Closed-Form Analytical Charge Response Model for Silicon Photomultipliers with Recursive Correlated Avalanches
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| Format: | Preprint |
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2026
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| _version_ | 1866911721351806976 |
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| author | Liu, Yiqi Liu, Xuewei Xu, Benda |
| author_facet | Liu, Yiqi Liu, Xuewei Xu, Benda |
| contents | Silicon photomultipliers (SiPMs) have become the preferred photodetectors in next-generation neutrino experiments, yet no unified closed-form analytical expression free of truncation and numerical convolution has been established for their full charge response spectrum, which must simultaneously capture correlated cross-talk and afterpulsing effects absent in conventional photomultiplier tubes (PMTs). We present a unified closed-form model for the SiPM charge response within the characteristic-function framework, treating pedestal noise, single-electron-response (SER) charge, internal optical cross-talk, and afterpulsing on equal footing. The characteristic-function representation factorises the full charge spectrum into three independent physical components: pedestal, single-electron response (SER), and avalanche count statistics. Prompt internal optical cross-talk is modelled as a Galton-Watson branching process with Poisson offspring; building on the Generalised Poisson count statistics identified by Vinogradov, we derive a Lambert $W$ closed form for the total-progeny PGF via Lagrange-Bürmann inversion, providing the analytical handle needed for efficient event-level reconstruction. Afterpulsing is modelled as a per-avalanche geometric chain, derived as the maximum-entropy Poisson-Gamma mixture: the exponential prior-maximum-entropy for a positive continuous yield with fixed mean-marginalised over a Poisson count yields the geometric per-avalanche distribution, whose $N$-avalanche total is Negative Binomial. This naturally encompasses the Poisson afterpulsing limit and recursive afterpulse chains while preserving analytical closure. The resulting eight-parameter expression is further applied to derive an explicit per-channel charge-time likelihood for event-level energy reconstruction without numerical convolution at inference time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_27340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closed-Form Analytical Charge Response Model for Silicon Photomultipliers with Recursive Correlated Avalanches Liu, Yiqi Liu, Xuewei Xu, Benda Instrumentation and Detectors High Energy Physics - Experiment Silicon photomultipliers (SiPMs) have become the preferred photodetectors in next-generation neutrino experiments, yet no unified closed-form analytical expression free of truncation and numerical convolution has been established for their full charge response spectrum, which must simultaneously capture correlated cross-talk and afterpulsing effects absent in conventional photomultiplier tubes (PMTs). We present a unified closed-form model for the SiPM charge response within the characteristic-function framework, treating pedestal noise, single-electron-response (SER) charge, internal optical cross-talk, and afterpulsing on equal footing. The characteristic-function representation factorises the full charge spectrum into three independent physical components: pedestal, single-electron response (SER), and avalanche count statistics. Prompt internal optical cross-talk is modelled as a Galton-Watson branching process with Poisson offspring; building on the Generalised Poisson count statistics identified by Vinogradov, we derive a Lambert $W$ closed form for the total-progeny PGF via Lagrange-Bürmann inversion, providing the analytical handle needed for efficient event-level reconstruction. Afterpulsing is modelled as a per-avalanche geometric chain, derived as the maximum-entropy Poisson-Gamma mixture: the exponential prior-maximum-entropy for a positive continuous yield with fixed mean-marginalised over a Poisson count yields the geometric per-avalanche distribution, whose $N$-avalanche total is Negative Binomial. This naturally encompasses the Poisson afterpulsing limit and recursive afterpulse chains while preserving analytical closure. The resulting eight-parameter expression is further applied to derive an explicit per-channel charge-time likelihood for event-level energy reconstruction without numerical convolution at inference time. |
| title | Closed-Form Analytical Charge Response Model for Silicon Photomultipliers with Recursive Correlated Avalanches |
| topic | Instrumentation and Detectors High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2605.27340 |