SPE Mean Charge Analysis

Background Information

  • Found another paper that gives further detail; some equations on this page are quoted from here (specifically pages 2-5): https://arxiv.org/pdf/1602.03150v1.pdf

  • Total integrated charge spectrum $TOT(q)$ is defined by convolution of two components: the pedestal i.e. background $PED(q)$ and signal $S(q)$:
\begin{equation} TOT(q) = PED(q) * S(q) \end{equation}

  • The mean charge for the SPE contribution can be found using the following equation:
\begin{equation} \mu_{\mathrm{SPE}} = \frac{\mu_{TOT(q)} - \mu_{PED(q)}}{\mu_{\mathrm{PE}}} \end{equation}

  • According to the link above, making the assumption that the number of photoelectrons $N_{\mathrm{PE}}$ follows a Poissonian distribution, $\lambda \equiv \mu_{\mathrm{PE}}$, where,:
\begin{equation} \hat{\lambda} = -\mathrm{ln}(\hat{N_{\mathrm{0}}}/N) \end{equation}

where $\hat{N_{\mathrm{0}}}$ is the estimate for the number of 0PE triggers and $N$ is the total number of sample triggers.

  • NOTE: this analysis only works for low occupancy data

SPE Mean Charge Calculation

  • Run 12617 (RT124; Detector AARFs, 1$\mu\mathrm{s}$ waveform, FWF, RAW 10% occupancy) - specifically focusing on subrun 0, PMTID 0. The spectra are found using SPESpectrumProc.cc
charge.png

  • To calculate $\mu_{TOT(q)}$, found the numerical mean of the entire spectrum
  • To calculate $\mu_{PED(q)}$, rerun processor with time window shifted to get histogram of just pedestal - find numerical mean of this histogram
  • To calculate $\mu_{\mathrm{PE}}$:
    • Normalised the charge spectrum histogram such that the integral = 1. Hence N = 1, and thus $\hat{N_{\mathrm{0}}}/N = \hat{N_{\mathrm{0}}}$ and $\hat{\lambda} = -\mathrm{ln}(\hat{N_{\mathrm{0}}})$
    • Took integral of part of histogram below and including Q = 2pC (which is assumed to only include 0PE triggers), to obtain $\hat{N_{\mathrm{0}}}$
  • Repeated this process for other PMTs in this subrun:
MeanSPE_vs_PMT.png

Statistical uncertainty on SPE Mean Charge

  • Statistical uncertainty on $\mu_{\mathrm{SPE}}$ will be found by comparing the SPE mean charge from data with MC to see how much the value changes
  • Plan: make a 'hybrid' charge spectra distribution, with real data noise/pedestal with MC SPE pulses
  • Repeat above analysis and recalculate SPE mean charge, see how much they differ to obtain UNCERTAINTY
  • Current status: HIT mixing tool in process of being adapted in order to make this hybrid, when it is ready I will have more to update!
-- AshleaKemp - 12 Sep 2016
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Topic revision: r7 - 09 Nov 2016 - AshleaKemp

 
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