interactions described later), the resolution is not limited by shower-development fluctuations and can be significantly smaller than 1 ns.

HCAL Time Reconstruction {#sec:reco}
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When the Level-1 trigger system [@cite:craftL1trig] identifies an event of potential physics interest, a set of 10 consecutive time samples per channel containing the triggered bunch-crossing is collected and sent to the high-level trigger software. The capability of the HCAL system to reconstruct the arrival time of the signal more precisely than the sample clock period derives from the spread of the HCAL pulse shape over three to four time-integrated samples (Fig. \[fig:HCALpulse\]). The time reconstruction software calculates a first order time estimate from a center-of-gravity technique using the three samples centered on the peak,

$$\label{eq:wpkbin}
\textrm{Weighted peak bin} =
   \bigg[\frac{(p-1)A_{p-1} + pA_p + (p+1)A_{p+1}}{A_{p-1} + A_p + A_{p+1}}\bigg]\times C\quad,$$

where $A_i$ represents the amplitude of an arbitrary time sample $i$, and $p$ is the value of $i$ such that $A_p$ is maximum over the set of samples. In the case of multiple samples with the same amplitude, the earliest one is picked. The constant $C$ is an amplitude-independent normalization constant that rescales the first order estimate to a range from zero to one. The weighted 