m_{\mathrm{top}}^{\mathrm{max}} 
- m_{\mathrm{top}}^{\mathrm{min}} \approx 0.50$ GeV}}\\
{\color{olive}
(in line with Sandhoff, Skands \& Wicke)}\\[2mm]
\end{column}
\end{columns}
{\color{white}.}\\
{\color{blue}Studies of top events could help constrain models:\\
$\bullet$ jet profiles and jet pull (skewness)\\
$\bullet$ underlying event}

\end{frame}

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\begin{frame}{Summary and Outlook}

\begin{itemize}
\item {\color{red}MPI key PYTHIA component since almost 30 years.}
\item {\color{red}Original concepts still hold: screening with 
$\pTo \approx 2$ GeV,\\ 
$\pT$-order, $n_{\mathrm{pert}} \geq 1$, reconnection, strings, \ldots}
\item {\color{magenta}Many aspects gradually becoming more sophisticated,\\
notably interleaved evolution MPI + ISR + FSR.}
\item {\color{magenta}Everything mixed up $\Rightarrow$ experimental tests 
indecisive,\\
e.g.\ rescattering and $x$-dependent proton size.}
\item {\color{blue}Colour reconnection one of big known unknowns.}
\item {\color{blue}Experimental $\Delta m_{\mathrm{top}}$ CR error 
out of control?}
\item {\color{blue}Need dedicated experimental studies of CR in top events.} 
\item {\color{blue}New CR model/framework by J.R. Christiansen and P. Skands 
coming up (next).} 

\end{itemize}

\end{frame}

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\end{document}