CPT Violation Research Articles

CPT and Lorentz symmetry tests with hydrogen using a novel in-beam hyperfine spectroscopy method applicable to antihydrogen experiments

We present a Rabi-type measurement of two ground-state hydrogen hyperfine transitions performed in two opposite external magnetic field directions. This puts first constraints at the level of ▪ on a set of coefficients of the Standard Model Extension, which were not measured by previous experiments. Moreover, we introduce a novel method, applicable to antihydrogen hyperfine spectroscopy in a beam, that determines the zero-field hyperfine transition frequency from the two transitions measured at the same magnetic field. Our value, ▪, is in agreement with literature at a relative precision of 0.44 ppb. This is the highest precision achieved on hydrogen in a beam, improving over previous results by a factor of 6.

Principles of Economic Externality Dynamics Economic Dynamics and the Standard Model (V)

The present paper discusses the importance of economic externality and the economic phenomena involved. Section 1 draws on the framework of weak force theory in physics, we propose a new approach of dynamic analysis for economic externality. From a mesoscopic (intermediate scale) perspective, no distinction is made between the macro-demand and individual micro-buyers nor between the macro-supply and individual micro-sellers. Section 2 applies the isospin modeling method to construct two economic isospin models. One is between the achieving impulse and the fear-of-failure impulse, under the effect of economic externality. The other is between the market behavior and market residues, namely, market aftertaste. Section 3 discusses the microstructural properties of the market, including Dirac's equation and the market, Dirac γmatrix notation, and the chirality and spin structure of market components. Section 4 discusses the helical structural characteristics of supply chains, including CPT theorems, Penrose zigzag helical processes, and several modeling directions of economic externality and buyer-seller interactions (weak interactions). Section 5 discusses the economic externality and the electroweak model, including extensive externality, externality mediations with Weinberg rotations, and economic analysis using lepton weak currents, including the analysis of lepton neutral weak currents. Finally, Section 6 provides a general discussion on the standard model of economic dynamics.

CPT Symmetry Searches in the Neutral Meson System

A review of the landscape of CPT symmetry tests is presented, centered around the Standard-Model Extension and focusing on tests in the neutral meson system. A discussion of the relevant theories summarizes original ideas. It is followed by a short transition into phenomenology. A more detailed parameterization is presented. Various experiments are used to deliver an overview of testing CPT from every angle that the theory suggested and that the neutral meson (NM) system could accommodate.

Deformation-induced CPT violation in entangled pairs of neutral kaons

In this paper we consider description of kaon-antikaon interference in the context of a theory with deformed CPT symmetry. In the case of such theoretical models, deviations from the standard CPT invariance is related to the momentum carried by the particles; in particular the rest masses of particles and antiparticles are equal. We find that the decay intensity of kaon-antikaon pair has three contributing terms: the correct-parity, the wrong-parity, and the interference between them, all of which are affected by deformation. Using the fact that the presence of such terms was not observed we estimate, under plausible assumptions, the magnitude of deformation parameter κ≳1017 GeV at the LHC energy. This limit can be possibly improved to values closer to the expected Planck mass scale κ≳1018 GeV using a next-generation collider with energy larger by an order of magnitude. This raises hopes that the effect, if it exists, could be detected in future accelerator experiments. Uncertainties of the energy measurement and time resolution are important for accuracy of these predictions. Published by the American Physical Society 2024

CPT, Majorana fermions, and particle physics beyond the Standard Model

Abstract After reviewing charge conjugation and the CPT theorem, we define Majorana fermions and clarify the relationship of Majorana, Weyl, and Dirac fields. Appearance of Majorana fermions in various scenarios of physics beyond the Standard Model is discussed, including neutrino masses, baryon asymmetry of the universe, grand unified theories, and supersymmetry.

Neutrino Lorentz invariance violation from cosmic fields

From a cosmological perspective, scalar fields are well-motivated dark matter and dark energy candidates. Several possibilities of neutrino couplings with a time-varying cosmic field have been investigated in the literature. In this work, we present a framework in which violations of Lorentz invariance (LIV) and CPT symmetry in the neutrino sector could arise from an interaction among neutrinos with a time-varying scalar field. Furthermore, some cosmological and phenomenological aspects and constraints concerning this type of interaction are discussed. Potential violations of Lorentz and CPT symmetries at present and future neutrino oscillation experiments such as IceCube and KM3NeT can probe this scenario.

Nonrelativistic limits of the Klein-Gordon and Dirac equations in the Amelino-Camelia DSR

This paper is devoted to the study of the nonrelativistic limit of Amelino-Camelia doubly special relativity and the corresponding modified Klein-Gordon and Dirac equations. We show that these equations reduce to the Schrödinger equations for the particle and the antiparticle with different inertial masses, however, their rest masses are the same. M. Coraddu and S. Mignemi have studied the nonrelativistic limit of the Magueijo-Smolin doubly special relativity. We compare their results with our study and show that these two models are reciprocal to each other in the nonrelativistic limit. We find that particle and antiparticle masses can be different. These different masses lead to the CPT violation. Also, we will find an upper limit on the photon mass.

How the unlikely friendship of Pauli and Jung led to the discovery of CPT symmetry

How the unlikely friendship of Pauli and Jung led to the discovery of CPT symmetry

Antimatter Gravity and the Results of the ALPHA‐g Experiment

AbstractBy combining general relativity and CPT symmetry, the theory of CPT gravity predicts gravitational repulsion between matter and CPT‐transformed matter, i.e., antimatter inhabiting an inverted space‐time. Such repulsive gravity turned out to be an excellent candidate for explaining the accelerated expansion of the Universe, without the need for dark energy. The recent results of the ALPHA‐g experiment, which show gravitational attraction between antihydrogen atoms and the Earth, seem to undermine this success in the cosmological field. Analyzing the above theory, two solutions are found that can be consistent with the experimental results, while preserving the large‐scale gravitational repulsion. The first highlights how repulsive gravity can be the result of the interaction with an inverted space‐time, but occupied by matter and not antimatter, and therefore the antimatter present in our space‐time has no reason to exhibit gravitational repulsion. The second retains the original CPT transformation, resulting in repulsive gravity between matter and antimatter, but with the caveat that antimatter immersed in our space‐time cannot exhibit the PT transformation which is the cause of the repulsion. Finally, it is shown that, in a Newtonian approximation of the geodesic equation, time reversal is not a necessary operation for repulsive gravity, therefore opening the possibility of an expanding cosmos with a single time direction.

Lorentz violation in γ-pair production (e + e − → γ γ)

In this paper, we investigate the production process of a photon pair in a regime of quantum electrodynamics, considering the presence of a constant four-vector that defines a privileged direction in spacetime, resulting in Lorentz symmetry violation. We explore Lorentz violation in the context of vectorial nonminimal coupling, where we analyze the modifications introduced by this coupling in the scattering amplitude at the vertex. Moreover, we delve into Lorentz violation with axial-like nonminimal coupling. Both analyses are conducted by examining the constant four-vector of both time-like and space-like types.

Reciprocal of the CPT theorem

The CPT theorem originally proven by Lüders and Pauli ensures the equality of masses, lifetimes, magnetic moments and cross sections of any particle and its antiparticle. We show that in a Lorentz invariant quantum field theory described by its Lagrangian, CPT-violating interaction alone does not split the masses of an elementary particle and its antiparticle but breaks only the equality of lifetimes, magnetic moments and cross sections. However, CPT violation in the mass term of a field in the Lagrangian, which can be attributed to be due to the size of the particle described by a form factor, breaks only the equality of masses. Also it is shown that the two separate effects of CPT violation in the interaction terms or in the mass term do not mix due to higher quantum corrections and remain distinguishable. Thus, we urge the experimentalists to search for such observable effects concerning differences in the masses, magnetic moments, lifetimes and cross sections between the elementary or bound state particles and their antiparticles. In the case of CPT violation only in the mass term, besides the difference in the masses of elementary bound state particles and their antiparticles, there will be also an extremely tiny difference in the lifetimes of bound states due to the difference in their phase spaces. From the details of calculations, it appears that the separate effects of the CPT violation described above are quite general, neither depending on how the nonlocality is achieved, nor depending on what this violation is due to: due to T violation, as considered in the present work, which can be attributed to a cosmological direction of time; to CP or to both T and CP violations. The latter two cases satisfy the Sakharov's conditions for explaining the baryon asymmetry in the Universe.

Gravitational entropy and the flatness, homogeneity and isotropy puzzles

We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are Einstein's theory of gravity and Hawking's method of computing the gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for “big bang” type singularities dominated by conformal matter, enforcing CPT symmetry and analyticity. Besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons from which we calculate the total gravitational entropy Sg of cosmologies including radiation, dark energy and space curvature of either sign. We find Sg∼SΛ1/4Sr, where SΛ is the de Sitter entropy and Sr is the total entropy in radiation, which is extensive in the comoving spatial volume. Thus, Sg can be larger than SΛ and we show it is largest for universes which are spatially flat. Extending our analysis to include linearized perturbations, we show that, for a given set of globally conserved quantities, Sg is greatest for universes that are also homogeneous and isotropic on large scales.

Review of physics program at J-PET

The Jagiellonian - Positron Emission Tomograph (J-PET) is a multi purpose detector for tests of discrete symmetries and quantum entanglement of photons originating from the decay of positronium atoms. The research is per formed by measurement of angular correlations between photons from the an nihilations of the lightest leptonic bound system. The J-PET detector is the only device which enables determination of polarisation of photons from positronium annihilation together with estimation of positronium spin axis on the event-by-event basis. The novelty of the system is based on a usage of plastic scintil-lators as active detection material and trigger-less data acquisition system. The aim of two independent detection setups currently in use together with different annihilation chambers is to improve limits on C, CP and CPT symmetries and to search for the entanglement of photons originating from electron-positron annihilation. Additionally a precise measurement of ortho-positronium life time would allow to test of non-relativistic quantum electrodynamics and search for Mirror Matter.

Research advances in antimatter

The asymmetric origin of matter and antimatter in the universe is an important unsolved mystery in science today. In this paper, we briefly review the history of antimatter research and the recent international hotspots of related research. This paper focuses on the advances in antimatter research made in recent years at the large-scale international RHIC-STAR experiment at the Relativistic Heavy Ion Collider, including the discovery of the first antimatter hypernucleus (anti-hypertriton), antimatter helium 4 and antihyperhydrogen 4, the first measurements of antiproton interactions, and the precise measurements of the mass and binding energy of the hypertriton and anti-hypertriton. The antimatter hypertriton nucleus, composed of an antiproton, an antineutron, and an anti-Λ hyperon, is the first anti-hypernucleu to be discovered, extending the three-dimensional nuclide map from the anti-strange quark degree of freedom. Antimatter Helium 4 is the heaviest stable antimatter nucleus yet discovered. Anti-hyperhydrogen 4, just discovered in 2024, is composed of an antiproton, two antineutrons, and an anti-Λ hyperon, and is the heaviest antimatter hypernucleus to date. Equivalence to the proton-proton interaction was established by measurements of the antiproton-antiproton interaction. At the same time, precise measurements of the mass of hypertriton and anti-hypertriton nuclei confirmed the equivalence of matter and antimatter. And these also fully demonstrate that the CPT symmetry is also valid for antimatter nuclei. Measurements of the binding energy of the hypertriton nucleus indicate that the interaction between Λ and the nucleus of the hypertriton (the deuterium nucleus) is strong, which differs from the earlier common belief that the hypertriton nucleus is a weakly bound system. Furthermore, we discuss different physical mechanisms for the production of (anti) light nuclei, mainly including thermal, coalescence and relativistic kinetic models. Finally, we also present recent results from antihydrogen atom experiments at CERN, antimatter space probes, etc., and discuss the implications of these advances for understanding the structure of matter. Overall, the existing studies of antimatter nuclei and atoms have not yet provided clear evidence for the asymmetric origin of matter and antimatter in the universe, which can help further improve the accuracy of various measurements in antimatter research. Of course, other efforts in this direction in nuclear and particle physics are well expected.

Improved Measurements of Muonic Helium Ground-State Hyperfine Structure at a Near-Zero Magnetic Field.

Muonic helium atom hyperfine structure (HFS) measurements are a sensitive tool to test the three-body atomic system and bound-state quantum electrodynamics theory, and determine fundamental constants of the negative muon magnetic moment and mass. The world's most intense pulsed negative muon beam at the Muon Science Facility of the Japan Proton Accelerator Research Complex allows improvement of previous measurements and testing further CPT invariance by comparing the magnetic moments and masses of positive and negative muons (second-generation leptons). We report new ground-state HFS measurements of muonic helium-4 atoms at a near-zero magnetic field, performed for the first time using a small admixture of CH_{4} as an electron donor to form neutral muonic helium atoms efficiently. Our analysis gives Δν=4464.980(20) MHz (4.5ppm), which is more precise than both previous measurements at weak and high fields. The muonium ground-state HFS was also measured under the same conditions to investigate the isotopic effect on the frequency shift due to the gas density dependence in He with CH_{4} admixture and compared with previous studies. Muonium and muonic helium can be regarded as light and heavy hydrogen isotopes with an isotopic mass ratio of 36. No isotopic effect was observed within the current experimental precision.

Anomaly cancellation in string theory

The anomaly cancellation in superstring theory is known to hold at leading order in the curvature for the gauge groups [Formula: see text] and [Formula: see text]. The coefficients of the next-to-leading order terms may be evaluated, and a mechanism for cancellation is described, which would remain valid at higher genus when there exists a global splitting of the coordinates of supermoduli space. Since the spin-[Formula: see text] fields transform under the adjoint representation in these models, compactification of the heterotic string over [Formula: see text] or a fundamental 12-dimensional theory, from which superstrings are produced through an elliptic fibration, over [Formula: see text], provides another phenomenologically viable theory at lower energies compatible with the standard description of the elementary particle interactions. The 96 spin-[Formula: see text] fields now would transform under the fundamental representation of [Formula: see text] and the spin-one gauge fields would belong to the adjoint representation. The sum of the anomaly polynomials for the particle content of the [Formula: see text] model vanishes at [Formula: see text]. The contributions to the gravitational anomaly from the particles and antiparticles cancel by the CPT theorem and the duality transformations of polynomials of degree 6 in the curvature and the field strength. The existence of the interaction of a spin-2 charge, which is conserved only over a finite time interval, can be traced to nonlocal terms in the reduction of the string field theory to the gravitational sector. The source of the global gravitational anomaly cancellation in the modular form equations derived from an elliptic fibration of a 12-dimensional theory would restrict the compactifications and provide a method for preserving the absence of anomalies in four dimensions.

Asymmetric particle-antiparticle Dirac equation: second quantization

We build the fully relativistic quantum field theory related to the asymmetric Dirac fields first presented in a prequel to this work. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and ‘negative’ frequency plane wave solutions’ dispersion relations are no longer degenerate. At the second quantization level, we show that this implies that particles and antiparticles sharing the same wave number have different energies and momenta. In spite of that, we prove that by properly fixing the values of the relativistic invariants that define the asymmetric Dirac free field Lagrangian density, we can build a consistent, fully relativistic, and renormalizable quantum electrodynamics (QED) that is empirically equivalent to the standard QED. We discuss the reasons and implications of this non-trivial equivalence, exploring qualitatively other scenarios in which the asymmetric Dirac fields may lead to beyond the standard model predictions. We give a complete account of how the asymmetric Dirac fields and the corresponding annihilation and creation operators transform under improper Lorentz transformations (parity and time reversal operations) and under the charge conjugation operation. We also prove that the present theory respects the CPT theorem.

Particles and antiparticles

In this paper, we review the concept of charge and chirality for particles and antiparticles. We point out that the commonly accepted equivalence of particles and antiparticles—with difference only in the opposite signs of their charges, which follows from the CPT invariance—is valid only for free non-chiral particles. We point out that the the equivalence of particles and antiparticles is violated if the weak interaction is turned on. We also discuss that within the standard model even free neutrinos are exceptions, as they can be produced only in chiral states. We conclude that in spite of a long history of antiparticles, interesting theoretical and experimental challenges remain in their complete understanding.

The joint conservation assumption of CPT and weak isospin and color charge

The conservation of CPT is considered applicable to all physical laws, but more and more research has discovered the possibility of CPT violation. This paper attempts to find a more complex and essential conservation than CPT conservation. This paper uses the method of theoretical structural analysis to discover the relationship between C, P, T symmetry, phase rotation symmetry, space rotation symmetry, and time translation symmetry, and prove the relationship between CPT symmetry, charge conservation, angular momentum conservation and energy conservation by studying the transformation modes of phase space, space, and time. Then the composition rules of uncertainty relationships and the fact that charge, weak isospin, and color charge are all related to the internal symmetry of matter are used to provide evidence for the inherent connection between charge, weak isospin rotation, and color charge demonstrating the similarity among these three. Finally, the joint conservation of CPT, weak isospin, and color charge are proposed.

Axion effective potentials induced by heavy sterile fermions

A model of (3 + 1)-dimensional leptogenesis, proposed previously by the authors, requires a CPT Violating (CPTV) background of the Kalb–Ramond (KR) axion field. The KR axion is a pseudoscalar, which is dual to the field strength of the spin-one field present in the massless gravitational multiplet in the theory of closed bosonic strings (compactified to four dimensions). Microscopic models for the emergence of such backgrounds are provided both by low-energy string-inspired gravitational theories with torsion (including (primordial) gravitational and axial gauge anomalies) and by Einstein–Cartan gravity, a closely related simpler model. In this work we examine the pseudoscalar quanta of the KR axion in this background using the methods of effective field theory. In our model for leptogenesis there is a single sterile right-handed neutrino (RHN) with mass m_N. At energies lower than m_N, an axion potential is derived by integrating out at one loop the sterile neutrino in the spirit of effective field theory. The stability of this axion potential is important for the viability of our model. The vacuum of this potential is generally metastable. The stability of the vacuum is determined by the ratio of the torsion-induced-axion coupling (which depends on the string mass scale) to m_N, which should be larger or equal to one, for the validity of our effective field theory. The vacuum is metastable only for axion couplings much larger than the sterile neutrino mass (large string mass scales, e.g. comparable to the four-dimensional Planck mass), with a lifetime much larger than the age of the observable Universe. By contrast, if axion couplings are comparable to the RHN mass the false vacuum is highly unstable, with a lifetime much smaller than the age of the observable Universe; in this case the CPTV leptogenesis scenario is not viable.