We consider neutral pseudoscalar mesons in an entangled or Einstein-Podolsky-Rosen state with $C=-1$. Due to quantum entanglement and antisymmetry of this state, the rates of the joint decays of the meson pair display various interesting features, as is well known. As functions of CP and CPT violating parameters, here we obtain some exact results about the joint decay rates and their asymmetries for a given time difference defined for joint decays to flavor eigenstates, as well as those for joint decays to CP eigenstates. The entanglement allows a meaningful and useful definition of the transition amplitude from a CP eigenstate of a meson. These results yield useful information and criteria on CP and CPT violations.
Neutral pseudoscalar mesons in an entangled or Einstein-Podolsky-Rosen state are routinely produced in phi and B factories. Based on the peculiar properties of an entangled state, we present some general exact theorems about parameters characterizing CP and CPT violations, by using various asymmetries defined for the correlated decays of the two entangled mesons, which are rigorously calculated.
Entangled pseudoscalar neutral meson pairs have been used in studying CP violation and searching CPT violation, but almost all the previous works concern $C=-1$ entangled state. Here we consider $C=+1$ entangled state of pseudoscalar neutral mesons, which is quite different from $C=-1$ entangled state and provides complementary information on symmetry violating parameters. After developing a general formalism, we consider three kinds of decay processes, namely, semileptonic-semileptonic, hadronic-hadronic and semileptonic-hadronic processes. For each kind of processes, we calculate the integra…
We present a general model-independent formalism of measuring CP and CPT violating parameters through time-ordered integrated rates of correlated decays of $C=\pm 1$ entangled states of neutral pseudoscalar mesons. We give the general formulae of CP and CPT violating parameters in terms of four measurable asymmetries defined for the time-ordered integrated rates, applicable to all kinds of decay product. Two special cases which are often realized in experiments are discussed specifically.
The observables used in the K-system to characterize T and CPT violation are no longer useful for the Bd-system, since the width difference between the physical states is vanishingly small. We show that only Im(epsilon) and Re(delta) can survive if Delta Gamma=0, and build alternative CP-odd, CPT-odd, T-odd and temporal asymmetries for the (B_CP -> B0, B0bar) transitions. These quantities enable us to test T and CPT invariances of the effective Hamiltonian for the B-system. The method needs the CP eigenstates B_CP, which can be tagged unambiguously to order lambda^3 from the entangled states o…
The neutral-kaon system constitutes a fantastic and unique laboratory for the study of CPT symmetry and the basic principles of quantum mechanics, and a $ϕ$-factory represents a unique opportunity to push forward these studies. The experimental results show no deviation from the expectations of quantum mechanics and CPT symmetry, while the extreme precision of the measure- ments, in some cases, reaches the interesting Planck-scale region. At present the KLOE-2 experiment is collecting data with an upgraded detector with the aim of significantly improving these kinds of experimental tests.
In this paper we present a novel CPT symmetry test in the neutral kaon system based, for the first time, on the direct comparison of the probabilities of a transition and its CPT reverse. The required interchange of "in" $\leftrightarrow$ "out" states for a given process is obtained exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs produced at a $ϕ$-factory. The observable quantities have been constructed by selecting the two semileptonic decays for flavour tag, the $ππ$ and $3π^0$ decays for CP tag and the time orderings of the decay pairs. The interpretation in terms …
Even though it is undoubtedly very appealing to interpret the latest T2K results as evidence of CP violation, this claim assumes CPT conservation in the neutrino sector to an extent that has not been tested yet. As we will show, T2K results are not robust against a CPT-violating explanation. On the contrary, a CPT-violating CP-conserving scenario is in perfect agreement with current neutrino oscillation data. Therefore, to elucidate whether T2K results imply CP or CPT violation is of utter importance. We show that, even after combining with data from NO$ν$A and from reactor experiments, no cla…
There may unique ("smoking-gun") signatures of the breakdown of CPT symmetry, induced in some models of Quantum Gravity entailing decoherence for quantum matter. Such effects can be observed in entangled states of neutral mesons via modifications of the respective Einstein-Podolsky-Rosen (EPR) correlators ("omega"-effect). In the talk I discuss experimental signatures and bounds of the omega-effect in Phi- and B-factories, and argue that the effect might be falsifiable at the next generation facilities.
In this paper we discuss experimental consequences of a novel kind of CPT violation which would manifest itself in the symmetry of the entangled initial state of $B ^0$ and $\bar B ^0$ through their loss of indistinguishability. The ``wrong'' symmetry component is proportional to $ω$. We focus our theoretical study on the $Δt$-dependence of observables concerning equal-sign dilepton events for which the intensity vanishes at $Δt = 0$ in absence of $ω$. We find that the charge asymmetry, $A_{sl}$, acquires a $Δt$-dependence linear in $ω$, whose relative importance appears on specific regions of…
We present a combined treatment of quantum-gravity-induced effects and intrinsic CPT violation in entangled neutral-Kaon states. Our analysis takes into consideration two types of effects: first, those associated with the loss of particle-antiparticle identity, as a result of the ill-defined nature of the CPT operator, and second, effects due to the non-unitary evolution of the Kaons in the space-time foam. By studying a variety of phi-factory observables, involving identical as well as general final states, we derive analytical expressions, to leading order in the associated CPT violating par…
The direct observation of time reversal symmetry violation (TV) is important for the test of $CPT$ conservation and the Standard Model. In this paper, we study both time-dependent and time-independent genuine TV signals in entangled $D^0-\bar{D}^0$ pairs. A possible $CPT$-violation effect called the $ω$ effect is also investigated. In the $C=-1$ entangled state, the asymmetries due to TV are calculated to be of the order of $10^{-5}$ to $10^{-4}$ within the Standard Model, but the modification due to the $ω$ effect in the $C=-1$ states is found to be about $10\%-30\%$ when $|ω|\sim 10^{-4}$. T…
In tagged cascade decays of the type P^0 (P^0-bar) -> M^0 / M^0-bar X -> f X there are two complex CPT-violating parameters: one in P^0 - P^0-bar mixing, the other one in M^0 - M^0-bar mixing. I analyze those decays and find that, in principle, the former parameter can be extracted from a careful comparison of their time dependences. CPT violation in M^0 - M^0-bar mixing, on the other hand, always appears entangled with ratios of decay amplitudes and cannot be extracted.
Entangled states of pseudoscalar mesons represent a very interesting tool for studying foundations of quantum mechanics, e.g. for testing Bell inequalities. Recently, they also emerged as a test bench for quantum information protocols. On the other hand, from a quantum information point of view, the characterization of the distance between two quantum states is a topic of the utmost importance. In this letter, with the purpose of providing a useful tool for further investigations, we address the problem of which distance allows a better discrimination between density matrices appearing in pseu…
Excluding Local Hidden Variables in $Λ\barΛ$ Production: The Incompatibility with Angular-Momentum Conservation and CPT Invariance
Institute of Physics, Henan Academy of Sciences（河南省科学院物理研究所）；School of Sciences, Xi’an Technological University（西安工业大学理学院）；School of Physics, Henan Normal University（河南师范大学物理学院）
We discuss the demise of flavour tagging due to the loss of the particle-antiparticle identity of neutral B-mesons in the Einstein-Podolsky-Rosen correlated states. Such a situation occurs in cases where the CPT operator is ill-defined, as happens, for example, in quantum gravity models with induced decoherence in the matter sector. The time evolution of the perturbed B0-B0bar initial state, as produced in B-factories, is sufficient to generate new two-body states. For flavour specific decays at equal times, we discuss two definite tests of the two body entanglement: (i) search for the would-b…
The precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the filtered neutral meson $B_d$ states and the experimental asymmetries between the double decay rate intensities for Flavour-CP eigenstate decay products in a B-factory of entangled states, is established. This allows the identification of genuine Asymmetry Parameters in the time distribution of the asymmetries and their measurability by disentangling genuine and possible fake terms. We express the nine asymmetry parameters -- three different observables for each one of the thr…
Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-indepedent separate measurements of the three CP, T and CPT symmetry violations for transitions involving the decay of the neutral meson systems in B- and Φ-factories. It makes use of the quantum-mechanical entanglement only, for which the individual state of each neutral meson is not defined before the decay of its orthogonal partner. The final proof of the independence of the three asymmetries is that no other theoretical ingredient…
In this paper, we review the approach leading to cosmic polarization rotation observation and present the current status with an outlook. In the study of the relations among equivalence principles, we found that long-range pseudoscalar-photon interaction is allowed. Pseudoscalar-photon interaction would induce a rotation of linear polarization of electromagnetic wave propagating with cosmological/astrophysical distance. In 2002, DASI successfully observed the polarization of the cosmological microwave background radiation. In 2003, WMAP observed the correlation of polarization with temperature…
In this work we analyze the observable asymmetries one can build from entangled B-meson states, in order to extract information on the parameters epsilon and delta which govern indirect violation of discrete symmetries. The traditionally proposed observables, based on flavour tags, are not helpful for the study of the Bd-system, where the tiny value of the width difference between physical states clears up such asymmetry effects. Our study makes instead use of CP tags in order to build new asymmetries where the different parameters can be separated out. For this separation, it is decisive to a…
In this review I classify the possible ways of CPT violation, and I describe briefly their phenomenology, in both terrestrial and astrophysical experiments, including antimatter factories, neutral mesons and neutrinos, and discuss the various sensitivities. I also pay attention to disentangling genuine quantum-gravity induced CPT violation from `fake' violation due to ordinary matter effects. A particularly interesting situation arises when the breaking of CPT invariance is through unitarity violations, in the sense of the matter theory being viewed as an effective field theory, entangled with…
We discuss two classes of semi-microscopic theoretical models of stochastic space-time foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of CPT invariance. One class of models deals with a specific model of foam, initially constructed in the context of non-critical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuat…
Quantum field theory, which is the basis for all of particle physics, requires that all processes respect $CPT$ invariance. It is therefore of paramount importance to test the validity of $CPT$ conservation. In this Letter, we show that the time-dependent, indirect $CP$ asymmetries involving $B$ decays to a $CP$ eigenstate contain enough information to measure $T$ and $CPT$ violation in $B^0$-${\bar B}^0$ mixing, in addition to the standard $CP$-violating weak phases. Entangled $B^0{\bar B}^0$ states are not required (so that this analysis can be carried out at LHCb, as well as at the $B$ fact…
The conclusions summarize the main, but not all, aspects of a two-days workshop held at MITP Mainz. The four covered aspects are T violation in decays of neutral B mesons, T and CPT studies in B0B0bar transitions with Belle, future measurements of T violation in B and D decays, and direct tests of T and CPT symmetries in the entangled neutral Kaon system at a ?Phi factory.
Discrete symmetry violation in the weak interaction is central to the Standard Model of particle physics, however the origin of these violations is not well understood. Nor are we able to provide a satisfactory explanation of the Universal dominance of matter over antimatter, an issue related to CP violation. As a result study of discrete symmetry violation remains a topic of broad interest. These proceedings discuss experimental prospects of studying C, P, T, CP and CPT symmetries in a number of contexts, including the use of triple product asymmetries and entangled neutral meson systems.
In this paper, we consider a pair of entangled charged lepton-neutrino embedded in a constant magnetic field, which can be produced in the purely leptonic decay of charged pseudoscalar mesons. Particles with nonzero magnetic dipole moment will precess in the present of external magnetic field and induce a nontrivial noncyclic geometric phase. The dependence of this geometric phase on neutrino mass can be used to determine the Dirac/Majorana nature of massive neutrinos.
In a $ϕ$ factory, neutral kaons are produced in Einstein-Podolsky-Rosen (EPR) states, furthermore, a $K_S$ is tagged if its entangled partner is detected as $K_L$, and vice versa. Here we point out that upon its detection as $K_L$, one of the EPR-entangled particles is projected into one of the orthogonal basis states, consequently the other particle should be projected to the state orthogonal to $K_L$, denoted as $K_{\perp L}$, rather than $K_S$, because $K_S$ is not orthogonal to $K_L$. Therefore the semileptonic charge asymmetry of what was previously regarded as $K_S$ is really that of $K_…
In the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the $ω$-effect. In the current paper we identify how to probe the complex $ω$ in the entangled $B_d$-system using Flavour(f)-CP(g) eigenstate decay channels: the connection between the Intensities for the two time-ordered decays (f, g) and (g, f) is lost. Appropriate observables are constructed allow…
We present a novel method to perform a direct T (time reversal) symmetry test in the neutral kaon system, independent of any CP and/or CPT symmetry tests. This is based on the comparison of suitable transition probabilities, where the required interchange of in <-> out states for a given process is obtained exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs produced at a $ϕ$-factory. In the time distribution between the two decays, we compare a reference transition like the one defined by the time ordered decays $(\ell^-,ππ)$ with the T -conjugated one defined by $(3π^0,…
I review first some theoretical motivations for violation of Lorentz and/or CPT Invariance. Although the latter symmetries may be violated in a quantum gravity setting, nevertheless there are situations in which these violations are due to a given classical background geometry that may characterised early epochs of our Universe, and in fact be responsible for the observed dominance of matter over antimatter in the Universe. In this way I estimate some of the coefficients of the Standard Model Extension (SME), which is a framework for a field theoretic study of such a breakdown of fundamental s…
In this brief review I discuss ways and tests of CPT-Violation in the context of quantum gravity theories with space-time foam vacua, which entail quantum decoherence of matter propagating in such backgrounds. I cover a wide variety of sensitive probes, ranging from cosmic neutrinos to meson factories. I pay particular emphasis on associating the latter with specific, probably unique ("smoking-gun"), effects of this type of CPT Violation, related to a modification of Einstein-Podolsky-Rosen (EPR) correlations in the entangled states of the relevant neutral mesons. I also present some semi-micr…
Clock-comparison experiments are among the sharpest existing tests of Lorentz symmetry in matter. We characterize signals in these experiments arising from modifications to electron or nucleon propagators and involving Lorentz- and CPT-violating operators of arbitrary mass dimension. The spectral frequencies of the atoms or ions used as clocks exhibit perturbative shifts that can depend on the constituent-particle properties and can display sidereal and annual variations in time. Adopting an independent-particle model for the electronic structure and the Schmidt model for the nucleus, we deter…
It was found that the vector meson pair from the pseudoscalar decays can form an entangled state. In this work we give out detailed explanations on the polarization correlation of the two entangled vector mesons. It is demonstrated that an experimental test of the Clauser-Horne inequality can be carried out through measuring the azimuthal distribution of four pseudoscalars in the cascade decay $η_c \to VV \to (PP)(PP)$, and the measurement of this process is feasible with the current running experiments in tau-charm factory. Moreover, a brief discussion on the polarization correlation of the t…
Symmetry transformations have been proven a bedrock tool for understanding the nature of particle interactions, formulating and testing fundamental theories. Based on the up to now unbroken CPT symmetry, the violation of the CP symmetry between matter and antimatter by weak interactions, discovered in the decay of kaons in 1964 and observed more recently in 2001 in B mesons, strongly suggests that the behavior of these particles under weak interactions must also be asymmetric under time reversal T. However, until the recent years there has not been a direct detection of the expected time-rever…
I discuss a model inspired from the string/brane framework, in which our Universe is represented as a three brane, propagating in a bulk space time punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the bulk, the D-particles cross it, and from an effective observer on D3 the situation looks like a ``space-time foam'' with the defects ``flashing'' on and off (``D-particle foam''). The open strings, with their ends attached on the brane, which represent matter in this scenario, can interact with the D-particles on the D3-brane universe in a topologically non-trivial manne…
If Lorentz and CPT violation exist, they could affect the decays of scalar and pseudoscalar particles. For a decay into a fermion and an antifermion (not necessarily of the same mass), both the total decay rate and the outgoing particle distribution may be modified, through interference between the conventional decay mechanism and a separate Lorentz-violating mechanism. The modifications are sensitive to forms of Lorentz violation that are otherwise rather difficult to study, since at tree level they do not affect particle propagation, but only interaction vertices. Using existing experimental…
In this letter, hadronic decay channels of light pseudoscalar mesons are realized in Yangian algebra. In the framework of Yangian, we find that these decay channels can be formulated by acting transition operators, composed of the generators of Yangian, on the corresponding pseudoscalar mesons. This new description of decays allows us to present a possible interpretation of the new unknown particle $X$ in the decay $K^0_L\to π^0 π^0 X$: it is an entangled state of $π^0$ and $η$.
The laws of quantum physics can be studied under the mathematical operation T that inverts the direction of time. Strong and electromagnetic forces are known to be invariant under temporal inversion, however the weak force is not. The BaBar experiment recently exploited the quantum-correlated production of pairs of B0 mesons to show that T is a broken symmetry. Here we show that it is possible to perform a wide range of tests of quark flavour changing processes under T in order to validate the Standard Model of particle physics covering b to u, d, s, and c transitions as well as c to u, d and …
Recent proposals to test Bell's inequalities with entangled pairs of pseudoscalar mesons are reviewed. This includes pairs of neutral kaons or B-mesons and offers some hope to close both the locality and the detection loopholes. Specific difficulties, however, appear thus invalidating most of those proposals. The best option requires the use of kaon regeneration effects and could lead to a successful test if moderate kaon detection efficiencies are achieved.
New data analysis with Pauli blocking and entanglement explains CP violation in $B^o\rightarrow Kπ$ decays, absence in $B^{\pm} \rightarrow Kπ$ decays and predicts unexpected contrast between pure I=1/2 in individual $B^{\pm}$ and $B^o$ final states and I=1/2 violation in relations between them. Analysis of $B\rightarrow Kπ$ data predicts these observed isospin relations and explains dependence on spectator quark flavor. $B^+ \rightarrow Kπ$ tree diagram $\bar b u\rightarrow \bar s u \bar u u$ has two identical $u$ quarks from weak vertex and spectator. The Pauli principle requires these quark…
