\contentsline {section}{\numberline {1}Introduction}{4}
\contentsline {section}{\numberline {2}A Factorized Multi-Level Jet Correction}{4}
\contentsline {section}{\numberline {3}Level 1: Offset}{5}
\contentsline {subsection}{\numberline {3.1}Early Corrections}{5}
\contentsline {subsection}{\numberline {3.2}Corrections including Zero Suppression effects}{6}
\contentsline {subsubsection}{\numberline {3.2.1}ECAL Selective Readout and HCAL Zero Suppression}{6}
\contentsline {subsubsection}{\numberline {3.2.2}Effect on jet energy scale}{6}
\contentsline {subsubsection}{\numberline {3.2.3}Run Strategy without Zero Suppression and Selective Readout}{7}
\contentsline {subsubsection}{\numberline {3.2.4}Corrections to jets for zero suppression}{8}
\contentsline {subsubsection}{\numberline {3.2.5}Correction to jets for pile-up}{8}
\contentsline {section}{\numberline {4}Level 2: $\eta $ dependence}{9}
\contentsline {subsection}{\numberline {4.1}Definition}{10}
\contentsline {subsection}{\numberline {4.2}MC Truth Determination of the Relative Correction}{11}
\contentsline {subsection}{\numberline {4.3}Data Driven Determination of the Relative Correction}{12}
\contentsline {subsubsection}{\numberline {4.3.1}Dijet $p_T$ Balance}{12}
\contentsline {subsubsection}{\numberline {4.3.2}MPF Method}{13}
\contentsline {section}{\numberline {5}Level 3: $p_T$ dependence}{15}
\contentsline {subsection}{\numberline {5.1}Monte Carlo based Energy Corrections}{16}
\contentsline {subsection}{\numberline {5.2}$\gamma $ + Jet and $Z$ + Jet Balancing}{16}
\contentsline {subsubsection}{\numberline {5.2.1}$\gamma /Z+$ Jet $p_T$ Balance}{16}
\contentsline {subsubsection}{\numberline {5.2.2}MPF Method}{19}
\contentsline {subsubsection}{\numberline {5.2.3}Jet Response vs. $p_T$}{20}
\contentsline {subsection}{\numberline {5.3}Reconstructed $\gamma $ + jet balance and Backgrounds}{20}
\contentsline {subsection}{\numberline {5.4}Early plan for combining $p_T$ dependent corrections}{21}
\contentsline {subsection}{\numberline {5.5}Jet plus track algorithm for energy correction}{24}
\contentsline {section}{\numberline {6}Level 4: EMF dependence}{24}
\contentsline {subsection}{\numberline {6.1}Motivation}{25}
\contentsline {subsection}{\numberline {6.2}JES EMF Correction}{25}
\contentsline {subsubsection}{\numberline {6.2.1}MC Truth Determination}{27}
\contentsline {subsubsection}{\numberline {6.2.2}Determination of the Correction in Data}{28}
\contentsline {subsection}{\numberline {6.3}Discussion}{28}
\contentsline {section}{\numberline {7}Level 5: Optional Flavour dependence}{29}
\contentsline {subsection}{\numberline {7.1}Flavour corrections from Monte Carlo}{29}
\contentsline {subsection}{\numberline {7.2}\relax \mathversion {bold}Flavour corrections from $t\mathaccent "7016\relax {t}$ events}{31}
\contentsline {subsection}{\numberline {7.3}\relax \mathversion {bold}Flavour corrections from $\gamma +b,\nobreakspace {}b\mathaccent "7016\relax {b}Z,\nobreakspace {}Z\to b\mathaccent "7016\relax {b}$ events}{31}
\contentsline {subsection}{\numberline {7.4}Biases from flavour dependent corrections and event topologies}{31}
\contentsline {section}{\numberline {8}Level 6: Optional UE correction}{32}
\contentsline {section}{\numberline {9}Level 7: Optional Parton correction}{32}
\contentsline {section}{\numberline {10}Corrections to Particle Flow Clusters}{34}
\contentsline {section}{\numberline {11}Closure Tests}{36}
\contentsline {subsection}{\numberline {11.1}Validation of Methods}{36}
\contentsline {subsection}{\numberline {11.2}Validation of Correction Values}{36}
\contentsline {subsubsection}{\numberline {11.2.1}Tests on $\gamma $/Z-jets Samples}{37}
\contentsline {subsubsection}{\numberline {11.2.2}Corrections from mass constraints in top quark events}{37}
\contentsline {subsection}{\numberline {11.3}Summary}{39}
\contentsline {section}{\numberline {12}Evolution of Corrections and the Role of the Monte Carlo}{39}
\contentsline {section}{\numberline {13}Software}{40}
\contentsline {section}{\numberline {14}Conclusions}{41}
