Pair-Wise Lifetime Correlator

• Pair-Wise Lifetime Correlator is a two-particle statistical observable designed to test for non-factorized decay-time correlations in entangled particles like Λ-Λ̄ pairs.
• It extends traditional spin-entanglement analysis into the time domain by correlating reconstructed decay times with spin-sensitive kinematic data.
• The method employs both relative and absolute lifetime correlators with mixed-event baselines and permutation tests to robustly isolate genuine temporal entanglement signals.

Searching arXiv for papers relevant to "pair-wise lifetime correlator" and adjacent usages of lifetime/pair-correlation terminology. A pair-wise lifetime correlator is a two-particle statistical observable designed to test whether the decay times of a pair carry nontrivial correlation beyond the factorized law expected for independent unstable particles. In the most explicit recent formulation, it is proposed for entangled $\Lambda$-$\bar{\Lambda}$ pairs produced in high-energy collisions, where the established spin-entanglement observable is extended into the time domain by correlating reconstructed decay times with spin-sensitive decay kinematics (Tang, 24 Jul 2025). In that setting, the central question is whether the joint decay-time structure remains compatible with $P_0(t_1,t_2)=P(t_1)P(t_2)$, or whether a pair-wise lifetime correlator reveals a non-factorized temporal sector aligned with known spin correlations. More broadly, the term connects to a family of pair-based correlation constructions in which a lifetime, survival time, or persistence interval is treated as the dynamical quantity of interest rather than a purely geometric or angular separation (Tang, 24 Jul 2025, Gudla et al., 2021, Hammond et al., 2011).

1. Definition in the context of entangled hyperon pairs

The most direct use of the pair-wise lifetime correlator appears in the proposal to probe spin-lifetime correlations in entangled $\Lambda$-$\bar{\Lambda}$ pairs (Tang, 24 Jul 2025). The physical setup is based on systems such as

$e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$

or on hadronic production at RHIC/LHC, with weak self-analyzing decays

$$\Lambda \to p + \pi^-, \qquad \bar{\Lambda} \to \bar{p} + \pi^+.$$

For each pair, the decay time is reconstructed from decay length and momentum via

$t = \frac{L\,m_\Lambda}{|\mathbf p|c}.$

The conceptual point is that standard hyperon entanglement measurements have focused on angular observables, whereas the proposed pair-wise lifetime correlator asks whether the decay times $t_1$ and $t_2$ themselves exhibit correlation (Tang, 24 Jul 2025). For independent unstable particles, the joint probability factorizes: $\bar{\Lambda}$0 and therefore the lifetime covariance vanishes. For an entangled pair, however, the paper writes a non-factorized survival amplitude

$\bar{\Lambda}$1

with joint decay probability

$\bar{\Lambda}$2

This is the formal location at which a pair-wise lifetime correlator can become nonzero (Tang, 24 Jul 2025).

The associated spin observable is the familiar opening-angle distribution

$\bar{\Lambda}$3

where $\bar{\Lambda}$4 is the fitted spin-correlation coefficient. The proposal does not replace this observable; it extends it by making the spin-correlation analysis sensitive to the temporal sector (Tang, 24 Jul 2025).

2. Construction of the correlator and associated observables

The construction begins from a per-pair spin weight

$\bar{\Lambda}$5

for which

$\bar{\Lambda}$6

in an isotropic uncorrelated sample (Tang, 24 Jul 2025). Acceptance and efficiency are handled with a mixed-event baseline using same-event and mixed-event counts,

$\bar{\Lambda}$7

and the acceptance-corrected joint distribution

$\bar{\Lambda}$8

This ratio is the basic object from which the lifetime tests are built (Tang, 24 Jul 2025).

Two complementary tests are then defined. The first is a relative lifetime correlation test, which bins in $\bar{\Lambda}$9 and fits, in each bin,

$P_0(t_1,t_2)=P(t_1)P(t_2)$0

Under the null hypothesis of independent exponential decays, $P_0(t_1,t_2)=P(t_1)P(t_2)$1 should be constant. Deviation from constancy is quantified by

$P_0(t_1,t_2)=P(t_1)P(t_2)$2

to be compared with a $P_0(t_1,t_2)=P(t_1)P(t_2)$3 distribution (Tang, 24 Jul 2025).

The second is the absolute lifetime correlation test, which defines a standardized spin weight

$P_0(t_1,t_2)=P(t_1)P(t_2)$4

and a centered lifetime product

$P_0(t_1,t_2)=P(t_1)P(t_2)$5

The same-event and mixed-event weighted correlators are then

$P_0(t_1,t_2)=P(t_1)P(t_2)$6

with mixed-event-subtracted signal

$P_0(t_1,t_2)=P(t_1)P(t_2)$7

This $P_0(t_1,t_2)=P(t_1)P(t_2)$8 is the most direct implementation of the pair-wise lifetime correlator in the paper’s terminology (Tang, 24 Jul 2025).

The paper also emphasizes a simpler baseline observable,

$P_0(t_1,t_2)=P(t_1)P(t_2)$9

By construction, this vanishes when the joint distribution factorizes. The refined correlators are introduced because a plain covariance can miss $\Lambda$0-dependent or spin-weighted structures (Tang, 24 Jul 2025).

3. Statistical interpretation and null-hypothesis structure

The pair-wise lifetime correlator is explicitly framed as a test against independent exponential decay (Tang, 24 Jul 2025). For a single unstable particle, the survival law is

$\Lambda$1

with decay-time density

$\Lambda$2

If both particles decay independently, then

$\Lambda$3

and no lifetime covariance or spin-weighted lifetime correlator should remain after proper baseline subtraction (Tang, 24 Jul 2025).

In the relative-time test, the null expectation is a flat $\Lambda$4. In the absolute-time test, the null expectation is a non-significant $\Lambda$5. Because $\Lambda$6 does not have a simple analytic null distribution, the paper proposes a permutation procedure: shuffle the spin weights among the lifetimes within the same-event sample,

$\Lambda$7

and estimate the $\Lambda$8-value from the fraction of shuffled trials satisfying

$\Lambda$9

This makes the correlator operationally data-driven rather than model-dependent (Tang, 24 Jul 2025).

A nontrivial signal is defined as any of the following: a non-flat $\bar{\Lambda}$0, a significant nonzero $\bar{\Lambda}$1, or a nonzero lifetime covariance. The most stringent interpretation would be a lifetime correlation that tracks the same entanglement structure already seen in spin observables (Tang, 24 Jul 2025). This suggests that the pair-wise lifetime correlator is not merely a measure of joint timing fluctuations, but a targeted probe of whether temporal statistics align with an already established spin-entangled state.

4. Relation to established spin-correlation measurements

The pair-wise lifetime correlator is methodologically anchored in the established spin-entanglement analysis of $\bar{\Lambda}$2-$\bar{\Lambda}$3 decays (Tang, 24 Jul 2025). The angular distribution

$\bar{\Lambda}$4

already tests whether the pair is spin-entangled. The new proposal asks whether this same entanglement has a temporal signature. The logical structure is therefore layered: the spin observable establishes entanglement in the angular sector; the lifetime correlator asks whether the decay-time sector also departs from the factorized law (Tang, 24 Jul 2025).

This relation is important because the lifetime correlator is not defined as a standalone lifetime statistic divorced from pair kinematics. Its most refined form uses the spin weight $\bar{\Lambda}$5 and its standardized version $\bar{\Lambda}$6, so the correlator is explicitly spin-weighted (Tang, 24 Jul 2025). The implication is that the correlator is designed to discriminate a generic timing correlation from one that is specifically aligned with the entangled two-body structure.

A plausible implication is that this construction is closer in spirit to correlation spectroscopy than to ordinary lifetime fitting. In optical-clock correlation spectroscopy, correlated observables are constructed so that a common-mode nuisance cancels and the remaining signal reflects a pairwise phase or lifetime limit (Clements et al., 2020). That work does not define a “pair-wise lifetime correlator” by name, but it does use a two-system parity observable,

$\bar{\Lambda}$7

whose contrast becomes lifetime-limited through

$\bar{\Lambda}$8

for two synchronously interrogated $\bar{\Lambda}$9 clocks (Clements et al., 2020). This suggests a broader methodological affinity: pairwise observables can be engineered so that the relevant dynamical timescale appears in a correlated two-body channel rather than in separate one-body fits.

5. Conceptual boundaries, significance, and controversy

The proposed pair-wise lifetime correlator is explicitly speculative in its physical implications (Tang, 24 Jul 2025). The paper states that successful observation of lifetime correlations between entangled partners would require a fundamental revision of quantum mechanics’ framework for entanglement, extending the concept beyond its current theoretical boundaries. This is not presented as an established phenomenon but as a sharply formulated test.

The significance attributed to a nonzero result is fourfold in the paper’s framing: it would constitute the first direct evidence of time-domain entanglement in unstable hadrons; it would show that entanglement can influence not just angular distributions but also decay dynamics; it would constrain or challenge decoherence and wavefunction-collapse models; and it would broaden entanglement studies in particle physics beyond spin and flavor into the dynamics of decay times themselves (Tang, 24 Jul 2025).

At the same time, the null model is simple and stringent. Independent exponential decay predicts vanishing covariance and no mixed-event-subtracted signal. The proposal is therefore not based on an incremental modification of standard lifetime fitting, but on a binary distinction between factorized and non-factorized time-domain behavior (Tang, 24 Jul 2025). A common misconception would be to treat the correlator as merely another way of fitting two lifetimes; the proposal instead treats each decay as a quantum measurement acting on a shared joint wavefunction.

Another potential misconception is that any nonzero covariance would automatically imply entanglement. The paper is more careful: mixed-event baselines and permutation tests are introduced precisely to remove acceptance-related and trivial statistical structures (Tang, 24 Jul 2025). This indicates that the pair-wise lifetime correlator is intended as a residual correlation observable after standard experimental baselines have been subtracted.

6. Broader meanings of pairwise lifetime and survival correlators

Although the hyperon proposal provides the most literal instance of a pair-wise lifetime correlator, related constructions appear in other domains where the basic object is a pair survival, residence, or persistence function. In polymer electrolytes, ion pairing is treated as a dynamical phenomenon, and the relevant observable is a pair residence or survival correlation function

$e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$0

which measures the probability that a cation-anion pair associated at $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$1 remains associated after time $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$2 (Gudla et al., 2021). The extracted lifetime $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$3 then governs the relation between ion-pair kinetics and the cation-anion distinct conductivity. This is not a quantum-entanglement observable, but it is a genuine pairwise lifetime correlation function in the sense that the elementary object is the temporal persistence of a pair (Gudla et al., 2021).

In Markov-process theory, a related link appears between pairwise decorrelation and the survival or “continual occurrence” event

$e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$4

with pairwise correlation of the event $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$5 defined by

$e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$6

The main result is that pairwise decorrelation implies decay of the probability of remaining in $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$7 throughout an interval (Hammond et al., 2011). Here the object is not a pair of particles but a single event observed at two times; nevertheless, it shows a close structural relation between two-point correlation functions and lifetime or exit-time tails.

These examples clarify the semantic range of the term. In some settings, a pair-wise lifetime correlator means a correlator of two reconstructed decay times for a particle pair (Tang, 24 Jul 2025). In others, it denotes a pair survival function for two constituents that remain associated over time (Gudla et al., 2021). In still others, it links two-time correlation to persistence probabilities (Hammond et al., 2011). The shared feature is that the correlator encodes a dynamical timescale through a pair-based statistical object rather than through a single-particle lifetime distribution alone.

7. Prospects and methodological implications

The hyperon proposal situates the pair-wise lifetime correlator within data-driven collider analysis. The required ingredients are already standard in entangled hyperon studies: reconstruction of decay products, extraction of $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$8, decay-time reconstruction from flight distance and momentum, same-event and mixed-event pairing, and binned or permutation-based significance testing (Tang, 24 Jul 2025). What is new is the coupling of these ingredients into observables that interrogate the temporal sector.

A plausible implication is that the most robust implementation will be one in which the correlator is examined simultaneously in unweighted, $e^+e^- \to J/\psi \to \Lambda\bar{\Lambda},$9-binned, and spin-weighted forms. The paper already organizes the search in exactly that hierarchy: lifetime covariance as the simplest model-independent statistic, $$\Lambda \to p + \pi^-, \qquad \bar{\Lambda} \to \bar{p} + \pi^+.$$0 as the relative-time test, and $$\Lambda \to p + \pi^-, \qquad \bar{\Lambda} \to \bar{p} + \pi^+.$$1 as the absolute-time spin-weighted correlator (Tang, 24 Jul 2025). This layered structure is methodologically significant because it distinguishes generic lifetime correlation from one that aligns with the known entanglement channel.

The broader significance of the concept lies in the extension of correlation analysis from geometry to dynamics. In hyperon entanglement, the traditional observables are angular; in polymer electrolytes, the distinction between thermodynamic and dynamical pairing depends on pair survival; in Markov persistence, pairwise decorrelation constrains exit-time tails (Tang, 24 Jul 2025, Gudla et al., 2021, Hammond et al., 2011). Across these settings, the pair-wise lifetime correlator is best understood as a technical device for asking whether a two-body or two-time structure leaves a measurable imprint on temporal statistics, and whether that imprint persists after baseline subtraction and null-hypothesis control.