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Support #1473 » MICE_PID_v9.tex

Orestano, Domizia, 09 September 2014 10:42

 
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\tolerance=50000
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\linenumbers 
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\title{\bf 
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Measurement of the pion contamination in the Muon Ionisation Cooling 
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Experiment (MICE) beam}
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\author{The MICE Collaboration~\footnote{draft 1 version v0: 22/4/2013. 
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 {\bf To be submitted to JINST}}}
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\author{M. Bogomilov, Y. Karadzhov~$^{1}$ D. Kolev, I. Russinov,
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R.~Tsenov, G.Vankova-Kirilova \\
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Department of Atomic Physics, St. Kliment Ohridski University of Sofia,
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Sofia, Bulgaria\\
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\llap{$^{~1}$}~{Now at DPNC, Universi\'e de Geneve, Geneva, Switzerland}
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}
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\author{L. Wang, F.Y. Xu, S.X. Zheng\\
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Institute for Cryogenic and Superconductivity Technology, Harbin Institute of
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Technology, Harbin,
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PR China}
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\author{R. Bertoni, M. Bonesini
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%%%~\footnote{Corresponding author.
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%%%%E-mail:Maurizio.Bonesini@mib.infn.it}
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, G. Lucchini \\
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Sezione INFN Milano Bicocca, Dipartimento di Fisica G. Occhialini,
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Milano, Italy 
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}
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\author{V. Palladino\\
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Sezione INFN Napoli and Dipartimento di Fisica, Universit\`{a} Federico II,
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Complesso Universitario di Monte S. Angelo, Napoli, Italy}
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\author{G. Cecchet, A. de Bari\\
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Sezione INFN Pavia and Dipartimento di Fisica Nucleare e Teorica, Pavia, Italy}
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\author{M.Capponi, A.Iaciofano, D. Orestano,F. Pastore, L. Tortora\\
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Sezione INFN Roma Tre e Dipartimento di Matematica e Fisica, Universit\`a 
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di Roma Tre, Roma, Italy  
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}
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%\author{P. Chimenti, G. Giannini\\
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%University of Trieste and INFN Trieste, Italy}
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\author{Y. Mori\\
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Kyoto University Research Reactor Institute, Osaka, Japan}
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\author{Y. Kuno, H. Sakamoto, A. Sato, T. Yano, M. Yoshida\\
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Osaka University, Graduate School of Science, Department of Physics, Toyonaka, Osaka, Japan}
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\author{S. Ishimoto, S. Suzuki, K. Yoshimura\\
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High Energy Accelerator Research Organization (KEK), Institute of Particle and Nuclear Studies, Tsukuba, Ibaraki, Japan}
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\author{
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F. Filthaut$^{~2}$\\
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NIKHEF, Amsterdam, The Netherlands\\
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\llap{$^{~2}$}~{Also at Radboud University Nijmegen, Nijmegen, The Netherlands}
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}
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%\author{N. Mezentsev, A. N. Skrinsky\\
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%Budker Institute of Nuclear Physics, Novosibirsk, Russian Federation}
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\author{
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O.M. Hansen$^{~3}$, H. Haseroth, S.~Ramberger, M.~Vretenar\\
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CERN, Geneva, Switzerland \\
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\llap{$^{~3}$}~{Also at University of Oslo, Norway}
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}
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\author{R. Asfandiyarov, A. Blondel, F. Cadoux, J.-S. Graulich, 
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V.~Verguilov\\
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DPNC, Section de Physique, Universit\'e de Gen\`eve, Geneva, Switzerland \\
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}
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\author{C. Petitjean\\
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Paul Scherrer Institut, Villigen, Switzerland}
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\author{R. Seviour\\
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The Cockcroft Institute, Daresbury Science and Innovation Centre,
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Daresbury, Cheshire, UK}
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\author{
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  J.~Alexander, G.~Charnley, S.~Griffiths,
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  B.~Martlew, A.~Moss, I.~Mullacrane, A.~Oates, 
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  S.~York                                                              \\
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  STFC Daresbury Laboratory, Daresbury, Cheshire, UK                                                                          \\
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}
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\author{
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  D.~Adams, P.~Barclay,
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  D.E.~Baynham, T.W.~Bradshaw, M.~Courthold,
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  T.~Hayler, 
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  A.~Jones, A.~Lintern, C.MacWaters,
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  C.~Nelson, A.~Nichols, R.~Preece, S.~Ricciardi,
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  C.~Rogers, J.~Tarrant,
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  S.~Watson, A.~Wilson                                      \\
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  STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, UK \\
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}
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\author{R. Bayes, D. Forrest, J.C. Nugent, F.J.P. Soler\\
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School of Physics and Astronomy, Kelvin Building, The University of Glasgow, Glasgow, UK\\
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}
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\author{P. Cooke, R. Gamet\\
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Department of Physics, University of Liverpool, Liverpool, UK}
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\author{
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  A.~Alekou, M.~Apollonio$^{~4}$, G.~Barber, 
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  D.~Colling, A.~Dobbs,
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  P.~Dornan, S.~Fayer,
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  R.~Hare, S.~Greenwood, A.~Jamdagni, V.~Kasey,
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  M.~Khaleeq, J.~Leaver, K.~Long, 
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  J.~Pasternak, T.~Sashalmi, T.~Savidge \\
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Department of Physics, Blackett Laboratory, Imperial College London,
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London, UK    \\                                     \\
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\llap{$^{~4}$}~{Now at Diamond Light Source, Harwell Science and
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               Innovation Campus, Didcot, Oxfordshire, UK}                  \\
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}
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\author{V. Blackmore, T. Carlisle, J.H. Cobb, M. Rayner~$^{5}$,
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 H. Witte~$^{6}$,  W. Lau,  C.D. Tunnell, S. Yang \\
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Department of Physics, University of Oxford, Denys Wilkinson Building, Oxford, 
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UK \\
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\llap{$^{~5}$}~{Now at DPNC, Universit\'e de Geneve, Geneva, Switzerland} \\
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\llap{$^{~6}$}~{Now at Brookhaven National Laboratory, Upton, NY, USA}
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}
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\author{C.N. Booth, P. Hodgson, R. Nicholson, E. Overton, M. Robinson, P. J. 
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Smith\\
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Department of Physics and Astronomy, University of Sheffield, Sheffield, UK}
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\author{D. Adey$^{7}$, J. Back, S. Boyd, P. Harrison, C. Pidcott, I. Taylor \\
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Department of Physics, University of Warwick, Coventry, UK \\
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\llap{$^{~7}$}~{Now at Fermi National Laboratory, Batavia, IL, USA}
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}
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\author{M. Ellis$^{8}$, P. Kyberd, M. Littlefield, J.J. Nebrensky\\
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Brunel University, Uxbridge, UK\\
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\llap{$^{8}$}~{Now at Westpac Institutional Bank, Sydney, Australia}
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}
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%%\author{J. Norem\\
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%%Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA}
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\author{A.D. Bross, S. Geer, D. Neuffer, A. Moretti, M. Popovic \\
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Fermilab, Batavia, IL, USA}
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\author{M.A.C. Cummings, T. J. Roberts\\
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Muons, Inc., Batavia, IL, USA}
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\author{A. DeMello, M.A. Green, D. Li,  S. Virostek, M.S. Zisman\\
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Lawrence Berkeley National Laboratory, Berkeley, CA, USA}
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\author{B. Freemire, P. Hanlet, G. Kafka, D.M. Kaplan, D. Rajaram, P. Snopok, Y. Torun\\
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Illinois Institute of Technology, Chicago, IL, USA \\
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}
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\author{S.~Blot, Y.K. Kim \\
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Enrico Fermi Institute, University of Chicago, Chicago, IL, USA}
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\author{U. Bravar\\
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University of New Hampshire, Durham, NH, USA}
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\author{Y. Onel\\
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Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA}
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%%\author{D. Cline \\
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%%Department of Physics and Astronomy, University of California, Los Angeles, CA,
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%%USA}
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\author{R.A. Rimmer\\
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Jefferson Lab, Newport News, VA, USA}
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\author{L.M. Cremaldi, G.~Gregoire $^{9}$, T.L. Hart, T. Lui, N. Pradhan, D.A. Sanders,
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D.J. Summers\\
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University of Mississippi, Oxford, MS, USA \\
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\llap{$^{~9}$}~{Permanent address Institute of Physics,
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Universit\'e Catholique de Louvain, Louvain-la-Neuve, Belgium}
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}
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\author{L. Coney, R. Fletcher, G.G. Hanson, C. Heidt\\
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University of California, Riverside, CA, USA}
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\author{S. Kahn$^{10}$, H. Kirk, R.B. Palmer\\
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Brookhaven National Laboratory, Upton, NY, USA\\
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\llap{$^{~10}$}~{Now at Muons, Inc., IL, USA}
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}
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\newpage
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\abstract{The international Muon Ionisation Experiment (MICE) will
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perform a systematic investigation of ionisation cooling of a $\sim200$~MeV/$c$ muon beam.
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A low pion contamination in the MICE %low momentum 
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muon beam is
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an essential requirement for a precise  measurement of ionisation cooling.
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In 2011, data were taken in the MICE ``Step I'' configuration in order to commission the MICE particle identification detectors  and to characterise the MICE beam.
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The pion contamination in the MICE muon beam is found to be $1 \%$ or below,
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at the entrance of the cooling channel,   
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as expected from Monte Carlo simulations and measured by the MICE particle
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identification  system using a statistical method. } 
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\keywords{Muon Ionisation Cooling; Neutrino Factory; Muon Collider; 
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MICE; Muon Beam}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%                                                %
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%    BEGINNING OF TEXT                           %
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%                                                %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%\linenumbers
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\begin{document}
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% ----------------------------------------------------------------
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\section{Introduction}
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\label{sec:Introduction}
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%%\input{introduction_v3.tex}
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The international Muon Ionisation Cooling Experiment (MICE)~\cite{Blondel:2003},
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under construction at the Rutherford Appleton Laboratory (RAL), will
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demonstrate the principle of ionisation cooling as a technique for
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reduction of the phase-space volume occupied by a muon beam.
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Ionisation cooling channels are required for neutrino factories
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\cite{Koshkarev:1974, Geer:1998, Alsharoa:2002wu,Blondel:2004ae,
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Choubey:2011zz} and muon colliders \cite{Tikhonin:2008pw,Geer:2010zz, Ankenbrandt:1999as}.
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Ionisation cooling \cite{Neuffer:1983} 
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is accomplished by passing the muon beam
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through a low-$Z$ material (the ``absorber''), in which it loses
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energy via ionisation, reducing both the longitudinal and
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transverse components of momentum.
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The lost energy is restored by accelerating the beam such that the
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longitudinal component of momentum is increased while the transverse
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component remain unchanged.
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The net effect is to reduce the divergence of the beam, hence the volume of transverse phase space that it
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occupies.
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Beam transport through the absorbers and accelerating structures is
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achieved using a solenoid focusing lattice.
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While a modest cooling factor ($\sim 3.4$) is needed in the current neutrino factory design 
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\cite{Choubey:2011zz}, much greater ($\sim 10^6$) cooling is needed for a muon collider.
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\section{MICE Apparatus}
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A schematic diagram of the MICE experiment is shown in figure
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\ref{fig:MICElayout}.
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The MICE cooling channel, which is based on a single lattice cell of the
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cooling channel described in \cite{Ozaki:2001bb}, comprises three
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  20 litre volumes  of liquid hydrogen and two linear accelerator modules 
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(LINAC) each
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consisting of four 201\,MHz cavities, with gradients of  $\sim 10$ MV/m. The superconducting ``focus coils'' focus the beam into the liquid-hydrogen
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absorbers, while a ``coupling coil'' surrounds each of the linac
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modules.
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\begin{figure*}
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 \begin{center}
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\includegraphics[width=\linewidth]{pics/MICE-fig-1-clean.pdf}
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%%\includegraphics[width=\linewidth]{pics/cooling_sectioned.pdf}
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 \end{center}
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\vskip -3cm 
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\caption{
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Schematic view of the MICE apparatus: the cooling
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channel, with its three liquid hydrogen absorbers and two RF cavity modules,
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is sandwiched between two identical trackers, inside superconducting 
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solenoids. The muon beam is incident from the left. The sequence of
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solenoids defining the MICE optics is also visible. The cooling cell starts
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at the first Focus Coil.}
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 \label{fig:MICElayout}
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\end{figure*}
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A reduction in normalised emittance of
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$10\%$ is expected for a muon beam entering the cell with a nominal momentum
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of 200\,MeV/$c$ and an emittance $\epsilon_N = 6.2 \pi $\,mm$\,\cdot$\,rad.
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To allow extrapolation to a full cooling channel, the instrumentation upstream and downstream of the cooling cell is
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required to measure this change in emittance, $\Delta \epsilon_N$,
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with a relative precision $\Delta \epsilon_N / \epsilon_N = 1\%$;
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i.e., measurements of $\epsilon_N$ upstream and downstream of the
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cooling cell with an absolute precision of 0.1\% are required.
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Conventional emittance measurement techniques based on beam-profile
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monitors barely reach a $10 \%$ precision.
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%While the muon-beam intensity in the ionisation-cooling channel at the
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%Neutrino Factory and the Muon Collider is in excess of
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%$10^{14}\,\mu^{\pm}$/s, the phase-space density is always low enough
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%for space-charge forces to be neglected.
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In order to achieve the required precision, MICE has been designed as a
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single-particle experiment, in which each muon is measured using
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state-of-the-art particle detectors and the bunched muon-beam  is
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reconstructed offline~\footnote{A preliminary application of this method
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to characterize MICE beams,
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using only the time-of-flight detectors, has been studied and is 
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reported in reference \cite{ref:mark}}.
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The instrumentation upstream of the MICE cooling cell includes a
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particle identification (PID) system, that allows a pure muon
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beam to be selected. The PID system consists of scintillator time-of-flight
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$x/y$ hodoscopes TOF0 and TOF1~\cite{Bertoni:2010by}  
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read at both edges by fast conventional Hamamatsu R4998 photomultipliers
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\cite{Bonesini:2011},
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and two threshold Cherenkov counters Ckova and
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Ckovb \cite{Cremaldi:2009zj}.
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%Together the two Cherenkov counters will provide $\pi/\mu$ separation up to 365\,MeV/$c$.
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The TOF system is required to reject pions in the incoming muon beam
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with an efficiency in excess of 99\%.
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In addition, the precision of the TOF time measurement must be
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sufficient to allow the phase at which the muon enters the RF cavities
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to be determined to 5$^\circ$.
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To satisfy these requirements, the resolution of each TOF station must
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be $\sim 50$\,ps.
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The two Cherenkov detectors have been designed to guarantee
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muon-identification purities better than $99.7$\% in the momentum
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range 210\,MeV/$c$ to 365\,MeV/$c$ \cite{Sanders:2009vn}.
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Both the TOF system and the Cherenkov system, giving only a velocity 
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measurement, may be used for single particle identification 
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once momentum of the incoming particles has been determined precisely. 
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This may be done only 
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in MICE STEP IV \cite{Bonesini2012}, where the first tracker 
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station~\cite{Ellis:2010bb} will measure momentum 
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of the incoming particles~\cite{Bogomilov:2012sr}. 
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For MICE Step I a preliminary determination of the pion contamination
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of the muon MICE beam was obtained on a statistical basis combining 
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the TOF velocity information with the calorimetric KL information. 
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%At lower momenta, $\pi/\mu$ separation is obtained using the TOF
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%measurement, both Cherenkov detectors being blind to both particle
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%types.
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Downstream of the cooling channel, a final scintillator time-of-flight
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$x/y$ hodoscope (TOF2 \cite{tof2})
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 and a
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calorimeter system allow muon decays to be identified and rejected.
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The calorimeter system is composed of a lead-scintillator section
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(KL), similar to the KLOE design \cite{Ambrosino:2009zza}  but
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with thinner lead
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foils, to be followed soon by a fully active scintillator detector (the
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electron-muon ranger,  EMR) in which the muons are brought to rest.
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Charged-particle tracking in MICE will be provided by two solenoidal
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spectrometers in which the position and momentum  of each muon is measured before and
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after the cooling cell.
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The KL detector is the most downstream part of the MICE Step I apparatus. It is designed to serve as a preshower for the EMR detector; however, in 2011 the 
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EMR was still under construction.
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The main role of the KL and EMR detectors is to distinguish muons from  decay electrons, but they can separate muons from pions and electrons more generally.
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KL is a sampling calorimeter, composed of scintillating fibers and extruded Pb foils
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with active volume of   93 $\times$  4  $\times$ 93 cm$^3$.
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KL has 21 cells and 42 readout channels.
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Light from its scintillating fibers is collected by 42 Hamamatsu R1355 PMTs. 
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The PMT signals are sent via a shaper module to 14 bit CAEN V1724 flash ADCs. 
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The shapers stretch the signal in time in order to match the flash ADC sampling
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rate. 
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A detailed description of KL is given in \cite{Bogomilov:2012sr}.
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%In the MICE Step I setup, KL is followed by three, 1 inch thick, 10 $\times$  100 cm$^2$ scintillator bars, placed vertically side by side behind the center of the detector, in order to tag any particles that pass through KL. These Tag counters  are not used in this study but are used for estimation of KL transparency as described in \cite{Bogomilov:2012sr}.
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%The two aerogel threshold Cherenkov counters, located within the Decay Solenoid Area (DSA)~\footnote{The DSA is a  shielded and interlocked
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%area within the MICE Hall, just outside the ISIS vault area,
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%within which elevated neutron rates are possible in the event of a mis-steering of the ISIS proton beam.} just after TOF0,  are used in support of muon and pion particle 
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%identification.  The refractive indices of the aerogels %in the counters 
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%are $n=1.12$ in Ckovb and $n=1.07$ in Ckova. The momentum thresholds for 
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%muons (pions) are  at  210 (275) MeV/$c$  and 278 (365) MeV/$c$ respectively. 
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%Light is collected in each counter by 4 eight inch UV-enhanced phototubes   
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% and  recorded by CAEN V1731 Flash ADCs. The light yields are pedestal 
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%subtracted and normalised to give a  photoelectron count in each counter.   
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%The asymptotic  $\beta$=1  response in each counter is measured 
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%in MICE electron beam runs giving 25 and 15 photoelectrons in Ckovb and 
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%Ckova respectively.
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The MICE instrumentation must perform
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efficiently in the presence of background induced by X-rays produced
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in the RF cavities and must operate in the presence of stray fringe fields from
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magnets.
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For a full description of the experiment see \cite{Gregoire:2003}. 
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Thus far, only the PID instrumentation and the MICE beam line have been
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installed (MICE Step I). They are fully described in \cite{Bogomilov:2012sr}.
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\section{MICE Muon Beam and 2011 data-taking}
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\label{sec:beam}
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%%\input{MiceBeam_v3.tex}
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In order to avoid detrimental effects on muon emittance 
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measurement, the MICE beam line must deliver muon beams with a pion
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contamination of less than  few per-cent.
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%%%less than 10\%.
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%%, which can be further suppressed by the PID system to 0.1\%.
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The required transverse emittance  range is
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$3 \leq \epsilon_N \leq 10 \ \pi $\,mm $\cdot$ rad, with mean momenta %($p_\mu$) in the range
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$140 \leq p_\mu \leq 240$\,MeV/$c$ and r.m.s. momentum widths of $\sim 20$ MeV/$c$;
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the full range of emittance is required over the full range of
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momentum.
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A tungsten or brass ``diffuser'' of variable thickness is placed at the
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entrance to the upstream spectrometer solenoid in order to generate the
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divergence necessary for the required range of emittance.
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The design of the MICE muon beam is reported in  \cite{Bogomilov:2012sr}; 
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we  summarize it here briefly (see figure \ref{fig:Beamline}).
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Pions produced by the momentary insertion of a titanium
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 target \cite{target:2013} into the ISIS proton beam
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 are (1) captured using a quadrupole triplet (Q1--3) and (2) transported to a 
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first dipole magnet (D1), which directs
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particles of a  desired momentum bite into the decay solenoid (DS);  (3) muons produced by pions decaying in the DS are momentum-selected using a
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second dipole magnet (D2) and (4) focused onto the diffuser by 
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 a quadrupole channel (Q4--6 and Q7--9). By capturing pions of transverse 
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momentum up to $\sim 70$  MeV/$c$,  and increasing their path length by deflecting them onto helical trajectories, the decay solenoid increases
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the probability of muon capture between
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D1 and D2 by an order of magnitude compared to a simple quadrupole channel.
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%The upstream PID detectors (TOF0, Ckova and Ckovb) are located inside the DSA.
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In positive-beam running, a borated polyethylene  absorber of variable thickness is inserted into the beam just downstream of DS in order to suppress a high rate of protons \cite{Blot-etal}.
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\begin{figure}
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\vskip -2cm 
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 \centering
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%%  \includegraphics*[width=0.8\linewidth]{03-MICE-Muon-Beam/Figures/MMB-schematic.pdf}
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%%%\includegraphics*[width=0.8\linewidth]{pics/BeamLineComposite_v5-8.pdf}
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\includegraphics*[width=0.8\linewidth]{pics/figure1_alternative.pdf}
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  \caption{Top view of the MICE beam line with its instrumentation, as
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used in Step I. The distances between TOF0 (TOF1) and TOF1 (TOF2) are
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respectively 773.3 cm and 198.8 cm.}
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 \label{fig:Beamline}
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\end{figure}
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The composition and momentum spectra of the beams delivered to MICE
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are determined by the interplay between the two bending magnets D1 and
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D2. In normal (``$\pi \to \mu$ mode,'' or ``muon'') operation, D2 is set to half the momentum of D1, selecting backward-going muons in the pion rest
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frame and producing an almost pure muon beam.
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The simulated momentum distribution at TOF0 for the beam particles in a positive $6 \pi$ mm 200 Mev/$c$ 
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muon beam is reported in figure \ref{fig:sim}-c. Undecayed pions at high momentum clearly prevent 
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particle identification on a single-particle basis, in absence of a precise momentum measurement, 
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with either TOF or Cherenkov velocity measurements. 
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Alternatively, by setting $p_{D1} \simeq p_{D2}$, a mixed beam containing %positive or negative 
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$\pi, \mu$, and $e$ 
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 is obtained. This  ``calibration mode'' is used to calibrate the PID  detectors. 
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The nominal values of the beam momenta $p_{\mu}$ are those evaluated at the centre 
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of the central liquid-hydrogen absorber in the final Step VI configuration.
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For example, $p_{D2} = 238$ MeV/$c$ gives a $p_{\mu}$ value
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of 200 MeV/$c$, the momentum decrease from D2 to the MICE cooling cell being primarily due to energy loss in the material of the PID detectors, the diffuser, and, for positive (+ve) beams, the proton absorber. %[PROTON ABSORBER OMITTED FROM ABOVE DESCRIPTION BUT SHOULD BE MENTIONED.]
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%[INSERT TABLE OF MOMENTUM CORRESPONDENCE AT D2, CKOV, AND NOMINAL.]
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The correspondence between beam momenta at various points in the MICE apparatus is summarized in table \ref{Table:calibruns}.
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%\section{2011 MICE data taking}
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\label{sec:cont}
432
%%\input{tof_kl_intro_v3.tex}
433
MICE Step I data were taken in Dec.\ 2011 with the apparatus setup
434
shown in figure \ref{fig:Beamline},  including the upstream PID 
435
detectors and the downstream TOF2 and KL detectors, which were operated in a temporary 
436
position about 2 m downstream of TOF1.
437
%Before the start of data taking TOF0 and TOF1 detectors have been
438
%refurbished. A resolution of $\sim 50$ ps has been measured  in the 
439
%2010 data-taking for
440
%TOF0 and TOF2, while it amounted to $\sim 60$ ps for TOF1 \cite{datax}.               
441
%The resolution of the TOF0
442
%station (4 cm wide slabs)  and that of the TOF2 station (6 cm wide slabs) are similar,
443
%showing that path length fluctuation effects  are negligible.
444
%This result prompted the idea to rebuild TOF0 and TOF1, changing the most
445
%older PMTs with refurbished ones by Hamamatsu Japan. This operation consisted
446
%mainly in the change of the active divider of the older H6533MOD assemblies
447
%with a new one. About 50 assemblies out of 68 were changed
448
%in a long refurbishing
449
%operation that involved also extensive laboratory tests to assess the quality
450
%and performances of the new mounted assemblies \cite{Bonesini:2012}.
451
%Looking to the performances of TOF0 and TOF1 in runs taken in the late 2011
452
%data-taking there is no evidence for different resolutions in TOF0
453
%and TOF1. 
454
After  refurbishing of TOF0 and TOF1, where the older PMT assemblies 
455
were replaced,  and after performing a detector calibration, the obtained TOF resolutions were 55 ps for TOF0, 53 ps for TOF1 and 
456
50 ps for TOF2  \cite{datax},\cite{Bonesini:2012}.
457
Table \ref{Table:calibruns} summarizes the  runs used in this analysis.
458

    
459
\begin{table}
460
\centering
461
\caption{Summary of runs used in this analysis. The muon runs correspond
462
to a nominal setting $(\varepsilon_N, p_\mu)= 6 \pi  mm \cdot rad$, 200 Mev/$c$. Reported momenta are
463
at the entrance of the quoted detectors.  \label{Table:calibruns}}
464
\vskip 0.2cm
465
\begin{tabular}{|c|c|c|c|c|}
466
\hline
467
$p_{D2}~({\rm MeV}/c)$&  $p_{TOF0}~({\rm MeV}/c$ & $p_{TOF1}~({\rm MeV}/c$ &
468
$p_{TOF2}~({\rm MeV}/c$ &\# events ($10^3$) 
469
\\ \hline\hline
470
\multicolumn{5}{|c|}{calibration runs} \\ \hline
471
222 &   xx & xx & xx &     195 \\
472
258 &   xx & xx & xx &      235 \\
473
280 &   xx & xx & xx &      167 \\
474
294 &   xx & xx & xx &      354 \\
475
320 &   xx & xx & xx &       265 \\
476
362 &   xx & xx & xx &       448 \\ \hline
477
\multicolumn{5}{|c|}{muon runs} \\ \hline
478
238 & 220 & 204 & 190      & 270 \\
479
\hline
480
\end{tabular}
481
\end{table}
482

    
483
%%\input{tof_analysis_v3.tex}
484
\section{Contamination in the MICE muon beam}
485

    
486
The pion contamination in the MICE muon beam was first estimated by 
487
Monte Carlo (MC) simulation, then measured, %using only the TOF information, 
488
by combining  KL information with that from the TOF. 
489
 
490
Figure \ref{tof} shows distributions of the time-of-flight between
491
TOF0 and TOF1.
492
Figure \ref{tof}-a shows data taken with a
493
 positive $\pi \rightarrow \mu$ beam with a nominal momentum of 200 MeV/$c$, which has only a small contamination of electrons and pions.
494
Similar beams will be used to demonstrate ionisation cooling.
495
Figure \ref{tof}-b shows data taken with a  calibration
496
beam with $p_{D2} \simeq$ 222 MeV/$c$. 
497
In this beam configuration, momentum selected electrons, muons and pions fall into three
498
well-defined peaks.
499
\begin{figure}
500
  \begin{center}
501
\includegraphics[scale=0.40]{pics/fig10new.pdf}
502
    \includegraphics[width=0.49\linewidth]%
503
%%      {pics/tof01_r2704e-mod.pdf}
504
      {pics/tof-mod.pdf}
505
  \end{center}
506
  \caption{
507
    Time of flight between TOF0 and TOF1 for a positive muon 
508
    beam  with a nominal momentum of 200 MeV/$c$ used in the following the analysis (a)  and a  positive ``calibration'' beam taken with $p_{D2} = 222$ 
509
    MeV/$c$ (b). In panel (a) the left peak is due to electrons,  the pion contamination will be  studied in 
510
three time-of-flight intervals, highlighted in grey.
511
  }
512
  \label{tof}
513
\end{figure}
514
In the $\pi\to\mu$ beam, while $e/\mu$ separation is never a problem, the level of the $\pi$
515
contamination under the $\mu$ peak may be difficult
516
to assess, as the two distributions  overlap.
517

    
518
%By looking at the particle time-of-flight between the
519
%TOF0 and TOF1 stations, particle identification was
520
%performed to determine the muon rate.
521
%The cuts applied to the TOF spectrum to isolate muon tracks are 26.2 ns < $\Delta$t < 32 ns.
522

    
523

    
524
The pion contamination under the
525
muon peak was estimated using the G4beamline simulation package \cite{G4beamline} 
526
developed by Muons, Inc. In this simulation, particles are recorded on 
527
``virtual planes'' placed at the detector positions, without any
528
attempt to simulate detector response; only the detector fiducial area 
529
is accounted for.  
530
Figure \ref{fig:sim}
531
compares distributions of flight time from
532
TOF0 to TOF1, obtained in typical beam configurations, 
533
 for reconstructed positive-beam data and corresponding MC simulations. MC particles are tagged according to their species (``MC truth''). 
534
Results on pion contamination under the muon peak are  summarised 
535
in figure \ref{fig:pi_cont}. 
536
%This simulation study gives predictions on an event-by-event basis of
537
%the $\pi$ 
538
The contamination %under the $\mu$ peak. It 
539
is always below $1 \%$  at the entrance of the MICE apparatus (TOF1) 
540
and increases  slowly with momentum. 
541

    
542
\begin{figure}
543
\vskip -3cm
544
\begin{center}
545
\includegraphics[width=.49\linewidth]{pics/TOF_140-mod.pdf}
546
%%\includegraphics[width=.49\linewidth]{pics/TOF_200.pdf}
547
\includegraphics[width=.49\linewidth]{pics/TOF_200_withAbsorber-mod.pdf}
548
\vskip -2cm
549
%%\includegraphics[width=.49\linewidth]{pics/MomentumAtTOF0_log.pdf}
550
%%\includegraphics[width=.49\linewidth]{pics/MomentumAtTOF1_log.pdf}
551
\includegraphics[width=.49\linewidth]{pics/mom_TOF0.pdf}
552
\includegraphics[width=.49\linewidth]{pics/mom_TOF1.pdf}
553
\end{center}
554
\caption{Time-of-flight distributions between TOF0 and TOF1 for data and  Monte Carlo simulation:
555
$ 6 \pi $ mm $\cdot$ rad positive muon 
556
beams with nominal beam momentum 
557
 $p_{\mu}=140$ MeV/$c$ (a) and  $p_{\mu}=200$ MeV/$c$ (b). The position of the electron peak in the raw
558
data has been renormalised to its nominal value. Momentum distribution 
559
for beam particles at TOF0 (c) and TOF1 (d) for 
560
a simulated positive $6 \pi$ mm $\cdot$ rad at 200 MeV/$c$ (a 
561
cut between 26.2 and 32 ns on the time--of--flight between
562
TOF0 and TOF1 is applied).}
563
 
564
%%[QUESTION: WHY ARE THERE 2 DISTINCT POPULATIONS OF ELECTRONS AND PIONS 
565
%%IN THE SIMULATION??? THIS SHOULD BE EXPLAINED  HERE.]
566
\label{fig:sim}
567
\end{figure}
568

    
569
\begin{figure}
570
\begin{center}
571
\includegraphics[width=0.49\linewidth]{pics/fig_pi_cont.pdf}
572
\end{center}
573
\caption{Pion contamination  in a $6 \pi $ mm\,$\cdot$\,rad muon beam, at various
574
nominal momenta $p_{\mu}$ and different positions along the beam line 
575
as deduced from G4beamline Monte Carlo simulations. Points refer to TOF0, TOF1,
576
TOF2 and KL positions in MICE Step I configuration. 
577
The $z$ coordinate is in mm in the MICE reference system,
578
where zero is at the target position. Simulations for positive-beams at 200 and 
579
240 MeV/$c$ include a proton absorber of 83 and 147 mm. A cut between 26.2 and 32 ns on the time--of--flight between TOF0 and TOF1 is applied.}
580
\label{fig:pi_cont}
581
\end{figure}
582

    
583
%The final measurement of the level of this 
584
%contamination has been done by combining the KL pulse height or Ckov 
585
%information with 
586
%TOF results on a statistical basis, as discussed next.
587
%%\input{ckov_analysis_v3.tex}
588

    
589

    
590
\subsection{Pion contamination measurement with TOF and KL detectors}
591
%%\input{pid_analysis_v3.tex}
592
The residual pion contamination in the beam, after the selection of the muon component 
593
via time-of-flight, can  be measured %on a statistical basis 
594
from the spectrum of energy released in KL.
595
%signals from pions and muons in the MICE beam can be modeled by that measured
596
%for particles with the same time-of-flight in separate calibration runs. [WHAT THIS MEANS IS UNCLEAR TO READER.]
597
Due to the broad momentum acceptance of the MICE beam line in
598
$\pi \rightarrow \mu$ mode, the pions contaminating the muon sample have higher momenta than
599
the muons, in order for the time-of-flight  to be consistent~\footnote{This feature prevents the
600
use of  Cherenkov detectors in MICE Step I to fully tag pions, in absence of a precise
601
determination of momentum for beam particles} (see figure \ref{fig:sim}).
602

    
603
The pion contamination is studied in positive muon beam runs with nominal 
604
beam momentum 200  MeV/$c$ ($p_{D2}= 238$ MeV/$c$) 
605
with a collected statistics of about 270 $\times 10^3$ triggers.
606
The study is performed as a function of the time-of-flight of the beam particles in three distinct 
607
time-of-flight intervals (referred to below as ``Points 1-3'') whose choice
608
is dictated by the availability of calibrations data for which
609
the specified interval is populated mainly by muons or mainly by pions.
610
Pairs of calibration runs
611
for which muons and pions present time-of-flight values within the same
612
range (see  table \ref{Table:pairs}) are defined for each point and are used to benchmark the KL response 
613
to muons or to pions of given time-of-flight.
614

    
615
%about 195/235/167/354/265 and 448 $\times 10^3$ triggers
616
%were collected with $p_{D2} = 222/258/280/294/320/362 $ MeV/$c$. 
617
%The time--of-flight distribution of the particles allows a clear distinction of the 
618
%different beam components (see the right panel of figure \ref{tof} for an example).
619
% The available calibration runs 
620
%have been used to identify pairs of beam settings
621
%for which muons and pions present time-of-flight values within the same range, hence emulating
622
%the situation in which after a time-of-flight selection the MICE beam would
623
%contain not only muons but also contaminating pions.
624
As an example, figure \ref{Fig:TOFpairing} shows the time-of-flight distributions in two paired beam settings.
625
The interval between 28.0--28.6 ns in the TOF0--TOF1 time-of-flight 
626
is populated mainly by muons for one beam setting and by pions for the other.
627

    
628

    
629
%%%%%%%%%%%%%%%%%%%%%%%%%% Figure %%%%%%%%%%%%%%%%%%%%%%%%%
630
\begin{figure}
631
\begin{center}
632
\includegraphics[scale=0.6]{pics/tof_pair.pdf}
633
\caption{Time-of-flight distributions in two paired beam settings. 
634
The interval 28.0--28.6 ns (shaded) is populated by muons (pions) in upper (lower) plot.}
635
\label{Fig:TOFpairing}
636
\end{center}
637
\end{figure}
638
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
639

    
640

    
641
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
642
\begin{table}
643
\begin{center}
644
\caption{Paired beam settings for three time-of-flight intervals (also called Points).}
645
\label{Table:pairs}
646
{\small
647
\begin{tabular}{|c|c|c|c|}
648
\hline
649
 & TOF interval, ns & muons from runs with & pions from runs with\\ 
650
 &   & P$_{D2}$ (MeV/$c$) & P$_{D2}$ (MeV/$c$)\\ 
651
\hline
652
\hline
653
Point 1    & 27.4 -- 27.9    & 294  &  362\\
654
\hline
655
Point 2    & 28.0 -- 28.6    & 258  &  320\\
656
\hline
657
Point 3    & 28.9 -- 29.6    & 222  &  280\\
658
\hline
659
\end{tabular}}
660
\end{center}
661
\end{table} 
662
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
663
Figure \ref{tof}-a  shows the time-of-flight distribution of particles in the MICE muon 
664
beam. The examined three Points are highlighted in grey. 
665
The widths of the intervals have been  determined by taking into account 
666
the overlap regions between the calibration runs.  
667
In each of these time-of-flight intervals
668
the spectra of the KL response can be extracted for muons and pions separately
669
from the calibration runs.
670
These spectra are then used as templates for the response to muons and pions 
671
in that time-of-flight interval for the muon runs. Figure \ref{Fig:pointX} shows examples 
672
of the muon and pion templates. 
673

    
674

    
675
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
676

    
677
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
678
%%%%%%%%%%%%%%%%%%%%%%%%%% Figure %%%%%%%%%%%%%%%%%%%%%%%%%
679
\begin{figure}
680
\begin{center}
681
%%%\includegraphics[scale=0.6]{pics/fig11.pdf}
682
\includegraphics[scale=0.6]{pics/nuovafig8.pdf}
683
\caption{Muon (red stars) and pion (blue squares) 
684
templates at Point 2 from calibration runs, compared to MICE
685
muon beam data (black dots). About 30 \% of the particles tagged as pions by 
686
TOF0--TOF1 decay to muons before KL. Plots are normalised to unity.}
687
\label{Fig:pointX}
688
\end{center}
689
\end{figure}
690

    
691
In the range 200--300 MeV/$c$, both muons and pions are minimum ionizing (MIP) particles, 
692
but in the KL detector material 
693
pions can undergo hadronic interactions as well, which are visible as a tail in the KL response 
694
to pions. %In general
695
In order to compensate for light attenuation in the scintillator, the KL response to a particle is defined in terms of the product
696
of the digitised signals from the left and right sides of each slab divided by their sum: 
697
$$ADC_{\rm product} = 2\, \frac{ADC_{\rm left}\times ADC_{\rm right}}{ADC_{\rm left}+ ADC_{\rm right}},$$
698
where 
699
the factor of 2 is present for normalisation.
700
The products are summed for all 
701
slabs in KL above threshold. 
702
%The product of two sides  compensates the effect of light attenuation 
703
%in the scintillator. 
704
It can be shown that the used normalized ADC product is the combination
705
of the PMTs signals that is less sensitive to the particle hit position
706
along the fiber length, in presence of two attenuation lengths of which
707
one is much shorter than the other \cite{DiDomenico},
708
\cite{Passeri:2012}.
709

    
710
The KL response to muons and pions in calibration runs and to an unknown particle 
711
mix in muon mode are shown in figure \ref{Fig:pointX}.
712
The distribution for the pions displays a larger tail than the muon one,
713
reflecting the presence of hadronic interactions.
714
This aspect is used in the following analysis, to estimate on a statistical
715
basis the MICE muon beam contamination. 
716

    
717
 
718
\subsubsection{Analysis  with KL and TOF information}
719

    
720
This  method exploits the information contained in the full KL response spectrum in order to extract the 
721
fractions of muons and pions in the MICE beam for each time-of-flight interval.
722
The method employs the ROOT TFractionFitter method \cite{Bib:ROOT} based upon 
723
\cite{Bib:fitter}, treating the muon and pion templates as if they were different
724
Monte Carlo components to be fitted to the actual KL spectrum in the MICE data.
725
This fit takes into account, through a standard likelihood fit using Poisson statistics, 
726
both data and template statistical uncertainties, allowing the templates to vary within 
727
statistics.
728

    
729
Due to the different momentum distributions some particles from calibration runs with a given time-of-flight measurement may  contribute more (or less) to the
730
final result, than the particles from muon run with the same time-of-flight value.
731
The uneven distributions can be taken into account by reducing the reference time-of-flight 
732
intervals, but this approach would require a large statistics.
733
Alternatively weights proportional to the time-of-flight density distributions could be used 
734
reweighting  the KL response templates
735
by the time-of-flight distribution, to account for the different distributions 
736
of this variable for muons or pions in calibration runs and
737
muon runs within the selected interval. Unfortunately the fluctuations of the reweighted templates would 
738
not follow the Poisson distribution anymore so this approach cannot be adopted here. Though there are 
739
methods to solve this problem \cite{Bib:CMSthesisBinclusive},
740
in the following this effect  is treated as a systematic, whose impact 
741
is assessed by splitting into finer intervals the time-of-flight ranges defined in table \ref{Table:pairs}.
742

    
743
Though fitting the full spectrum should in principle provide 
744
a better description of the relative muon and pion fractions, it should be noted that, despite the
745
requirement of a single particle in the TOF counters, a two MIPs peak 
746
(between 1900 and 2700 counts) is visible in  the KL response distribution of figure \ref{Fig:pointX}. %, comparing the MICE beam data to the muon and pion templates for point 2.
747
For this reason, %the fit was performed also in the KL response range 
748
%corresponding to 
749
%two minimum ionizing particles.
750
a fit was performed  excluding the ADC product region
751
from 1900 to 2700  counts. 
752
The results are shown in figure \ref{Fig:fitPointY} for Point 2.
753
%The MICE beam data are represented by the black dots with error bars, the    
754
%uncertainties on the muon and pion templates after the fit by red or blue rectangles respectively, the
755
%fit by the black histogram. 
756

    
757
The pion contaminations obtained with this method are reported in Table \ref{Table:picont}.
758
Errors include both statistical and systematic uncertainties. 
759
The sources of systematics and the way their impact is assessed are summarized in table \ref{Tab:FitSys}.
760
%\begin{itemize}
761
%\item dependence on the time-of-flight distribution, determined by further subdiving the time-of-flight ranges associated to each point; 
762
%\item dependence on time-of-flight calibration, determined by shifting independently the time-of-flight values in the calibration runs by an amount compatible with the electron peak position ($\pm0.1$~ns) ;
763
%\item dependence on the fitted range, determined by varying the size of the region excluded from the fit; 
764
%\item dependence on the histogram binning, assessed by doubling and halfing the bin-size.
765
%\end{itemize}
766
%The limited significance of the observed pion contamination does not allow, within the large statistical errors, to appreciate most of the effects  listed above. For this reason the systematic uncertainties have been evaluated from the  relative variation of the pion contamination measured adding pion events from the pion calibration data to the MICE beam sample.  Table \ref{Tab:FitSys} presents the estimated impact of each of the above uncertainties obtained at Point 2. 
767

    
768

    
769
%Table \ref{Tab:FitResults} summarizes for each point the result of the fit, the first error is statistical
770
%and the second is systematical.
771
    
772
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
773
\begin{table}[hbt]
774
\begin{center}
775
\caption{Sources of systematic errors in the evaluation of the pion contamination  } 
776
\label{Tab:FitSys}
777
\vskip 0.2cm
778
{\small
779
\begin{tabular}{|l|l|c|}
780
\hline
781
Effect & Assessment method & Impact on pion contamination \\
782
\hline
783
\hline
784
Time-of-flight distribution & finer subdivision & 40\% \\
785
Time-of-flight calibration & shift calibrations by $\pm0.1$ ns & 3\% \\
786
Fitted range & vary exclusion region & 15\% \\
787
Histogram binning & double/halve bin sizes & 3\% \\
788
\hline
789
\end{tabular}
790
}
791
\end{center}
792
\end{table}
793
%%%%%%%%%%%%%%%%%%%%%%%%%% Figure %%%%%%%%%%%%%%%%%%%%%%%%%
794
\begin{figure}[htb]
795
\begin{center}
796
\includegraphics[scale=0.6]{pics/fig13bis.pdf}
797
\caption{
798
MICE beam data (black dots), muon (red dotted area) and pion (blue solid area) fractions, are normalised to the  
799
the template fit (black histogram) performed 
800
to the KL product spectrum excluding  the window from 1900 to 2700 counts. 
801
}
802
\label{Fig:fitPointY}
803
\end{center}
804
\end{figure}
805
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
806

    
807
\subsubsection{Cross-check  with a classical method}
808
A simpler  method consists in applying a threshold on KL product in order to identify only those pions having 
809
hadronic interactions, and counting the fraction of events with KL response above this 
810
threshold (see figure \ref{Fig:pointX}). This fraction is then expressed as 
811
a function of the fractions of muons and pions in paired calibration runs at the same threshold.
812
If in a muon run $R^{tot}$ is the total number of particles and $R^{cut}$ 
813
is the number 
814
of particles that pass the cut on the KL product, then 
815
\begin{equation*}
816
\begin{cases}
817
 R^{tot} = R_{\mu} + R_{\pi} \\
818
 R^{cut} = k_{\mu} R_{\mu} + k_{\pi} R_{\pi}
819
\end{cases}
820
\end{equation*}
821
where $R_{\mu}$ and  $R_{\pi}$ are numbers of muons and pions in the 
822
muon run 
823
and $k_{\mu}$ and $k_{\pi}$ are the fractions of muons and pions in the 
824
corresponding calibration runs.  
825
$R_{\mu}$ and  $R_{\pi}$ are then used to extract fraction of muons in the beam,
826
$q_{\mu}$, and the pion contamination fraction, $q_{\pi}$:
827
\begin{equation*}
828
q_{\mu} = \frac {R_{\mu}} {R^{tot}}  \hspace{1cm} \text{and} \hspace{1cm} q_{\pi} = \frac {R_{\pi}} {R^{tot}}\,.
829
\end{equation*}
830

    
831
Results are plotted in figure \ref{Fig:Pion_cont} for the three 
832
time-of-flight points and for three values of the threshold on the KL product. Table 
833
\ref{Table:Pion_cont} gives all details for Point 2.
834
 
835
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
836
\begin{table}
837
\begin{center}
838
\caption{Pion and muon fractions in calibration and muon runs for time-of-flight Point 2 for 
839
three cuts on KL product: $N_{\mu}^{tot}$ and $N_{\mu}^{cut}$ are numbers  of muons, and $N_{\pi}^{tot}$ and $N_{\pi}^{cut}$ of pions, before and after
840
cut. Uncertainties are statistical only.}
841
\label{Table:Pion_cont}
842
\vskip .2cm
843
{\small
844
\begin{tabular}{|c|c|c|c|}
845
\hline
846
 KL cut & 3000 & 4500 & 7000\\ 
847
\hline
848
\hline
849
$N_{\mu}^{tot}$	    &  53334 &  53334 &  53334\\
850
\hline
851
$N_{\mu}^{cut}$	    &  234 &   53 &  7\\
852
\hline
853
$N_{\pi}^{tot}$	    & 68933 &   68933 & 68933 \\
854
\hline
855
$N_{\pi}^{cut}$	    & 7785 & 4330  &  1390\\
856
\hline
857
$k_{\mu}, \%$	    & 0.439 $\pm$ 0.029&  0.099 $\pm$ 0.014 &  0.013 $\pm$ 0.005\\
858
\hline
859
$k_{\pi}, \%$       & 11.29 $\pm$ 0.12 &  6.28 $\pm$ 0.09 &  2.01 $\pm$ 0.05\\
860
\hline
861
$R^{tot}$    	    & 72709 &  72709 & 72709 \\
862
\hline
863
$R^{cut}$    	    & 391 &  92 &  16\\
864
\hline
865
$R_{\mu}$    	    &  72045.8 & 72389.6  & 72386.7 \\
866
\hline
867
$R_{\pi}$    	    &  663.2 &  319.4 &  322.3\\
868
\hline
869
$q_{\mu}, \%$       &  99.08 $\pm$ 0.52& 99.56 $\pm$ 0.48  &  99.56 $\pm$ 0.52\\
870
\hline
871
$q_{\pi}, \%$       &  0.91 $\pm$ 0.36 &  0.44 $\pm$ 0.31 &  0.44 $\pm$ 0.36\\
872
\hline
873
\end{tabular}
874
}
875
\end{center}
876
\end{table} 
877
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
878
An estimate of the systematic pion-contamination uncertainty related to the dependence upon the threshold value is
879
reported in table \ref{tbx}. 
880
A second source of systematic uncertainty (muon contamination) results
881
from tails of the muon distribution overlapping the pion time-of-flight peak
882
(see Fig.\ref{tof}). Assuming a contamination of 30\% results in a reduction of less than 0.2\% of the
883
pion fraction in the muon beam.
884
A third source of systematic uncertainty (difference in TOF distributions)
885
results, as already discussed above, from the differences time-of-flight spectra
886
between the analyzed particles and the calibration ones.
887
In this analysis the KL product distributions can be reweighted using the 
888
time-of-flight ones, thus making all time-of-flight distributions flat.
889
This approach produces results deviating by less than 0.2\% from the default one, without any preferred direction.
890

    
891
The pion contaminations obtained with a KL product cut at 
892
4500 counts are reported in Table \ref{Table:picont}. 
893
Errors include both statistical and systematics uncertainties. 
894
 
895
%The systematics affecting this method are as follows: 
896
%\begin{itemize}
897
%\item Threshold value: 
898
%figure \ref{Fig:Pion_cont} shows the pion contamination in percent for three cuts on KL product and for all three time-of-flight intervals. For Points one and two the resulting contamination varies within $\pm$0.5\% while  for Point three the variation is within $\pm$1\%. There is no preferred direction for the variation (negative or positive) and  all results are within statistical uncertainties. Results are described in table \ref{Table:Pion_cont}.
899

    
900
%\item Muon background in calibration runs: muon contamination can result  from tails of the muon distribution overlapping the pion time-of-flight peak (see figure\ref{tof}). A contamination of 30\% results in a reduction of less than 0.2\% of the pion fraction in the muon beam.
901

    
902
%\item 
903
%Different time-of-flight particle distributions in paired calibration runs and in muon run: some particles from calibration runs with a given time-of-flight contribute more (or less) to the  final result, than the particles from muon run with the same time-of-flight. The uneven distributions can be taken into account by shrinking time-of-flight intervals, thus minimizing the weight of the particles with different time-of-flights, but this approach requires large statistics. Alternatively the KL product distributions can be reweighted using the time-of-flight ones, thus making all the time-of-flight distributions flat. This approach produces results deviating by less than 0.2\% from the default one, without any preferred direction. [MEANING OF THIS BULLET UNCLEAR TO READER.]
904

    
905
%\end{itemize}
906

    
907
   
908
%%%%%%%%%%%%%%%%%%%%%%%%%% Figure %%%%%%%%%%%%%%%%%%%%%%%%%
909
\begin{figure}
910
\begin{center}
911
\includegraphics[scale=0.6]{pics/pion_fraction.pdf}
912
\caption{Pion contamination  in a muon run for time-of-flight
913
Points 1--3, estimated for three 
914
different cuts on KL product (with slight horizontal shifts for clarity).
915
Horizontal bars indicate  widths of time-of-flight intervals;
916
 vertical error bars are statistical only.}
917
\label{Fig:Pion_cont}
918
\end{center}
919
\end{figure}
920
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
921

    
922

    
923
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
924
\begin{table}[hbt]
925
\begin{center}
926
\caption{Sources of systematic errors in the evaluation of the pion 
927
contamination  for the cross-check. Values in parenthesis refer to Point 3. } 
928
\label{tbx}
929
\vskip 0.2cm
930
{\small
931
\begin{tabular}{|l|l|c|}
932
\hline
933
Effect & Assessment method & syst. error \\
934
\hline
935
\hline
936
KL threshold value & change of threshold value for KL cut & 0.5(1.0) \% \\ \hline
937
$\mu$ contamination & $\mu$ background in calibration runs  & 0.2 \% \\ \hline
938
difference in TOF distribution & change reference TOF intervals & 0.2 \% \\ 
939
between calibration  and $\mu$ runs &  & \\
940
\hline
941
\end{tabular}
942
}
943
\end{center}
944
\end{table}
945

    
946
\subsubsection{Estimation of the pion contamination in the MICE muon beam}
947
Results  to estimate the MICE muon beam pion
948
contamination are summarized in table \ref{Table:picont}.
949
Taking into account the number of beam particles in each TOF interval analyzed
950
(Point 1--3), the pion contamination averages  to 
951
 $$(1.11 \pm 0.29 \pm 0.32) \% $$, where the systematic uncertainty includes
952
 the small variation, $\pm 0.1\%$, associated to the lack of knowledge of the pion contamination in the 
953
 time-of-flight intervals in which the analysis was not performed (white area in figure \ref{tof}-a). 
954

    
955
This number is in  agreement with MonteCarlo estimates, 
956
taking into account errors (see figure \ref{fig:pi_cont}) and is
957
compatible to what computed with a simple classical method, used as
958
a cross-check. 
959
It translates to a pion contamination of 
960
%$(0.84 \pm 0.22 \pm 0.33)\%$ old value 
961
% Domizia - May 10th 2013: I have exp -(3.36*140/7.8/200 )~0.74  if it is correct to assume p~200 MeV for these guys at TOF1
962
% so I get 0.82 for the central value
963
% errors become 0.22 and 0.24 respectively
964
$(0.82 \pm 0.22 \pm 0.24)\%$ 
965
at the entrance of the
966
MICE cooling channel (first Focus coil $\sim 3.36$ m downstream TOF1).   
967

    
968
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
969
\begin{table}
970
\centering
971
\caption{Summary of results on pion contamination. The average of the results for Point 1 to 3 
972
takes into account the fraction of particles in each interval. 
973
Statistical and systematic errors are reported.} 
974
\vskip 0.2cm
975
\begin{tabular}{|l|c|c|c|c|}
976
\hline
977
Method & $\pi (\%)$   at Point 1 & $\pi (\%)$  at Point 2 & $\pi (\%)$ at 
978
Point 3 (\%) & average $\pi$ cont.  (\%)  
979
\\ \hline\hline
980
analysis & $0.65 \pm 0.46 \pm 0.30  $    & $0.84 \pm 0.27 \pm 0.34 $ & $ 1.90 \pm 0.37 \pm 0.80 $ & $ 1.11 \pm 0.29 \pm 0.30 $ \\
981
cross-check & $0.46 \pm 0.52 \pm 0.57  $    & $0.44 \pm 0.31 \pm 0.57 $ & $ 1.69 \pm 0.53 \pm 1.04 $ & $ 0.81 \pm 0.24 \pm 0.44 $ \\
982
MC          &                               &                           &                            &  0.33 \\                             
983
\hline
984
\end{tabular}
985
\label{Table:picont}
986
\end{table}
987
 
988

    
989

    
990
\section{Conclusions}
991
%%\input{conclusions_v3.tex}
992

    
993
%A preliminary estimation of the $\pi$ contamination in the MICE $\mu$ 
994
%beam, based on the MC simulations and the TOF informations only, gave 
995
%on an event-by-event basis a value around 1 $\%$ .
996

    
997
%The pion contamination in the MICE muon beam has been measured 
998
%on a statistical basis
999
%comparing the KL product response to calibration beams, in which the time-of-flight of the particles is used to discriminate muons from pions.
1000
%Two techniques have been developed for the comparison, one using only the high KL product tail, one extending the comparison over most of the KL spectrum. The two approaches give comparable results and are both consistent with a pion contamination reaching at most the 1\% level.
1001
%This result has been cross-checked with a method based on CHKOV and  
1002
%TOF informations, that gives a result compatible within errors. 
1003

    
1004

    
1005
The pion contamination in the MICE muon beam has been measured, %on a statistical basis
1006
using precision time-of-flight counters in combination with the KL
1007
sampling calorimeter.
1008
All measurements are in agreement with contamination at or 
1009
below the 1\% level at the entrance of the cooling channel ($\sim 3.36$ m 
1010
downstream TOF1). 
1011
%%By combining the 
1012
%%three measurements, we obtain the best estimate of the contamination fraction 
1013
%%(at TOF1) as XXX$\pm$YYY$\pm$ZZZ.
1014
Thus the MICE beam line meets the requirement set for it on pion 
1015
contamination, in order to demonstrate and characterise ionisation cooling.
1016

    
1017

    
1018
\newpage
1019
% ----------------------------------------------------------------
1020
\section*{Acknowledgements}
1021
% ----------------------------------------------------------------
1022

    
1023

    
1024

    
1025
We gratefully acknowledge the help and support of the ISIS staff 
1026
and of the numerous technical collaborators who have contributed to
1027
the design, construction, commissioning and operation of the
1028
experiment. In particular we would like to thank S.~Banfi, 
1029
F.~Chignoli, 
1030
R.~Gheiger, A.~Gizzi, V.~Penna, R. Mazza and W. Spensley.
1031
We wish to acknowledge the essential contributions in the conceptual
1032
development of a muon cooling 
1033
experiment  made by P.~Drumm, R. Edgecock, P. Fabbricatore, R. Fernow, D.~Findlay,  
1034
W. Murray, J. Norem, P.R.~Norton, K. Peach, C.~Prior and N. McCubbin. 
1035
We would also wish to acknowledge the work done in the early stages of
1036
the experiment by G. Barr, P. Chimenti, S. Farinon, 
1037
G.~Giannini, E. Radicioni, G. Santin, C. Vaccarezza, S. Terzo and K. Tilley.
1038
The experiment was made possible by grants from
1039
National Science Foundation and Department of Energy (USA),
1040
the Istituto Na\-zio\-na\-le di Fisica Nucleare (Italy), 
1041
the Science and Technology 
1042
Facilities Council (UK), the European Community under the European Commission Framework Programe 7,  the Japan Society for the Promotion of Science (Japan)
1043
and the Swiss National Science Foundation (Switzerland), in the framework
1044
of the SCOPES programme.
1045
We gratefully acknowledge their support.
1046

    
1047

    
1048

    
1049
\newpage
1050
\bibliographystyle{JHEP}
1051
\bibliography{MICE_PID_v9}
1052
\end{document}
1053

    
1054

    
(5-5/22)