BTL Time Resolution from <span class="highlight-yellow">Energy Sharing</span> Events

Claudio Quaranta¹, Leyan Li¹

¹ Peking University (CN)

Apr 24^th 2026

Introduction
Intercalibration & Energy Cut
Time Resolution Results
Summary

Introduction

BTL time resolution study using energy sharing events from 2025 Sep test beam
Two modules on beam: DUT (forward, rotated ~45°) and REF (backward, ~52°)
- DUT at 45° → MIP crosses 2 adjacent bars → energy sharing topology
New in this report:
- Energy intercalibration using factors from a reference run
- 1 MeV energy cut to reject noise
Previous talks:
- Dec 19, 2025
- Mar 6, 2026

Test beam setup (Sep 2025)

Beam geometry: DUT (~45°) + REF (~52°)

Intercalibration & Energy Cut

Run 4482, $V_{\text{OV}}$ = 3.00 V
Our configuration: Conf 95 (DM9005, SM 1220, Cat D)
- ALDO correction: 2, 3 ok → avg OV residual = 1
Chosen to avoid effects from large miscalibration of OV in SiPM pair at lower $V_{\text{OV}}$

Reference: Simona, ER studies, slide 4

$Nominal OV vs OV0/OV1$

The single-channel energy spectrum is not Landau-shaped due to the energy-sharing effect
- Therefore the standard analysis to get intercalibration factors could not be applied
Used intercalibration factors from run 4257 (same $V_{\text{OV}}$=3V, same TOFHIR settings)
- REF module DM_348, provided by Simona
- Calibration factors

Right panel: distorted single-channel spectrum from standard step1 code on run 4482 — the Landau fit fails.
Shown: bar 07 Left, threshold = 10 DAC. More plots

bar 07 Left — V_OV = 3.00 V, th = 10 DAC

Module rotated 45°, LYSO thickness = 3.75 mm
MIP path = $3.75 / \sin(45°)$ = 5.3 mm
$dE/dx$ in LYSO = 0.89 MeV/mm → total deposit ≈ 4.7 MeV
Fit doubleHit energy spectrum ($E_{\text{sum}} = E_1 + E_2$)
Average Landau MPV ≈ 367 ADC (run 4482, VoV=3V)
1 MeV = 367 / 4.7 ≈ 78 ADC

Note: This is an approximate threshold — we average the Landau peaks of several bar pairs that are not perfectly calibrated.

1Hit = 1 bar with both L and R channels above energy threshold. Only 2-hit events are retained for ES analysis.
Left: without 1 MeV cut | Right: with 1 MeV cut (78 ADC) — shown for th=10
Cut suppresses 3-hit events (~13% → ~2%) but increases 1-hit fraction (~10% → ~33%) at low threshold
The trend is consistent across all threshold values (th = 5, 10, 20 DAC) — see backup for full comparison

th=10, no cut

th=10, with cut

Example spectra for bar pair 6, th=10. Left: no cut | Right: with 78 ADC cut.
With the 1 MeV cut, a MIP peak appears in singleHit events: a significant fraction of 2-hit events where one bar carries the larger energy deposit now fall below threshold in the other bar, becoming single-hit events.
The doubleHit spectrum improves (becomes more Landau-shaped): the cut reclassifies 3-hit events (likely 2 real hits + 1 from cross-talk/noise) back into the 2-hit category.

SingleHit, no cut

SingleHit, with cut

DoubleHit, no cut

DoubleHit, with cut

Time Resolution Results

Landau MPV vs bar number — Red = with intercalib, Blue = without intercalib. 1 MeV cut applied in both cases.
MPV comparison shows intercalibration moves in the right direction (flatter distribution across bars), though the overall impact on time resolution may not be dramatic. Further refinement needed — extend to both singleHit and doubleHit cases separately.
Shown: LR-averaged, th=10. Full set (L, R, LR × singleHit/doubleHit × all thresholds): MPV_comparison plots

SingleHit MPV (L+R avg)

DoubleHit MPV (L+R avg)

For 2-hit events, arrival time computed by energy-weighted average of $\bar{t}_1$ and $\bar{t}_2$
$E_0 = E_1 + E_2$
Events divided into bins of energy fraction: $f = E_1 / E_0$
The $\overline{\Delta T}$ resolution estimated from its Gaussian width
Final time resolution is derived as: $\sigma_{t_{ave}} = \frac{1}{2}\,\sigma_{\overline{\Delta T}}$

[1*] $t_{ave} = \frac{E_1 t_1 + E_2 t_2}{E_0}$

$\sigma_{t_{ave}} = \frac{1}{2E_0}\sqrt{E_1^2(\sigma_{L1}^2 + \sigma_{R1}^2) + E_2^2(\sigma_{L2}^2 + \sigma_{R2}^2)}$

[2*] $\overline{\Delta T} = \frac{E_1 \Delta T_1 + E_2 \Delta T_2}{E_0}$

$\sigma_{\overline{\Delta T}} = \frac{1}{E_0}\sqrt{E_1^2(\sigma_{L1}^2 + \sigma_{R1}^2) + E_2^2(\sigma_{L2}^2 + \sigma_{R2}^2)}$

[3] $\sigma_{t_{ave}} = \frac{1}{2}\,\sigma_{\overline{\Delta T}}$

Ref: Previous Report, Mar 6 2026, slide 4

Events classified by energy fraction: $f = E_{\text{bar}(i)} / (E_{\text{bar}(i)} + E_{\text{bar}(i+1)})$
$\sigma_t$ vs bar pair for f Bin 4 $[0.56, 0.68)$, 2Hits, weighted $\overline{\Delta T}$, best threshold per bar pair
Bars 0, 1, and 13–15 removed (low statistics); bar N = bar pair N–(N+1)
Three configurations compared:
- W/ calib — 1 MeV cut + intercalibration
- W/O calib — 1 MeV cut, no intercalibration
- W/O calib & cut — original (no cut, no calib)

f Bin	f interval	W/O calib & cut	W/O calib	WITH calib
2	[0.32–0.44)	26.1 ± 1.7 ps	25.6 ± 1.4 ps	25.7 ± 2.0 ps
3	[0.44–0.56)	25.1 ± 1.0 ps	25.1 ± 0.9 ps	24.9 ± 1.0 ps
4	[0.56–0.68)	24.7 ± 0.6 ps	24.8 ± 0.7 ps	24.6 ± 0.6 ps
5	[0.68–0.80)	24.9 ± 0.7 ps	24.4 ± 1.0 ps	24.6 ± 0.7 ps

Tab. avg ± RMS across bar pairs (pol0 fit).

Conclusion: Intercalibration impact on time resolution is minimal (Δ < 0.5 ps). The downstream energy corrections in step2 largely mitigate bar-to-bar gain variations.

3-configuration overlay — f Bin 4

Studied time resolution of energy sharing events (2-hit, weighted $\overline{\Delta T}$) from Sep 2025 test beam data (Run 4482, $V_{OV}$ = 3 V)
Applied energy intercalibration (from run 4257, same $V_{OV}$ and TOFHIR settings) and a 1 MeV energy cut (~78 ADC) to reject noise hits
MPV comparison shows intercalibration moves in the right direction (flatter MPV distribution across bar pairs)
Time resolution consistent across energy fraction bins (~24.6–25.7 ps); f Bin 4 $[0.56, 0.68)$ shown as representative:
- 24.6 ± 0.6 ps (with calib) — uniform across 10 bar pairs
- Impact of intercalibration on time resolution is minimal (Δ < 0.5 ps)
The downstream energy corrections in step2 largely mitigate bar-to-bar gain variations → intercalibration has limited additional benefit for time resolution

Back Up

Full comparison of nHits distribution across thresholds (5, 10, 20 DAC). Top row: without 1 MeV cut | Bottom row: with 1 MeV cut (78 ADC)

th=5, no cut

th=10, no cut

th=20, no cut

th=5, with cut

th=10, with cut

th=20, with cut

Run 4482 — 31,762,722 raw events → 2,078,932 reconstructed events

nActiveBars	No cut (>0 ADC)	With 1 MeV cut (>120 ADC)
0-hit	71,029 (3.4%)	101,473 (4.9%)
1-hit	179,327 (8.6%)	612,699 (29.5%)
2-hit	1,456,866 (70.1%)	1,264,125 (60.8%)
3-hit	371,710 (17.9%)	100,635 (4.8%)

3-hit fraction: 17.9% → 4.8% (cut removes cross-talk/noise hits)
1-hit fraction: 8.6% → 29.5% (2-hit events where one bar falls below threshold become 1-hit)
2-hit (ES analysis): 1.46M → 1.26M events retained

$\sigma_t$ vs $V_{OV}$: left = non-irradiated, right = $2 \times 10^{14}\ n_{eq}/cm^2$. Black dots = data; colored lines = electronics (blue), photo-stat. (green), DCR (orange).
NIM A, 1081, 170823 (2025)

$\sigma_t^{BTL} \sim \sigma_t^{ele} \oplus \sigma_t^{phot} \oplus \sigma_t^{DCR} \sim \frac{1}{E^{\alpha}}$

$N_{pe}$ = number of photo-electrons
$E$ proportional to $N_{pe}$
DCR = Dark Current Rate

$\sigma_t^{ele} \sim 1/N_{pe}$

$\sigma_t^{phot} \sim 1/\sqrt{N_{pe}}$

$\sigma_t^{DCR} \sim \sqrt{DCR/N_{pe}}$

Initial Performance & V_OV Trend: In the non-irradiated stage (left), the time resolution is primarily limited by electronic noise and photo-statistics. It improves significantly with increasing V_OV, reaching an optimal precision of ~30 ps.
Impact of Radiation Damage: Post-irradiation (right), the DCR increases significantly and dominates the resolution. Although increasing V_OV still helps improve timing, the overall resolution is degraded to ~60 ps due to the massive noise floor.
Scaling & N_pe Dependence: All noise terms scale with 1/N_pe; the convolution parameter $\alpha$ shifts from 0.5 (stochastic) toward 1.0 (DCR-dominated) as the detector ages.

                                /eos/cms/store/group/dpg_mtd/comm_mtd/TB/MTDTB_H8_Sep2025/TOFHIR/reco
                            

CONF 95.00

ASIC: TOFHIR2C
Reference: ASIC 7, FE4587 class AA PKU @ 52deg
DUT: ASIC 4, DM348, FE4519 @ 45deg
Operating temperature: 18C

Run Number	Overvoltage (OV) [V]	Threshold (th) [DAC]
4482	3.0 V	3, 5, 7, 10, 15, 20
4497	0.9 V	3, 5, 7, 10, 15, 20
4507	1.2 V	3, 5, 7, 10, 15, 20
4510	2.0 V	3, 5, 7, 10, 15, 20

OV (overvoltage):

excess bias above the breakdown voltage of the SiPM
higher OV → larger signal but higher dark current rate

NIM A, 1081, 170823 (2025)

th (threshold):

TOFHIR signal threshold — each channel triggers independently
when signal > th1 DAC = 0.313 μA

F. Addesa et al 2024 JINST 19 P12020

BTL Time Resolution from Energy Sharing Events

Intercalibration and 1 MeV energy cut study — Run 4482 (VOV = 3V)