[Paper Review] CP, T and CPT analyses in EPR - correlated $ B^0 \bar B ^0 $ decays

Ezequiel Álvarez|ArXiv.org|Mar 14, 2006

Particle physics theoretical and experimental studies14 references3 citations

TL;DR

This thesis investigates T, CP, and CPT symmetries in entangled $B^0\bar{B}^0$ pairs produced at B-factories, proposing new observables—particularly the $A_{sl}$ asymmetry in same-sign dilepton decays—for detecting CPT violation via loss of $B^0$-$\bar{B}^0$ indistinguishability. It derives linear corrections in the CPT-violating parameter $\omega$, showing that $A_{sl}$ exhibits strong $\Delta t$-dependence at small times, enabling the first experimental bounds on $\omega$ using existing $A_{sl}$ data.

ABSTRACT

In this work we study the T, CP and CPT symmetries in the B-meson system. Our analysis and results are addressed to the case of correlated mesons in the B-factories. In the first set of theory and results we investigate the consequences of these discrete symmetries in the B-mixing and interference between mixing and decay. With the help of the CP-tag we compute all possible intensities and asymmetries which concern flavour-specific and CP Golden Plate decays. Our proposed observables are a new self-consistency check for the Standard Model, as well as a new exploration for the traces of the discrete symmetries in the B-system. In the second set of results we study CPT violation in the initial state of the B-factories through the loss of indistinguishability of $B^0$ and $\bar B^0$. We show that, if the consequence of Bose statistic is relaxed, then the equal-sign dilepton events are considerably modified. We analyze the demise of flavour tagging and we also prove that the equal-sign charge asymmetry, $A_{sl}$, is an optimal observable where to look for this new CPT violation effect. The detailed study of this asymmetry allows us to predict different behaviours according to the possible values of the CPT violating parameter $\w$. We conclude that the best observable where to find traces of this novel kind of CPT violation is the analysis of $A_{sl}$ at small $\Dt$'s. We use existing data on $A_{sl}$ to put the first limits on $\w$.

Motivation & Objective

• To develop new, self-consistent observables to test CP, T, and CPT symmetries in entangled $B^0\bar{B}^0$ decays at B-factories.
• To investigate the implications of CPT violation arising from the loss of $B^0$-$\bar{B}^0$ indistinguishability in the initial state, parameterized by $\omega$.
• To identify optimal, linear-in-$\omega$ observables sensitive to this novel CPT-violating effect, particularly in the small-$\Delta t$ regime.
• To derive the first experimental limits on the CPT-violating parameter $\omega$ using existing measurements of the $A_{sl}$ asymmetry.
• To assess the feasibility and sensitivity of probing $\omega$ through time-dependent same-sign dilepton asymmetries, especially in the $\Delta t \sim \Gamma^{-1}$ region.

Proposed method

• The analysis uses the CP-tag formalism to compute intensities and asymmetries for flavor-specific and CP-Golden-Plate decays in entangled $B^0\bar{B}^0$ pairs.
• The time evolution is modeled using rephasing-invariant parameters $\epsilon$ and $\delta$, incorporating mixing-decay interference effects.
• A new parameter $\omega$ is introduced to quantify the relaxation of Bose statistics, breaking the anti-symmetry of the initial state and allowing $|B^0B^0\rangle$ and $|\bar{B}^0\bar{B}^0\rangle$ components.
• The intensity for same-sign dilepton decays, $I(\ell^{\pm},\ell^{\pm},\Delta t)$, is computed, revealing linear corrections in $\omega$ due to interference terms.
• The $A_{sl}$ asymmetry is derived as a function of $\Delta t$, showing a pronounced peak at small $\Delta t \sim |\omega|\Gamma^{-1}$, with a quasi-time-independent shift at larger $\Delta t$.
• Existing $A_{sl}$ data are used to set bounds on $\omega$ via a figure of merit analysis, confirming sensitivity in the small-$\Delta t$ region.

Experimental results

Research questions

• RQ1 How does the loss of $B^0$-$\bar{B}^0$ indistinguishability, parameterized by $\omega$, modify the time evolution and decay intensities in entangled $B^0\bar{B}^0$ pairs?
• RQ2 What are the observable signatures of $\omega \neq 0$ in same-sign dilepton decays, particularly in the $A_{sl}$ asymmetry?
• RQ3 Can the $A_{sl}$ asymmetry serve as a linearly sensitive probe to detect $\omega$-induced CPT violation, especially at small $\Delta t$?
• RQ4 What are the first experimental limits on $\omega$ that can be derived from existing $A_{sl}$ measurements?
• RQ5 How does the $\omega$-effect impact the viability of flavor tagging and the interpretation of decay observables?

Key findings

• The $A_{sl}$ asymmetry exhibits a strong, non-trivial $\Delta t$-dependence at small times when $\omega \neq 0$, with a pronounced peak at $\Delta t \sim |\omega|\Gamma^{-1}$, unlike the constant behavior expected for $\omega = 0$.
• The $A_{sl}$ asymmetry shows a quasi-time-independent shift at $\Delta t \gtrsim \Gamma^{-1}$, which is sensitive to $\omega$ and provides a direct handle on its value.
• Using existing $A_{sl}$ data, the first experimental bounds on $\omega$ are established at 95% confidence level: $-0.084 \leq \text{Re}(\omega) \leq 0.0100$.
• The analysis shows that the region of small $\Delta t$ is optimal for detecting $\omega$-induced CPT violation, as the signal is strongest there and the figure of merit favors this domain.
• The demise of flavor tagging is shown to occur due to non-vanishing projections onto $|B^0B^0\rangle$ and $|\bar{B}^0\bar{B}^0\rangle$ states when $\omega \neq 0$, invalidating standard tagging assumptions.
• The study confirms that same-sign dilepton events are significantly modified by $\omega$, with opposite linear corrections in $\omega$ for $\ell^+\ell^+$ and $\ell^-\ell^-$ final states, making $A_{sl}$ a sensitive, linear-in-$\omega$ observable.