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\begin{center}
  {\Large \bf Proceedings of the Workshop on }\\[0.25cm]
  {\Large \bf High precision $\alphas$ measurements: from LHC to FCC-ee}\\[4mm]
  {\large CERN, Geneva\\
  October 12th--13th, 2015}\\[1cm] 
  
  {\bf \it Editors}\\[0.25cm]
   David d'Enterria (CERN), Peter Z. Skands (Monash)\\[0.3cm]
  {\bf  \it Authors}\\[0.25cm]
  A.~Banfi~(U.~Sussex)  S.~Bethke~(MPI, M\"unchen), J.~Bl\"umlein~(DESY),  D.~d'Enterria~(CERN),  X.~Garcia-Tormo~(Bern), 
  A.~Hoang~(U.~Wien), B.~Kniehl~(U.~Hamburg),  M.~Klasen~(U.~M\"unster),  S.~Kluth~(T.U.~M\"unchen),  J.L.~Kneur~(U.~Montpellier 2),
  J.~K\"uhn~(KIT, Karlsruhe),  P.~Mackenzie~(Fermilab),  B.~Malaescu~(LPNHE, Paris), L.~Mihaila~(KIT, Karlsruhe), A.~Mitov~(Cambridge),
  K.~M\"onig~(DESY),  R.Perez-Ramos~(Paris),  A.~Pich~(U.~Val\`encia),  J.~Pires~(Milano Bicocca),  K.~Rabbertz~(KIT, Karlsruhe),
  G.~Salam~(CERN), F.~Sannino~(CP3-Origins, Odense), P.Z.~Skands~(Monash), J.~Soto i Riera~(U.~Barcelona), M.~Srebre~(U.~Ljubljana)

\end{center}

\vspace*{0.50cm}

\begin{abstract}
  \baselineskip 1.5em This document collects a summary of all contributions of the workshop on 
  {\it ``High precision measurements of $\alpha_s$: from LHC to FCC-ee''} held at CERN, October~12-13, 2015
  (\ttt{http://indico.cern.ch/e/alphas2015}).
  The workshop explored in depth the latest developments on the determination of
  the QCD coupling $\alphas$ from the key categories where high precision measurements are (or will be) 
  available. Those include low-energy observables: (i) lattice QCD, (ii) pion decay factor, (iii)
  quarkonia and (iv) $\tau$ decays, (v) soft parton-to-hadron fragmentation functions; as well as 
  high-energy observables: (vi) global fits of parton distribution functions, (vii) hard parton-to-hadron
  fragmentation functions, (viii) jets in $e^\pm$-p DIS and  photoproduction, (ix) event shapes and (x)
  jet cross sections in $\epem$ collisions, (xi) W boson and (xii) Z boson decays, and (xiii) top-quark and
  (xiv) jet cross sections in p-p collisions.  
  The current status of the theoretical and experimental uncertainties associated to each extraction method,
  the improvements expected at the end of the LHC running, and future perspectives achievable in $\epem$
  collisions at the Future Circular Collider (FCC-ee) with multi-inverse-attobarn integrated luminosities
  yielding 10$^{12}$ Z bosons and jets, and 10$^{8}$ W bosons and $\tau$ leptons, are thoroughly reviewed and discussed.
%  These proceedings contain a short summary contribution from the speakers, as well as the lists of  authors,
%  participants, and talks.
\end{abstract}

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{\em Authors and Speakers}\\[0.5cm] 

\small
{\bf A.~Banfi~(U.~Sussex),
  S.~Bethke~(MPI, M\"unchen), 
  J.~Bl\"umlein~(DESY),
  D.~d'Enterria~(CERN),
  X.~Garcia-Tormo~(Bern), 
  A.~Hoang~(U.~Wien),
  B.~Kniehl~(U.~Hamburg),
  M.~Klasen~(U.~M\"unster), 
  S.~Kluth~(T.U.~M\"unchen), 
  J.L.~Kneur~(U.~Montpellier 2),
  J.~K\"uhn~(KIT, Karlsruhe),
  P.~Mackenzie~(Fermilab),
  B.~Malaescu~(LPNHE, Paris)
  L.~Mihaila~(KIT),
  A.~Mitov~(Cambridge),
  K.~M\"onig~(DESY),
  R.Perez-Ramos~(Paris),
  A.~Pich~(U.~Val\`encia),
  J.~Pires~(Milano Bicocca), 
 K.~Rabbertz~(KIT, Karlsruhe),
 G.~Salam~(CERN),
 F.~Sannino~(CP3-Origins, Odense),
 P.Z.~Skands~(Monash),
 J.~Soto i Riera~(U.~Barcelona),
 M.~Srebre~(U.~Ljubljana)
}\\[1cm]


{\em Additional Participants}\\[0.5cm]
\small 
{\bf A.~Ali~(DESY), A.~Blondel~(U.~Geneva), C.~Gracios~(Puebla), M.~Klute~(MIT), I.~Kolbe~(U.~Cape Town),
  A.~Larkoski~(MIT/Harvard), B.~Meiring~(U.~Cape Town), R.~Morad~(U.~Cape Town), A.N.~Rasoanaivo~(U.~Cape
  Town), P.~Telles-Rebello~(CBPF, Rio de Janeiro), ...
}\\[1cm]

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\newabstract



\section{Introduction}

The strong coupling $\alphas$ is one of the fundamental parameters of the Standard Model (SM), setting the
scale of the strength of the strong interaction theoretically described by Quantum Chromodynamics (QCD).
%Starting from a value of $\lqcd\approx$~0.2~GeV, where the perturbatively-defined coupling diverges, 
%$\alphas$ decreases with increasing energy scale $Q$ following a $\sim1/\ln(Q^2/\lqcd^2)$ dependence. 
At the reference Z pole mass scale, its measured value amounts to $\alphasmZ$~=~0.1185~$\pm$~0.0006. %~\cite{PDG}.
Given its current $\delta \alpha_s \approx 0.6\%$ uncertainty---orders of magnitude %In comparison, our knowledge of 
larger than that of the gravitational ($\delta G\approx 10^{-5}$), Fermi ($\delta G_F\approx 10^{-8}$) and QED
($\delta \alpha\approx 10^{-10}$) couplings---the strong coupling is the least precisely known of all fundamental
constants in nature. % are orders of magnitude more precise. 
Improving our knowledge of $\alphas$ is a prerequisite to reduce the theoretical uncertainties in the calculations of 
all high-precision perturbative QCD (pQCD) processes whose cross sections or decay rates depend on
higher-order powers of $\alpha_s$, as is the case for virtually all those measured at the
LHC. In the Higgs sector, in particular, the uncertainty on $\alphas$ is currently the second major
contributor (after the bottom mass) to the parametric uncertainties of its dominant $H\to\bbbar$ partial
decay. The same applies for the extraction of the charm Yukawa coupling via future  $H\to c\bar{c}$
measurements.\\ 

The workshop {\it ``High precision measurements of $\alpha_s$: from LHC to FCC-ee''} was held at CERN,
October~12-13, 2015 (\ttt{http://indico.cern.ch/e/alphas2015}), as part of the FCC-ee {\it QCD and gamma-gamma
physics} working group activities in the context of the preparation of the FCC-ee Yellow Report in 2016.
The meeting brought together experts from several different fields to explore in depth the latest developments
on the determination of the QCD coupling $\alphas$ from the key categories where high precision measurements
are (or will be) available, and put its emphasis on the following issues: 
\begin{itemize}
\item What is the current state-of-the-art of each one of the $\alphas$ determination methods, from the
  theoretical and experimental points of view? 
\item What is the current size of the theoretical (missing higher orders, electroweak corrections,
  power corrections, hadronization corrections,...) and experimental uncertainties associated to each
  measurement? 
\item What is the expected $\alphas$ uncertainty in $\sim$10 years from now thanks to the ongoing (or expected)
  theoretical developments, plus $\cO{1\,\rm ab^{-1}}$ collected p-p data at 14 TeV at the LHC ? 
\item What are the improvements expected to be brought about by $\epem$ collisions at the FCC-ee
  ($\sqrts$~=~91, 160, 240 and 350~GeV) with 10$^{12}$ Z bosons and jets, 
  %collected at $\sqrts=m_{\rm Z}$; a similar number of jets collected at all $\sqrts=m_{\rm Z}$, 
  and 10$^{8}$ W bosons and $\tau$ leptons collected ?
 % atsqrt(s)=mWW; similar orders-of-magnitude for tau, jets,...? 
\item What are the systematic errors that the FCC-ee detectors should target in order to match the expected
  statistical precision, or where that is not possible, what are the important theoretical targets that should
  be met or exceeded ? 
\end{itemize}

With those goals in mind, the workshop was organized along four broad sessions:
\begin{enumerate}
\item  An introductory session, presenting the motivations of the workshop, the current status of the world
  average of the strong coupling, the impact of $\alphas$ on Higgs cross sections and branching ratios, and on
  new physics constraints.
\item A session dedicated to $\alphas$ determination at low energy including results from: lattice QCD, pion
  decay factor, $\tau$ decay, $\QQbar$ decays, and soft parton-to-hadron FFs.
\item A session dedicated to $\alphas$ determination at higher energy scales including: global fits of parton
  distribution functions, hard parton-to-hadron fragmentation functions,  jets in deep-inelastic scattering
  and photoproduction in $e^\pm$-p collisions, 
  $\epem$ event shapes, $\epem$ jets, hadronic Z and W decays, $\sigma(\epem \to$~hadrons), electroweak fit,...
\item Recent experimental and theoretical results and plans for $\alphas$ measurements at the LHC via top-quark
  pair and jets cross sections.
\end{enumerate}

One important goal of the workshop was to facilitate discussion between the different groups, and in
particular to give speakers the opportunity to explain details that one would normally not be able to present
at a conference, but which have an important impact on the analyses.
There were 40 physicists who took part in the workshop, and 24 talks were presented.  Slides as well as
background reference materials are available on the conference website
\begin{center}
    \ttt{http://indico.cern.ch/e/alphas2015}
\end{center}

The sessions and talks in the workshop program were:
\begin{itemize}
\itemsep -1.mm
\item Introduction
\vspace{-1ex}
\begin{itemize}
\itemsep -1.5mm
 \item ``Introduction and goals of the workshop'', D.~d'Enterria and P.Z. Skands 
 \item ``World Summary of $\alphas$ (2015)'', S.~Bethke
 \item ``$\alphas$ and physics beyond the Standard Model'', F. Sannino
 \item ``Impact of $\alphas$ on Higgs production and decay uncertainties'', L. Mihaila
\end{itemize}
\item Measurements of $\alphas$ at low energy scales:
%$\alpha_s$ from low-energy measurements
\vspace{-1ex}
\begin{itemize}
\itemsep -1.5mm
 \item ``$\alphas$ from lattice QCD'', P. Mackenzie
 \item ``$\alphas$ from the QCD static energy'', X. Garcia i Tormo
 \item ``$\alphas$ from pion decay factor'', J.L. Kneur
 \item ``$\alphas$ from hadronic tau decays'', A. Pich
 \item ``$\alphas$ from hadronic quarkonia decays'', J. Soto i Riera
 \item ``$\alphas$ from soft parton-to-hadron FFs'', R. Perez-Ramos and D. d'Enterria
\end{itemize}
\vspace{-1ex}
%
\item Measurements of $\alphas$ at high energy scales:
\vspace{-1ex}
\begin{itemize}
\itemsep -1.5mm
 \item ``$\alpha_s$ from global fits of parton distribution functions'', J. Bl\"umlein
 \item ``$\alpha_s$ from jets in DIS and photoproduction'', M. Klasen
 \item ``$\alphas$ from scaling violations of hard parton-to-hadron FFs'', B. Kniehl
 \item ``$\alphas$ from $\epem$ event shapes'', S. Kluth
 \item ``$\alphas$ from $\epem$ C-parameter event shape'', A. Hoang
 \item ``$\alphas$ from $\epem$ jet cross sections'', A. Banfi
 \item ``$\alphas$ from hadronic Z decays and from the full electroweak fit'', K. M\"onig
 \item ``$\alphas$ from hadronic W decays'', M. Srebre
 \item ``$\alphas$ from $\sigma(\epem\to$~hadrons)'', J. K\"uhn
\end{itemize}
\vspace{-1ex}
%
\item Measurements of $\alpha_s$ at the LHC and conclusions:
\vspace{-1ex}
\begin{itemize}
\itemsep -1.5mm
 \item ``$\alphas$ from top-pair cross sections at the LHC and beyond'', A. Mitov
 \item ``$\alphas$ from top-pair cross sections'', G. Salam
 \item ``Future prospects of $\alphas$ from NNLO jets at the LHC and beyond'', J. Pires
 \item ``$\alphas$ determinations from ATLAS (status and plans)'', B. Malaescu
 \item ``$\alphas$ determinations from CMS (status and plans)'', K. Rabbertz
 \item Final discussion
 \item Conclusions (FCC-ee Yellow Report preparation)
\end{itemize}
\vspace{-1ex}
%

\end{itemize}
\noindent This proceedings represent a collection of extended abstracts and references
for the presentations, summarizing the most important results and issues. 
These written contributions will be incorporated into the FCC-ee Yellow Report under preparation. 
%In these writeups, unless otherwise indicated, the strong coupling $\alpha_s(\mu)$
%is defined in the $\overline {\rm MS}$ scheme, and $\alpha_s(m_Z)$ is the
%coupling with five light quark flavors.

\bigskip\bigskip

%\noindent {\em Acknowledgments}\\[-5pt]
%We would like to thank all participants for making the Workshop on High-Precision Measurements of $\alphas$ a
%very stimulating meeting.
%\bigskip

\noindent CERN, October 2015

\bigskip\bigskip\bigskip

\hspace*{10.cm} David d'Enterria

\hspace*{10.cm} Peter Skands

\bigskip\bigskip


\newpage


\section{Proceedings Contributions}

\vskip.1cm

\noindent\mbox{}\hfill{\bf Page}

\talk{{\bf D.~d'Enterria and P.Z. Skands }}{Introduction and goals of the workshop}{abs:Intro}

\talk{{\bf S.~Bethke}}{World Summary of $\alphas$ (2015)}{abs:SiggiBethke}

\talk{{\bf F. Sannino}}{$\alphas$ and physics beyond the Standard Model}{abs:FSannino}

\talk{{\bf L. Mihaila}}{Impact of $\alphas$ on Higgs production and decay uncertainties}{abs:LMihaila}

\talk{{\bf P. Mackenzie}}{$\alphas$ from lattice QCD}{abs:PMackenzie}

\talk{{\bf X. Garcia i Tormo}}{$\alphas$ from the QCD static energy}{abs:XGaTormo}

\talk{{\bf J.L. Kneur}}{$\alphas$ from pion decay factor}{abs:JLKneur}

\talk{{\bf A.~Pich}}{$\alphas$ from hadronic tau decays}{abs:APich}

\talk{{\bf J. Soto i Riera}}{$\alphas$ from hadronic quarkonia decays}{abs:JSotoRiera}

\talk{{\bf R. Perez-Ramos and D. d'Enterria}}{$\alphas$ from soft parton-to-hadron FFs}{abs:RPerezRamos}

\talk{{\bf J.~Bl\"umlein}}{$\alpha_s$ from fits of parton distribution functions}{abs:JBluemlein}

\talk{{\bf M. Klasen}}{$\alpha_s$ from jets in DIS and photoproduction}{abs:MKlasen}

\talk{{\bf S.~Kluth}}{$\alphas$ from $\epem$ event shapes}{abs:SKluth}

\talk{{\bf A. Hoang}}{$\alphas$ from $\epem$ C-parameter event shape}{abs:AHoang}

\talk{{\bf A. Banfi}}{$\alphas$ from $\epem$ jet cross sections}{abs:ABanfi}

\talk{{\bf K. M\"onig}}{$\alphas$ from hadronic Z decays and from the full electroweak fit}{abs:KMoenig}

\talk{{\bf M. Srebre}}{$\alphas$ from hadronic W decays}{abs:MSrebre}

\talk{{\bf J.~K\"uhn}}{$\alphas$ from $\sigma(\epem\to$~hadrons)}{abs:JKuehn}

%\newpage

\talk{{\bf A. Mitov}}{$\alphas$ from top-pair cross sections at the LHC and beyond}{abs:AMitov}

\talk{{\bf G. Salam}}{$\alphas$ from top-pair cross sections}{abs:GavinSalam}

\talk{{\bf J. Pires}}{Future prospects of $\alphas$ from NNLO jets at the LHC and beyond}{abs:JPires}

\talk{{\bf B. Malaescu}}{$\alphas$ determinations from ATLAS (status and plans)}{abs:BMalaescu}

\talk{{\bf K.~Rabbertz}}{$\alphas$ determinations from CMS (status and plans)}{abs:KlausRabbertz}

\talk{{\bf D.~d'Enterria}}{Conclusions}{abs:Conclusion}

\newpage


%\hspace*{1.cm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\talkin{Intro.in}{abs:Intro}

\talkin{SiggiBethke.in}{abs:SiggiBethke}

\talkin{FSannino.in}{abs:FSannino}

\talkin{LMihaila.in}{abs:LMihaila}

\talkin{PMackenzie.in}{abs:PMackenzie}

\talkin{XGaTormo.in}{abs:XGaTormo}

\talkin{JLKneur.in}{abs:JLKneur}

\talkin{APich.in}{abs:APich}

\talkin{JSotoRiera.in}{abs:JSotoRiera}

\talkin{RPerezRamos.in}{abs:RPerezRamos}

\talkin{JBluemlein.in}{abs:JBluemlein}

\talkin{MKlasen.in}{abs:MKlasen}

\talkin{SKluth.in}{abs:SKluth}

\talkin{AHoang.in}{abs:AHoang}

\talkin{ABanfi.in}{abs:ABanfi}

\talkin{KMoenig.in}{abs:KMoenig}

\talkin{MSrebre.in}{abs:MSrebre}

\talkin{JKuehn.in}{abs:JKuehn}

\talkin{AMitov.in}{abs:AMitov}

\talkin{JPires.in}{abs:JPires}

\talkin{BMalaescu.in}{abs:BMalaescu}

\talkin{KlausRabbertz.in}{abs:KlausRabbertz}

\talkin{Conclusion.in}{abs:Conclusion}


\end{document}

 
