Absolute Lifetime Correlations

• Absolute lifetime correlations are relationships formulated using directly measured decay times rather than relative differences.
• They encompass diverse methods including covariance tests in entangled systems, calibration in heavy-flavor baryon analyses, and direct fit techniques in charm metrology.
• Their applications span multiple fields, informing predictive modeling in reliability engineering, battery life estimation, astrophysics, and financial market analyses.

Searching arXiv for recent and directly relevant papers on absolute lifetime correlations and related lifetime-correlation measurements. Absolute lifetime correlations are relationships formulated in terms of absolute lifetimes or absolute decay times, rather than solely in terms of relative ordering, time differences, or normalized ratios. In the arXiv literature, the phrase does not denote a single universal statistic. Instead, it spans several technically distinct constructions: covariance of the two absolute decay times in entangled $\Lambda$–$\bar\Lambda$ pairs; propagated dependence of a measured absolute lifetime on an external calibration lifetime in heavy-flavor baryon analyses; direct decay-length-based absolute lifetime measurements that avoid such external normalization; lifetime–energy correlations in threshold few-body decays; and correlations between absolute time-to-failure and engineered or physical covariates in reliability and population-synthesis studies (Tang, 24 Jul 2025, Aaij et al., 2016, Collaboration et al., 2022, Grigorenko et al., 2013, Abdelli et al., 2022, Li et al., 2023, Mordasini et al., 2012, Buda, 2011).

1. Terminological scope and domain-specific meanings

The literature uses closely related language for several non-equivalent objects. In one usage, “absolute lifetime correlations” refers to correlations involving the full pair of decay times $(t_1,t_2)$, not merely the relative time $\Delta t=t_2-t_1$. In another, an absolute lifetime is obtained from a lifetime ratio by multiplication with a reference-mode lifetime, so the final result inherits an extra uncertainty from that external input. Elsewhere, “absolute lifetime” denotes a directly measured proper lifetime or a predicted time-to-failure, and the correlation is between that lifetime and explanatory variables such as degradation features, operating conditions, or disk properties (Tang, 24 Jul 2025, Aaij et al., 2016, Collaboration et al., 2022, Abdelli et al., 2022, Li et al., 2023, Mordasini et al., 2012).

Domain	Absolute lifetime quantity	Correlation form
Entangled hyperons	Pair $(t_1,t_2)$	Covariance and spin-weighted correlator
Heavy-flavor baryons	$\tau_{\Omega_b^-}$ from calibration	Dependence on $\tau_{\Xi_b^-}$
Charm-baryon metrology	$\tau(\Lambda_c^+)$	Direct fit to proper-time distribution
Two-neutron decay	$T_{1/2}$ of $^{26}$O	Lifetime–decay-energy dependence
Semiconductor lasers	TTF	Nonlinear dependence on sequence and operating features
Li-ion batteries	EOL lifetime	Pearson correlations and predictive regression
Planet formation	Disk lifetime	Correlation with giant-planet frequency, mass, migration
Financial markets	Life time of correlation	Duration of strong-correlation episodes

This suggests that the phrase is best treated as a family of constructions unified by one criterion: the observable of interest is an absolute lifetime scale, not only a relative or normalized surrogate. The technical consequences of that choice differ sharply by field. In unstable-particle measurements it governs null hypotheses, calibration structure, and uncertainty propagation; in predictive settings it governs target definition, feature engineering, and extrapolation behavior.

2. Absolute-time correlations in entangled unstable hadrons

A precise and explicit formulation appears in the proposal to test spin-lifetime correlations in entangled $\bar\Lambda$0–$\bar\Lambda$1 pairs. There the individual proper times are reconstructed as

$\bar\Lambda$2

and the distinction between relative and absolute lifetime correlations is central. Relative lifetime correlations are organized around $\bar\Lambda$3 and a possible $\bar\Lambda$4-dependence of the spin-correlation coefficient $\bar\Lambda$5. Absolute lifetime correlations, by contrast, involve the full two-time structure and are sensitive to correlations in $\bar\Lambda$6 and $\bar\Lambda$7 themselves, including common-mode shifts invisible to a $\bar\Lambda$8-only analysis (Tang, 24 Jul 2025).

The null hypothesis is independent exponential decay: $\bar\Lambda$9 which implies

$(t_1,t_2)$0

The simplest absolute-time observable is therefore

$(t_1,t_2)$1

To make the test spin-sensitive, the paper introduces the event-wise weight

$(t_1,t_2)$2

standardizes it with mixed-event moments,

$(t_1,t_2)$3

defines the lifetime product

$(t_1,t_2)$4

and constructs

$(t_1,t_2)$5

followed by the acceptance-corrected statistic

$(t_1,t_2)$6

Because $(t_1,t_2)$7 is a constructed statistic, the proposed significance assessment is nonparametric. The lifetime products are held fixed, the spin weights are permuted within the same-event sample, and an empirical $(t_1,t_2)$8-value is obtained from repeated trials. Factually, the work is a proposal rather than an observation: it states that hadronic entanglement studies have so far focused on angular observables, and that a positive signal in decay-time observables would imply that the standard picture of independent exponential decays is incomplete for the entangled pair. The importance of the “absolute” qualifier is therefore operational: it selects tests sensitive to the joint distribution of the two decay times, not merely to their difference.

3. Calibration-induced absolute lifetimes and inherited uncertainties

A different technical meaning arises in heavy-flavor lifetime metrology when an absolute lifetime is not extracted in isolation but inferred from a measured lifetime ratio. The $(t_1,t_2)$9 analysis reconstructs

$\Delta t=t_2-t_1$0

using a proton-proton data sample corresponding to $\Delta t=t_2-t_1$1 collected at $\Delta t=t_2-t_1$2 and $\Delta t=t_2-t_1$3, and calibrates the result with

$\Delta t=t_2-t_1$4

Because the two chains have the same visible final-state topology and very similar kinematics, many detector, reconstruction, trigger, and selection effects cancel in the ratio. The analysis reconstructs $\Delta t=t_2-t_1$5 $\Delta t=t_2-t_1$6 candidates, fits the efficiency-corrected yield ratio as a function of decay time with an exponential, obtains $\Delta t=t_2-t_1$7, measures

$\Delta t=t_2-t_1$8

and then converts this to

$\Delta t=t_2-t_1$9

using the previously measured

$(t_1,t_2)$0

The third uncertainty on $(t_1,t_2)$1 is explicitly the uncertainty propagated from the reference-mode $(t_1,t_2)$2 lifetime used for calibration (Aaij et al., 2016).

This construction is not a covariance test in the sense of entangled-pair analyses. Instead, the correlation is metrological and inferential: the absolute lifetime depends on an external lifetime input, so the final estimator inherits an additional uncertainty component absent from the ratio itself. The same calibration logic appears in the accompanying mass measurement, where

$(t_1,t_2)$3

and

$(t_1,t_2)$4

with the final uncertainty on the absolute mass arising from the external $(t_1,t_2)$5 mass input. In this usage, “absolute lifetime” is operationally downstream of a relative measurement, and the relevant correlation is the dependence of the absolute estimate on the calibration observable.

4. Direct absolute lifetime measurements without normalization modes

The Belle II measurement of the $(t_1,t_2)$6 lifetime exemplifies the complementary regime in which the absolute lifetime is extracted directly from reconstructed decay geometry and momentum, rather than by reference to another hadron lifetime. Using $(t_1,t_2)$7 of data collected at center-of-mass energies at or near the $(t_1,t_2)$8 resonance, the analysis reconstructs

$(t_1,t_2)$9

defines the proper decay time as

$\tau_{\Omega_b^-}$0

and performs an unbinned maximum-likelihood fit to the two-dimensional distribution in $\tau_{\Omega_b^-}$1 and per-candidate decay-time uncertainty $\tau_{\Omega_b^-}$2. The signal region

$\tau_{\Omega_b^-}$3

contains about $\tau_{\Omega_b^-}$4 events and is about $\tau_{\Omega_b^-}$5 signal. The fit includes an exponential signal component convolved with a Gaussian resolution whose width depends on $\tau_{\Omega_b^-}$6, an empirical background model constrained by sidebands, a free scale factor $\tau_{\Omega_b^-}$7 multiplying $\tau_{\Omega_b^-}$8, and a floated resolution mean. The fit finds $\tau_{\Omega_b^-}$9 and a resolution mean of $\tau_{\Xi_b^-}$0 fs, yielding

$\tau_{\Xi_b^-}$1

The main systematic contributions are $\tau_{\Xi_b^-}$2 fs from $\tau_{\Xi_b^-}$3 contamination, $\tau_{\Xi_b^-}$4 fs from the resolution model, $\tau_{\Xi_b^-}$5 fs from non-$\tau_{\Xi_b^-}$6 backgrounds, $\tau_{\Xi_b^-}$7 fs from detector alignment, and $\tau_{\Xi_b^-}$8 fs from the momentum scale (Collaboration et al., 2022).

The significance of this method for the theory of absolute lifetime correlations lies in what it omits. Since the lifetime is not normalized to another hadron lifetime, there is no reference-lifetime uncertainty term analogous to the $\tau_{\Xi_b^-}$9 analysis. The proper-time observable is itself absolute, and the dominant correlations to be controlled are experimental ones: vertexing, resolution, contamination, alignment, and momentum scale. For heavy-flavor and charm metrology, this marks a sharp distinction between absolute determination and calibrated inference.

5. Lifetime–energy correlations in threshold few-body decay

In nuclear few-body theory, the relevant absolute-lifetime correlation is often a correlation between half-life and decay energy. The three-body $\tau(\Lambda_c^+)$0 model for the unbound ground state of $\tau(\Lambda_c^+)$1O treats the system as a true $\tau(\Lambda_c^+)$2 emitter and solves a three-body Schrödinger problem to obtain the decay width from

$\tau(\Lambda_c^+)$3

For a pure interior $\tau(\Lambda_c^+)$4 configuration one expects approximately

$\tau(\Lambda_c^+)$5

but the calculation shows that this naive scaling is strongly modified by subbarrier configuration mixing induced by core recoil and neutron-neutron final-state interaction. Core recoil drives migration into lower centrifugal-barrier channels, while the $\tau(\Lambda_c^+)$6-$\tau(\Lambda_c^+)$7 interaction accelerates rearrangement into $\tau(\Lambda_c^+)$8-wave-dominated asymptotics. The result is a very narrow lifetime-vs.-decay-energy dependence for true $\tau(\Lambda_c^+)$9 emission, much tighter than earlier broad estimates from simplified models (Grigorenko et al., 2013).

The paper compares three limiting cases: no FSI and no recoil; no FSI but with proper core recoil; and full $T_{1/2}$0-$T_{1/2}$1 FSI. The calculated correlation patterns evolve correspondingly from an internal $T_{1/2}$2 “triple-ridge” structure to a recoil-smeared double-ridge pattern and then to an $T_{1/2}$3-like asymptotic configuration. Since

$T_{1/2}$4

small changes in low-energy asymptotics produce large changes in the half-life. Using the cited experimental value

$T_{1/2}$5

the calculation infers roughly

$T_{1/2}$6

Here the phrase “absolute lifetime correlation” is naturally interpreted as a functional dependence between an absolute half-life and a structural control variable, namely decay energy, with the dependence narrowed by realistic three-body dynamics. The paper further emphasizes that the sensitivity is stronger than in true $T_{1/2}$7 emitters because there is no Coulomb barrier, recoil-driven mixing is stronger, and $T_{1/2}$8-$T_{1/2}$9 FSI is particularly effective at reshaping the asymptotic decay path.

6. Covariate-based absolute lifetime correlations in predictive modeling

Outside unstable-particle decay, the same general idea appears as correlation between absolute time-to-failure and physical or engineered predictors. In semiconductor-laser reliability, the target is the time-to-failure, defined as the time at which the laser output power has dropped by $^{26}$0 dB, corresponding to about $^{26}$1 of its initial value. A federated-learning framework distributes a shared model across $^{26}$2 heterogeneous clients built from a dataset of $^{26}$3 VCSEL aging samples collected under $^{26}$4 and controlled current $^{26}$5. The architecture fuses a GRU-attention sequence branch operating on $^{26}$6 with a branch for kurtosis $^{26}$7, skewness $^{26}$8, temperature $^{26}$9, and current $\bar\Lambda$00. The paper states explicitly that it does not present a separate explicit statistical correlation matrix or a formal linear-correlation analysis; the dependence is modeled implicitly through the deep network. Reported performance reaches a mean absolute error of about $\bar\Lambda$01 years, with improvements over localized models of $\bar\Lambda$02 in RMSE, $\bar\Lambda$03 in SDEV, and $\bar\Lambda$04 in MAE, and the federated model reaches the same MAE as the centralized model after about $\bar\Lambda$05 communication rounds (Abdelli et al., 2022).

In lithium-ion batteries, the correlations are made explicit. Using $\bar\Lambda$06 NMC/graphite pouch cells aged under varying charge rate, discharge rate, and depth of discharge, with end of life defined at $\bar\Lambda$07 mAh or $\bar\Lambda$08 of rated capacity, the study reports Pearson linear correlations with $\bar\Lambda$09 for early-life features extracted from periodic reference performance tests. The strongest reported feature is

$\bar\Lambda$10

with

$\bar\Lambda$11

The best condition-level feature is $\bar\Lambda$12 with $\bar\Lambda$13. Using no more than the first $\bar\Lambda$14 of data, the best in-distribution model achieves $\bar\Lambda$15 mean absolute percentage error, while a hierarchical Bayesian regression model improves extrapolation to $\bar\Lambda$16 mean absolute percentage error for out-of-distribution cells (Li et al., 2023).

A broader astrophysical analogue appears in planet population synthesis, where disk lifetime correlates with giant-planet outcomes. Longer-lived disks form giant planets more often and produce more massive giant planets, with the giant-planet occurrence in the nominal population fitted approximately as

$\bar\Lambda$17

For planets ending as giants, the migration extent $\bar\Lambda$18 shifts in the bulk from about $\bar\Lambda$19 AU for the shortest lifetimes that still form giants to about $\bar\Lambda$20 AU at $\bar\Lambda$21 Myr. The paper also stresses that the apparent lifetime trend is amplified by a built-in disk mass–lifetime correlation in the nominal population (Mordasini et al., 2012).

A financial analogue uses the “Life Time of Correlation” between stock prices, defined as the length of time during which the correlation coefficient $\bar\Lambda$22 is permanently on the strong level. This is a threshold-based duration statistic rather than decay-time covariance. Across DJIA, DAX, FTSE 100, and WIG 20, the paper concludes that it is reasonable to use at least $\bar\Lambda$23 or $\bar\Lambda$24 months of recent data to estimate correlations efficiently, and states that the mean lifetime of correlations inside the WIG portfolio is not bigger than $\bar\Lambda$25 trading days (Buda, 2011).

Taken together, these studies show that once “absolute lifetime” is adopted as the target variable, the correlation concept splits into at least three technical classes: direct time-domain dependence between two decay times, dependence of an absolute estimate on a calibration lifetime, and dependence of a lifetime target on covariates. The common feature is not a shared estimator, but a shared insistence that the lifetime itself, rather than a purely relative proxy, is the object being correlated.