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\section{Calibration Using Di-Jet Balancing}
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Di-jet balancing was proposed for calibrating HF and the HE region not covered by the tracking system.
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This calibration procedure is performed after the phi symmetry corrections are available and
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after HB is fully calibrated.
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The procedure makes use of the $p_T$ balance in di-jet events and propagates the absolute energy
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scale obtained with isolated tracks to the high-$\eta$ regions.
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We select events with one "reference" jet with $E^{ref}_T>$30~GeV in the barrel ($\eta<$1) and another
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"probe" jet in the endcap or forward region ($\eta>$2). The two jets must be well separated in
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$\phi$: $\Delta\phi(j_1, j_2)>$150$^{\circ}$. No additional jets with $E_T>$5~GeV are allowed.
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The expected energy of the probe jet is
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$$E_{exp}^{probe} = E^{ref}_T/\sin(\theta^{ref})$$
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Taking into account that the EM energy resolution and scale are known with much higher precision than for HCAL,
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the $expected$ hadronic energy of a probe jet in HE is
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$$E_{exp~had}^{probe} = E^{probe} - E^{probe}_{EM}$$
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while for a probe jet in HF it is
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$$E^{probe}_{exp~had} = E^{ref}_T/\sin(\theta^{ref})$$
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The minimization procedure for obtaining the correction coefficients is similar to the one used for isolated tracks.
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The expected hadronic energy is the target energy in minimization. In the case of jets one can have contributions from a much larger number of calorimeter cells. Like in the case of isolated tracks, the energies in HCAL depths are summed, and after applying the phi symmetry correction factors, the energies of cells in the same $\eta$ ring are also added together.
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The L3 minimization algorithm is used to obtain correction factors that are common for the HCAL calorimeter cells in the same $i\eta$ ring.
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Unfortunately, the conceptual simplicity of the original idea is countered by a number of
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issues that need resolution before this techniques can be used for detector calibration.
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In the near term we expect to use jets in a more restricted way: for validation and monitoring
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of the relative responses in the +/- sides of the detector, different depths in HE, and long/short
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fiber in HF.
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The development of related, but significantly modified methods is in progress and will be presented
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for review when more mature results are obtained.
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