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arXiv:2607.12015

Decoherence and More Coherence in the Radiative Decay of the $Z$ Boson

Kun Cheng, Tao Han, Harman Singh, Youle Su

hep-phhep-exquant-phSubmitted Jul 13, 2026• Announced Jul 15, 2026• 0 citations
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Abstract

Final state radiation in collider processes can be interpreted as interactions with unobserved degrees of freedom and is often discussed within the context of decoherence of an entangled state. We consider the radiative decay of the $Z$ boson as a representative example and perform a detailed analytical study of the $τ^-τ^+γ$ spin state, as determined by the chiral interactions of the Standard Model, over the complete three-body phase space. We explore various quantum information observables to quantify how the $τ^-τ^+$ spin state changes with the photon radiation. We find some striking features, for example that the emitted photon could either lead to decoherence or monotonic enhancement of entanglement for the fermion pair.

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Decoherence and More Coherence in the Radiative Decay of the ZZZ Boson
Final state radiation in collider processes can be interpreted as interactions with unobserved degrees of freedom and is often discussed within the context of decoherence of an entangled state. We consider the radiative decay of the ZZZ boson as a representative example and perform a detailed analytical study of the τ−τ+γτ^-τ^+γτ−τ+γ spin state, as determined by the chiral interactions of the Standard Model, over the complete three-body phase space. We explore various quantum information observables to quantify how the τ−τ+τ^-τ^+τ−τ+ spin state changes with the photon radiation. We find some striking features, for example that the emitted photon could either lead to decoherence or monotonic enhancement of entanglement for the fermion pair.
Recent measurements at the Large Hadron Collider have observed entanglement in the spins of t t ¯ pairs. The effects of radiation, which are expected to lead to quantum decoherence and a reduction of entanglement, are generally neglected in such measurements. In this work we calculate the effects of decoherence from various different types of radiation for a maximally entangled pair of fermions—a bipartite system of qubits in a Bell state. We identify the Kraus operators describing the evolution of the open quantum system with the integrated Altarelli-Parisi splitting functions.
We study the impact of radiation on quantum systems defined by the spins of elementary fermion-antifermion pairs produced at colliders. We present predictions for several processes, showing that energetic final-state radiation can induce decoherence and significantly reduce the entanglement of quantum systems formed by elementary fermion pairs. We investigate the feasibility of observing this effect experimentally in exclusive samples with energetic radiation. A statistically significant signal can be obtained with current data in associated pp→ttˉ(g)pp \rightarrow t\bar{t}(g)pp→ttˉ(g) production at the LHC and in e+e−→τ+τ−(γ)e^+e^- \rightarrow τ^{+}τ^{-}(γ)e+e−→τ+τ−(γ) production at Belle 2. Future electron-positron colliders operated at the ZZZ pole or well above the ttˉt\bar{t}ttˉ production threshold will extend these prospects further.
Momentum entanglement at colliders: the H→WW,ZZH \to WW,ZZH→WW,ZZ case
We address momentum entanglement in Higgs decays to weak boson pairs, H→WW,ZZH \to WW,ZZH→WW,ZZ, by discretising momentum space. The momenta of the two weak bosons are entangled, as well as the degrees of freedom in momentum and spin spaces. For H→ZZH \to ZZH→ZZ in the four-lepton final state, we also estimate the statistical sensitivity of entanglement measures at the Large Hadron Collider and future upgrades. The discretisation method introduced here is broadly applicable, offering a framework for studies of momentum entanglement at the energy frontier.
Abstract In this article, we study quantum entanglement properties of the three-body H→γllˉH\rightarrow \gamma l{\bar{l}}H→γllˉ H → γ l l ¯ decays (for l=e,μ,τl=e,\mu ,\tau l=e,μ,τ l = e , μ , τ ) within the context of the Standard Model augmented with CP-violating interactions in the lepton Yukawa sector. Our aim is to elucidate the distribution of entanglement between the final photon, lepton and antilepton across the phase-space. These rare Higgs boson decays occur at 1-loop level, presenting a unique opportunity to scrutinize quantum correlations of fundamental interactions in tripartite systems by computing concurrence measures and investigating Bell non-locality. Moreover, we explore post-decay and autodistillation phenomena. Multipartite entanglement measures have much richer structure than those in the bipartite case, thus deserve more attention in collider phenomenology. In this line, we analyze here novel observables for these three-body Higgs boson decays, which can be extended to other multiparticle systems within the high-energy regime. We found that entanglement manifests among final particles, occasionally achieving a maximally entangled state in specific kinematical configurations. Also, these decay channels are promising for Bell non-locality tests but CP-effects are suppressed by lepton masses in this kind of observables.
We present a comprehensive theoretical framework for probing quantum entanglement in the decay angular distributions of a spin-SSS particle-antiparticle pair AAˉA\bar{A}AAˉ, where each particle decays sequentially into a two-body final state, A→B+CA\to B+CA→B+C and Aˉ→Bˉ+Cˉ\bar{A}\to\bar{B}+\bar{C}Aˉ→Bˉ+Cˉ, with B(Bˉ)B(\bar{B})B(Bˉ) carrying spin bbb and C(Cˉ)C(\bar{C})C(Cˉ) being spinless. Starting from the most general polarized initial state, we derive the fully differential angular distribution W(θ1,θ2,ϕ1,ϕ2)\mathcal{W}(θ_1,θ_2,ϕ_1,ϕ_2)W(θ1​,θ2​,ϕ1​,ϕ2​) and identify observables ⟨cos⁡(2S(ϕ1∓ϕ2))⟩\langle\cos(2S(ϕ_1\mpϕ_2))\rangle⟨cos(2S(ϕ1​∓ϕ2​))⟩ whose expectation values directly depend on the entanglement-sensitive coefficients Re(α−S,∓SαS,±S∗)\text{Re}\left(α_{-S,\mp S}α_{S,\pm S}^*\right)Re(α−S,∓S​αS,±S∗​) of the initial state. The proportionality factor C(S,b)\mathcal{C}(S,b)C(S,b) in these relations is computed explicitly. For bosonic decays (b=0,1,2,…b=0,1,2,\ldotsb=0,1,2,…), C(S,b)\mathcal{C}(S,b)C(S,b) is universal and independent of decay dynamics; in particular, C(S,0)=1/2\mathcal{C}(S,0)=1/2C(S,0)=1/2 for any SSS, and C(1,1)=1/8\mathcal{C}(1,1)=1/8C(1,1)=1/8, matching known results for W+W−W^+W^-W+W− decays. For fermionic decays (b=12,32,52…b=\frac{1}{2},\frac{3}{2},\frac{5}{2}\ldotsb=21​,23​,25​…), C(S,b)\mathcal{C}(S,b)C(S,b) depends explicitly on the spin analysis powers αA/Aˉα_{A/\bar{A}}αA/Aˉ​, making entanglement extraction more decay-dependent. We further demonstrate, within the context of e+e−→γ∗→AAˉe^+e^-\toγ^*\to A\bar{A}e+e−→γ∗→AAˉ production, how αA/Aˉα_{A/\bar{A}}αA/Aˉ​ can be determined experimentally using specific angular observables restricted to the beam-axis region. Our results highlight the special role of bosonic decays in providing clean, model-independent tests of quantum entanglement at colliders, while outlining a pathway for entanglement measurement in fermionic cases through supplementary polarization information.
In this article, we study quantum entanglement properties of the three-body H→γllˉH\toγl\bar{l}H→γllˉ decays (for l=e,μ,τl=e,μ,τl=e,μ,τ) within the context of the Standard Model augmented with CP-violating interactions in the lepton Yukawa sector. Our aim is to elucidate the distribution of entanglement between the final photon, lepton and antilepton across the phase-space. These rare Higgs boson decays occur at 1-loop level, presenting a unique opportunity to scrutinize quantum correlations of fundamental interactions in tripartite systems by computing concurrence measures and investigating Bell non-locality. Moreover, we explore post-decay and autodistillation phenomena. Multipartite entanglement measures have much richer structure than those in the bipartite case, thus deserve more attention in collider phenomenology. In this line, we analyze here novel observables for these three-body Higgs boson decays, which can be extended to other multiparticle systems within the high-energy regime. We found that entanglement manifests among final particles, occasionally achieving a maximally entangled state in specific kinematical configurations. Also, these decay channels are promising for Bell non-locality tests but CP-effects are suppressed by lepton masses in this kind of observables.