Studies of Quantum Entanglement in the $\Upsilon(4S) \to B^0 \bar{B}^0$ system at Belle II using $B^0 \to D^{(*)-}\pi^+$ decays

M. Hattenbach

Published Apr 1, 2025• 0 citations

Abstract

This thesis presents a study of quantum entanglement in the $\Upsilon(4S) \to B^0⁢\bar{B}^0$ system using the hadronic $B^0 \to D^{(∗)-}\pi^+$. As it is the first study of such kind at Belle II, this work is focused on establishing an analysis framework, which enables testing disentanglement in hadronic $B^0$ modes. A novel event generator model has been implemented within basf2 to create a Signal MC samples with 1 Mio. $B\bar{B}$ events, corresponding to an integrated luminosity of 1 ab^-1 which are reconstructed in $B^0 \to D^{(*)-}\pi^+$ decays. The model of partial spontaneous disentanglement is implemented, where a fraction $\zeta$ of $B^0⁢\bar{B}^0$ pairs disentangle right at production. The implementation is proven to be successful, as the model is sensitive to such entanglement effects. Fits to $\Delta t$ distributions for different values of $\zeta_{gen}$ in Signal MC samples return consistently the correct values for free parameter $\zeta$ within uncertainties. A subsequent Toy Monte Carlo study once more shows the model's and fitting processes' suitability for disentanglement studies, although some biased behavior for parameter $\zeta$ could not be fully resolved. However, this thesis provides a proof-of-concept for future probes of entanglement at Belle II. The question, whether unaccounted disentanglement effects introduce a bias in time-dependent CP violation measurements at Belle II is answered. Such effects in the region of $\zeta \sim O(1-10\%)$ is absorbed in form of a bias of 1-2% in wrong tag parameters. However, slight biases in these parameters do in general not translate to a shift in parameters ACP and SCP, thus the worry of an unaccounted systematic effect is for now mitigated.

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Entanglement studies with Belle Upsilon(5S) Monte Carlo data

V. Geier

Nov 1, 20250 citations

Study of Quantum Decoherence in Neutral B Meson pairs produced at the $\Upsilon(5S)$ Resonance

Louise Beriet

Jan 1, 20260 citations

Probing entanglement and testing Bell inequality violation with $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at Belle II

K. Ehatäht, Marco E. Fabbrichesi, Luca Marzola +1 more

arXiv:2311.17555Nov 29, 20230 citations

Entanglement and Coherence at Belle II

E. Nogueira

Dec 15, 20250 citations

Quantum entanglement and Bell inequality violation in semi-leptonic top decays

Tao Han, Matthew Low, Tong Arthur Wu

A bstract Quantum entanglement is a fundamental property of quantum mechanics. Recently, studies have explored entanglement in the $$ t\overline{t} $$ t t ¯ system at the Large Hadron Collider (LHC) when both the top quark and anti-top quark decay leptonically. Entanglement is detected via correlations between the polarizations of the top and anti-top and these polarizations are measured through the angles of the decay products of the top and anti-top. In this work, we propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b -flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel. In 139 fb − 1 (3 ab −1 ) of data at the LHC (HL-LHC), it should be feasible to measure entanglement at a precision of ≲ 3% (0 . 7%). Detecting Bell inequality violation, on the other hand, is more challenging. With 300 fb −1 (3 ab −1 ) of integrated luminosity at the LHC Run-3 (HL-LHC), we expect a sensitivity of 1 . 3 σ (4 . 1 σ ). In our study, we utilize a realistic parametric fitting procedure to optimally recover the true angular distributions from detector effects. Compared to unfolding this procedure yields more stable results.

arXiv:2310.17696Journal of High Energy PhysicsJul 22, 202457 citations

Probing entanglement and testing Bell inequality violation with e+e−→τ+τ− at Belle II

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Studies of Quantum Entanglement in the $\Upsilon(4S) \to B^0 \bar{B}^0$ system at Belle II using $B^0 \to D^{()-}\pi^+$ decaysStudies of Quantum Entanglement in the $\Upsilon(4S) \to B^0 \bar{B}^0$ system at Belle II using $B^0 \to D^{()-}\pi^+$ decays

M. Hattenbach

Published Apr 1, 2025• 0 citations

OpenAlex

Abstract

This thesis presents a study of quantum entanglement in the

\Upsilon(4S) \to B^0⁢\bar{B}^0

system using the hadronic

B^0 \to D^{(∗)-}\pi^+

. As it is the first study of such kind at Belle II, this work is focused on establishing an analysis framework, which enables testing disentanglement in hadronic

B^0

modes. A novel event generator model has been implemented within basf2 to create a Signal MC samples with 1 Mio.

B\bar{B}

events, corresponding to an integrated luminosity of 1 ab^-1 which are reconstructed in

B^0 \to D^{(*)-}\pi^+

decays. The model of partial spontaneous disentanglement is implemented, where a fraction

\zeta

B^0⁢\bar{B}^0

pairs disentangle right at production. The implementation is proven to be successful, as the model is sensitive to such entanglement effects. Fits to

\Delta t

distributions for different values of

\zeta_{gen}

in Signal MC samples return consistently the correct values for free parameter

\zeta

within uncertainties. A subsequent Toy Monte Carlo study once more shows the model's and fitting processes' suitability for disentanglement studies, although some biased behavior for parameter

\zeta

could not be fully resolved. However, this thesis provides a proof-of-concept for future probes of entanglement at Belle II. The question, whether unaccounted disentanglement effects introduce a bias in time-dependent CP violation measurements at Belle II is answered. Such effects in the region of

\zeta \sim O(1-10\%)

is absorbed in form of a bias of 1-2% in wrong tag parameters. However, slight biases in these parameters do in general not translate to a shift in parameters ACP and SCP, thus the worry of an unaccounted systematic effect is for now mitigated.

Related papers

Entanglement studies with Belle Upsilon(5S) Monte Carlo data

V. Geier

In this work, we study the entanglement of the B mesons produced in Upsilon(5S) decays into the final states each with C = ±1 eigenvalue Upsilon(5S) to B0B0-bar (C = -1), Upsilon(5S) to B0B0-bar* + c.c. (C = +1), Upsilon(5S) to B0*B0-bar* (C = -1). For this purpose, we use Belle Monte Carlo data. The B mesons are reconstructed from hadronic decays: B0 to D-pi+, with D- to K+pi-pi- B0 to D*-pi+, with D*- to D0-bar pi_s- and D0-bar to K+pi-, B0 to D*-pi+, with D*- to D0-bar pi_s- and D0-bar to K+pi-pi+pi-. We then determine the decay–time difference of the B meson pairs to investigate the time depen- dence of their quantum entanglement. Since an entanglement analysis has never been performed for Upsilon(5S) decays, this thesis establishes the foundation for such a study. This includes deriving the theoretical framework of entanglement at the Upsilon(5S), performing the necessary kinematic consider- ations for the decaytime calculation, and developing new time and flavor variables for the analysis, since the Belle II software framework is only partially applicable to the Upsilon(5S)) case. In addition, we generate Signal Monte Carlo samples of 1 x 10^6 B0(*)B0-bar(*) events to increase statistical precision. In the Upsilon(5S) system, it is possible to obtain two different types of entanglement. When these two types are mixed, one obtains a disentangled state, with the degree of disentanglement being equal to the mixing ratio of the two entangled states. By applying the model of partial spontaneous disentanglement (PSD), which introduces a fraction zeta, we can measure this disentanglement frac- tion when mixing the states and thereby validate the theoretical prediction. To achieve this, we implemented the PSD framework for the Upsilon(5S) case. We verified that, when mixing the two en- tangled states in equal proportions, the expected disentanglement fraction of 100% is successfully reproduced.In this work, we study the entanglement of the B mesons produced in Upsilon(5S) decays into the final states each with C = ±1 eigenvalue Upsilon(5S) to B0B0-bar (C = -1), Upsilon(5S) to B0B0-bar* + c.c. (C = +1), Upsilon(5S) to B0*B0-bar* (C = -1). For this purpose, we use Belle Monte Carlo data. The B mesons are reconstructed from hadronic decays: B0 to D-pi+, with D- to K+pi-pi- B0 to D*-pi+, with D*- to D0-bar pi_s- and D0-bar to K+pi-, B0 to D*-pi+, with D*- to D0-bar pi_s- and D0-bar to K+pi-pi+pi-. We then determine the decay–time difference of the B meson pairs to investigate the time depen- dence of their quantum entanglement. Since an entanglement analysis has never been performed for Upsilon(5S) decays, this thesis establishes the foundation for such a study. This includes deriving the theoretical framework of entanglement at the Upsilon(5S), performing the necessary kinematic consider- ations for the decaytime calculation, and developing new time and flavor variables for the analysis, since the Belle II software framework is only partially applicable to the Upsilon(5S)) case. In addition, we generate Signal Monte Carlo samples of 1 x 10^6 B0(*)B0-bar(*) events to increase statistical precision. In the Upsilon(5S) system, it is possible to obtain two different types of entanglement. When these two types are mixed, one obtains a disentangled state, with the degree of disentanglement being equal to the mixing ratio of the two entangled states. By applying the model of partial spontaneous disentanglement (PSD), which introduces a fraction zeta, we can measure this disentanglement frac- tion when mixing the states and thereby validate the theoretical prediction. To achieve this, we implemented the PSD framework for the Upsilon(5S) case. We verified that, when mixing the two en- tangled states in equal proportions, the expected disentanglement fraction of 100% is successfully reproduced.

Nov 1, 20250 citations

Study of Quantum Decoherence in Neutral B Meson pairs produced at the $\Upsilon(5S)$ ResonanceStudy of Quantum Decoherence in Neutral B Meson pairs produced at the $\Upsilon(5S)$ Resonance

Louise Beriet

This thesis presents the development and validation of an analysis framework to study quantum decoherence in neutral B-meson pairs produced at the $\Upsilon(5S)$ resonance, using Monte Carlo simulated data from the Belle experiment. Unlike the $\Upsilon(4S)$ , the $\Upsilon(5S)$ provides access to both antisymmetric ( $C=-1$ ) and symmetric ( $C=+1$ ) quantum states through the channels $B^0\bar{B}^0$ , $B^{0*}\bar{B}^0+c.c.$ , and $B^{0*}\bar{B}^{0*}$ . Decoherence effects are studied with the Partial Spontaneous Disentanglement model, which introduces a fraction $\zeta$ of $B^{0*}\bar{B}^{*0}$ pairs disentangled at production. The analysis exploits the decay times of both neutral B mesons, for which time-dependent probability density functions are derived and extended to include detector-resolution effects. The framework is first validated on Signal Monte Carlo samples, where one-dimensional fits to $\Sigma t$ successfully recover the expected decoherence values for both entangled and disentangled configurations. Fits to Generic Monte Carlo samples, which include realistic backgrounds and event compositions, reveal strong correlations between the decoherence parameter and flavour-tagging wrong-tag fractions, particularly in the $C=-1$ channels. The results from these fits show significant deviations from expected $\zeta$ values and large uncertainties. Pure Toy Monte Carlo studies confirm that the fitter behaves linearly with respect to the injected decoherence parameter and show only small biases consistent with those observed in the nominal fits, but too small to fully explain them. To address the limitations of the single fits, a two-dimensional analysis in $(\Delta t,\Sigma t)$ is developed. By exploiting the full time-dependent information, the two-dimensional fit significantly reduces the statistical uncertainty on the decoherence parameter from $\sim\mathcal{O}(10\%)$ to $\sim\mathcal{O}(4\%)$ and mitigates correlations with the flavour-tagging parameters. This work constitutes a proof of concept for future analyses on Belle data and demonstrates the potential of the $\Upsilon(5S)$ system for studying quantum entanglement and decoherence in neutral B mesons.This thesis presents the development and validation of an analysis framework to study quantum decoherence in neutral B-meson pairs produced at the $\Upsilon(5S)$ resonance, using Monte Carlo simulated data from the Belle experiment. Unlike the $\Upsilon(4S)$, the $\Upsilon(5S)$ provides access to both antisymmetric ($C=-1$) and symmetric ($C=+1$) quantum states through the channels $B^0\bar{B}^0$, $B^{0*}\bar{B}^0+c.c.$, and $B^{0*}\bar{B}^{0*}$. Decoherence effects are studied with the Partial Spontaneous Disentanglement model, which introduces a fraction $\zeta$ of $B^{0*}\bar{B}^{*0}$ pairs disentangled at production. The analysis exploits the decay times of both neutral B mesons, for which time-dependent probability density functions are derived and extended to include detector-resolution effects. The framework is first validated on Signal Monte Carlo samples, where one-dimensional fits to $\Sigma t$ successfully recover the expected decoherence values for both entangled and disentangled configurations. Fits to Generic Monte Carlo samples, which include realistic backgrounds and event compositions, reveal strong correlations between the decoherence parameter and flavour-tagging wrong-tag fractions, particularly in the $C=-1$ channels. The results from these fits show significant deviations from expected $\zeta$ values and large uncertainties. Pure Toy Monte Carlo studies confirm that the fitter behaves linearly with respect to the injected decoherence parameter and show only small biases consistent with those observed in the nominal fits, but too small to fully explain them. To address the limitations of the single fits, a two-dimensional analysis in $(\Delta t,\Sigma t)$ is developed. By exploiting the full time-dependent information, the two-dimensional fit significantly reduces the statistical uncertainty on the decoherence parameter from $\sim\mathcal{O}(10\%)$ to $\sim\mathcal{O}(4\%)$ and mitigates correlations with the flavour-tagging parameters. This work constitutes a proof of concept for future analyses on Belle data and demonstrates the potential of the $\Upsilon(5S)$ system for studying quantum entanglement and decoherence in neutral B mesons.

Jan 1, 20260 citations

Probing entanglement and testing Bell inequality violation with $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at Belle IIProbing entanglement and testing Bell inequality violation with $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at Belle II

K. Ehatäht, Marco E. Fabbrichesi, Luca Marzola +1 more

We present a feasibility study to probe quantum entanglement and Belle inequality violation in the process $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at a center-of-mass energy of $\sqrt{s} = 10.579$ GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle $\vartheta$ in the $τ^{+}τ^{-}$ center-of-mass frame. We analyze events in which both $τ$ leptons decay to hadrons, using a combination of decay channels $τ^{-} \rightarrow π^{-}ν_τ$ , $τ^{-} \rightarrow π^{-}π^{0}ν_τ$ , and $τ^{-} \rightarrow π^{-}π^{+}π^{-}ν_τ$ . The spin orientation of the $τ$ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of $200$ million $τ^{+}τ^{-}$ events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations.We present a feasibility study to probe quantum entanglement and Belle inequality violation in the process $\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}$ at a center-of-mass energy of $\sqrt{s} = 10.579$ GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle $\vartheta$ in the $τ^{+}τ^{-}$ center-of-mass frame. We analyze events in which both $τ$ leptons decay to hadrons, using a combination of decay channels $τ^{-} \rightarrow π^{-}ν_τ$, $τ^{-} \rightarrow π^{-}π^{0}ν_τ$, and $τ^{-} \rightarrow π^{-}π^{+}π^{-}ν_τ$. The spin orientation of the $τ$ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of $200$ million $τ^{+}τ^{-}$ events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations.

arXiv:2311.17555Nov 29, 20230 citations

Entanglement and Coherence at Belle II

E. Nogueira

In this thesis we study the robustness of entanglement in the B0 meson pairs at the Belle II and if andhow different quantum states can be distinguished. The first objective is to quantitatively analyse the influence of CP violation and ∆Γ ̸= 0 on concurrence, which is used to measure entanglement, of the quantum states |ψ−⟩ =1/√2 (|B0B ̄0 − |B ̄0B0⟩⟩) and |ψ⟩ = 1/2 [(|B0B ̄0⟩ − |B ̄0B0⟩) + i(|B0B ̄0⟩ + |B ̄0B0⟩)]. For the first state it remains constanteven for CP violation but for the second it is possible to see the effects of the parameters in discussion. Furthermore we study scattering among the B mesons in vacuum, scattering with matter and finally radiative emission at Υ(5S), the first scenario is rather trivial due to the simplified assumptions, such as only strong/electromagnetic interactions. As result one observes no change in the concurrence, which is therefore concluded to be affected only by weak interaction (mixing). The second and third scenarios are investigated with the help of open quantum systems and for both the concurrence decreases after the application of the quantum channels built with Kraus operators. At the last part of the thesis the relations between entanglement and the measurement basis are studied introducing an arbitrary phase φ in the Bloch sphere representation. One finds that |ψ(φ)⟩ can violate CHSH or not depending on φ and the choice of the measurement basis. The distinction of states on the equator of the Bloch sphere is possible using the correlation function Ef1,f2(t1,t2) constructed for flavor and CP tags. Further it is also possible to distinguish entangled states of the family |ψ(φ)⟩ from some separable states also using the correlation function and choosing the flavor-CP tag. A distinction of any kind using only flavor tags on both arms of the correlation function is shown not to be possible. Finally we show that the CP-violating parameter Cf and Sf , used to measure CP violation, are biased if a wrong assumption on the nature of the quantum state is made.In this thesis we study the robustness of entanglement in the B0 meson pairs at the Belle II and if andhow different quantum states can be distinguished. The first objective is to quantitatively analyse the influence of CP violation and ∆Γ ̸= 0 on concurrence, which is used to measure entanglement, of the quantum states |ψ−⟩ =1/√2 (|B0B ̄0 − |B ̄0B0⟩⟩) and |ψ⟩ = 1/2 [(|B0B ̄0⟩ − |B ̄0B0⟩) + i(|B0B ̄0⟩ + |B ̄0B0⟩)]. For the first state it remains constanteven for CP violation but for the second it is possible to see the effects of the parameters in discussion. Furthermore we study scattering among the B mesons in vacuum, scattering with matter and finally radiative emission at Υ(5S), the first scenario is rather trivial due to the simplified assumptions, such as only strong/electromagnetic interactions. As result one observes no change in the concurrence, which is therefore concluded to be affected only by weak interaction (mixing). The second and third scenarios are investigated with the help of open quantum systems and for both the concurrence decreases after the application of the quantum channels built with Kraus operators. At the last part of the thesis the relations between entanglement and the measurement basis are studied introducing an arbitrary phase φ in the Bloch sphere representation. One finds that |ψ(φ)⟩ can violate CHSH or not depending on φ and the choice of the measurement basis. The distinction of states on the equator of the Bloch sphere is possible using the correlation function Ef1,f2(t1,t2) constructed for flavor and CP tags. Further it is also possible to distinguish entangled states of the family |ψ(φ)⟩ from some separable states also using the correlation function and choosing the flavor-CP tag. A distinction of any kind using only flavor tags on both arms of the correlation function is shown not to be possible. Finally we show that the CP-violating parameter Cf and Sf , used to measure CP violation, are biased if a wrong assumption on the nature of the quantum state is made.

Dec 15, 20250 citations

Quantum entanglement and Bell inequality violation in semi-leptonic top decays

Tao Han, Matthew Low, Tong Arthur Wu

A bstract Quantum entanglement is a fundamental property of quantum mechanics. Recently, studies have explored entanglement in the $t\overline{t}$ t t ¯ system at the Large Hadron Collider (LHC) when both the top quark and anti-top quark decay leptonically. Entanglement is detected via correlations between the polarizations of the top and anti-top and these polarizations are measured through the angles of the decay products of the top and anti-top. In this work, we propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b -flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel. In 139 fb − 1 (3 ab −1 ) of data at the LHC (HL-LHC), it should be feasible to measure entanglement at a precision of ≲ 3% (0 . 7%). Detecting Bell inequality violation, on the other hand, is more challenging. With 300 fb −1 (3 ab −1 ) of integrated luminosity at the LHC Run-3 (HL-LHC), we expect a sensitivity of 1 . 3 σ (4 . 1 σ ). In our study, we utilize a realistic parametric fitting procedure to optimally recover the true angular distributions from detector effects. Compared to unfolding this procedure yields more stable results.A bstract Quantum entanglement is a fundamental property of quantum mechanics. Recently, studies have explored entanglement in the $$ t\overline{t} $$ t t ¯ system at the Large Hadron Collider (LHC) when both the top quark and anti-top quark decay leptonically. Entanglement is detected via correlations between the polarizations of the top and anti-top and these polarizations are measured through the angles of the decay products of the top and anti-top. In this work, we propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b -flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel. In 139 fb − 1 (3 ab −1 ) of data at the LHC (HL-LHC), it should be feasible to measure entanglement at a precision of ≲ 3% (0 . 7%). Detecting Bell inequality violation, on the other hand, is more challenging. With 300 fb −1 (3 ab −1 ) of integrated luminosity at the LHC Run-3 (HL-LHC), we expect a sensitivity of 1 . 3 σ (4 . 1 σ ). In our study, we utilize a realistic parametric fitting procedure to optimally recover the true angular distributions from detector effects. Compared to unfolding this procedure yields more stable results.

arXiv:2310.17696Journal of High Energy PhysicsJul 22, 202457 citations

Probing entanglement and testing Bell inequality violation with e+e−→τ+τ− at Belle II

K. Ehatäht, Marco E. Fabbrichesi, Luca Marzola +1 more

We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process e+e−→τ+τ− at a center-of-mass energy of s=10.579 GeV . The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ in the τ+τ− center-of-mass frame. We analyze events in which both τ leptons decay to hadrons, using a combination of decay channels τ−→π−ντ , τ−→π−π0ντ , and τ−→π−π+π−ντ . The spin orientation of the τ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process e+e−→τ+τ− at a center-of-mass energy of s=10.579 GeV . The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ in the τ+τ− center-of-mass frame. We analyze events in which both τ leptons decay to hadrons, using a combination of decay channels τ−→π−ντ , τ−→π−π0ντ , and τ−→π−π+π−ντ . The spin orientation of the τ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024

Physical review. D/Physical review. D.Feb 12, 202453 citations

Studies of Quantum Entanglement in the

\Upsilon(4S) \to B^0 \bar{B}^0

system at Belle II using

B^0 \to D^{(*)-}\pi^+

decays

This thesis presents a study of quantum entanglement in the

\Upsilon(4S) \to B^0⁢\bar{B}^0

system using the hadronic

B^0 \to D^{(∗)-}\pi^+

. As it is the first study of such kind at Belle II, this work is focused on establishing an analysis framework, which enables testing disentanglement in hadronic

B^0

modes. A novel event generator model has been implemented within basf2 to create a Signal MC samples with 1 Mio.

B\bar{B}

events, corresponding to an integrated luminosity of 1 ab^-1 which are reconstructed in

B^0 \to D^{(*)-}\pi^+

decays. The model of partial spontaneous disentanglement is implemented, where a fraction

\zeta

B^0⁢\bar{B}^0

pairs disentangle right at production. The implementation is proven to be successful, as the model is sensitive to such entanglement effects. Fits to

\Delta t

distributions for different values of

\zeta_{gen}

in Signal MC samples return consistently the correct values for free parameter

\zeta

within uncertainties. A subsequent Toy Monte Carlo study once more shows the model's and fitting processes' suitability for disentanglement studies, although some biased behavior for parameter

\zeta

\zeta \sim O(1-10\%)

Study of Quantum Decoherence in Neutral B Meson pairs produced at the

\Upsilon(5S)

Resonance

This thesis presents the development and validation of an analysis framework to study quantum decoherence in neutral B-meson pairs produced at the

\Upsilon(5S)

resonance, using Monte Carlo simulated data from the Belle experiment. Unlike the

\Upsilon(4S)

, the

\Upsilon(5S)

provides access to both antisymmetric (

C=-1

) and symmetric (

C=+1

) quantum states through the channels

B^0\bar{B}^0

B^{0*}\bar{B}^0+c.c.

, and

B^{0*}\bar{B}^{0*}

. Decoherence effects are studied with the Partial Spontaneous Disentanglement model, which introduces a fraction

\zeta

B^{0*}\bar{B}^{*0}

pairs disentangled at production. The analysis exploits the decay times of both neutral B mesons, for which time-dependent probability density functions are derived and extended to include detector-resolution effects. The framework is first validated on Signal Monte Carlo samples, where one-dimensional fits to

\Sigma t

successfully recover the expected decoherence values for both entangled and disentangled configurations. Fits to Generic Monte Carlo samples, which include realistic backgrounds and event compositions, reveal strong correlations between the decoherence parameter and flavour-tagging wrong-tag fractions, particularly in the

C=-1

channels. The results from these fits show significant deviations from expected

\zeta

values and large uncertainties. Pure Toy Monte Carlo studies confirm that the fitter behaves linearly with respect to the injected decoherence parameter and show only small biases consistent with those observed in the nominal fits, but too small to fully explain them. To address the limitations of the single fits, a two-dimensional analysis in

(\Delta t,\Sigma t)

is developed. By exploiting the full time-dependent information, the two-dimensional fit significantly reduces the statistical uncertainty on the decoherence parameter from

\sim\mathcal{O}(10\%)

\sim\mathcal{O}(4\%)

and mitigates correlations with the flavour-tagging parameters. This work constitutes a proof of concept for future analyses on Belle data and demonstrates the potential of the

\Upsilon(5S)

system for studying quantum entanglement and decoherence in neutral B mesons.

Probing entanglement and testing Bell inequality violation with

\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}

at Belle II

We present a feasibility study to probe quantum entanglement and Belle inequality violation in the process

\textrm{e}^{+}\textrm{e}^{-} \rightarrow τ^{+}τ^{-}

at a center-of-mass energy of

\sqrt{s} = 10.579

GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle

\vartheta

in the

τ^{+}τ^{-}

center-of-mass frame. We analyze events in which both

τ

leptons decay to hadrons, using a combination of decay channels

τ^{-} \rightarrow π^{-}ν_τ

τ^{-} \rightarrow π^{-}π^{0}ν_τ

, and

τ^{-} \rightarrow π^{-}π^{+}π^{-}ν_τ

. The spin orientation of the

τ

leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of

200

million

τ^{+}τ^{-}

events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations.

A bstract Quantum entanglement is a fundamental property of quantum mechanics. Recently, studies have explored entanglement in the

t\overline{t}

t t ¯ system at the Large Hadron Collider (LHC) when both the top quark and anti-top quark decay leptonically. Entanglement is detected via correlations between the polarizations of the top and anti-top and these polarizations are measured through the angles of the decay products of the top and anti-top. In this work, we propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b -flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel. In 139 fb − 1 (3 ab −1 ) of data at the LHC (HL-LHC), it should be feasible to measure entanglement at a precision of ≲ 3% (0 . 7%). Detecting Bell inequality violation, on the other hand, is more challenging. With 300 fb −1 (3 ab −1 ) of integrated luminosity at the LHC Run-3 (HL-LHC), we expect a sensitivity of 1 . 3 σ (4 . 1 σ ). In our study, we utilize a realistic parametric fitting procedure to optimally recover the true angular distributions from detector effects. Compared to unfolding this procedure yields more stable results.