Feasibility of Bell inequality violation at the ATLAS experiment with flavor entanglement of $B^0{\overline{B}}^0$ pairs from $pp$ collisions

We examine the feasibility of the Bell test (i.e., detecting a violation of the Bell inequality) with the ATLAS detector at the Large Hadron Collider (LHC) at CERN through the flavor entanglement between the $B$ mesons. After addressing the possible issues that arise associated with the experiment and how they may be treated based on an analogy with conventional Bell tests, we show in our simulation study that under realistic conditions (expected from the LHC Run 3 operation) that the Bell test is feasible under mild assumptions. The definitive factor for this promising result lies primarily in the fact that the ATLAS detector is capable of measuring the decay times of the $B$ mesons independently, which was not possible in the previous experiment with the Belle detector at KEK. This result suggests the possibility of the Bell test in much higher energy domains and may open up a new arena for experimental studies of quantum foundations.

Figure 1

Minkowski diagrams for the spacetime events related to the decay of a pair of $B$ mesons considered for the Bell test. After the $pp$ collision emerge a pair of $B$ mesons, which subsequently decay at $t_2$ (or $t_2^{\prime }$) in the region (A) and at $t_1$ (or $t_1^{\prime }$) in the region (B). The red and blue solid lines depict the actual spacetime trajectories (world lines) of the respective $B$ mesons, while the shaded zones depict the forward light cones of the activated times of the RNG embedded in the $B$ mesons in the first two decays. The flavor measurements, which are to be performed simultaneously with the RNG within a typical short period of time allocated for weak interactions colored in green, are completed retroactively after the decay modes are determined by identifying the decayed particles. For the combination of the correlations $S(\mathrm{\Delta }t)$ used for the Bell test, the locality condition requires that the final measurement at $t_2^{\prime }$ be completed before the information of the first measurement at $t_1^{\prime }$ reaches. Our simulation indicates that this condition can be fulfilled with the ATLAS experiment.

Figure 2

Distributions of the squared proper distances $s^2$ of the $B^0{\overline{B}}^0$ decay events before and after the acceptance and selection cuts. The events are spacelike when $s^2>0$.

Figure 3

$|S^Q(|\mathrm{\Delta }t|)|$ after the acceptance and selection cuts in the case of QM with the theory line. The dotted line at $|S(|\mathrm{\Delta }t|)|=2$ shows the upper bound of the Bell inequality.