The mass of the 4\pi^+$

The most precise value for the pion mass was determined from a precision measurement at PSI of the muon momentum in pion decay at rest, \pi^+ \rightarrow \mu^+ + \nu_{\mu}π+→μ++νμ. The result is m_{\pi^+} = 139.570\,21(14)mπ+=139.57021(14)~MeV/c^22. This value is more precise, however, in agreement with the recent compilation of the Particle Data Group for m_{\pi^-}mπ−. The agreement of m_{\pi^+}mπ+ with the recent measurement. This yields a new quantitative measure of CPT invariance in the pion sector: (m_{\pi^+} - m_{\pi^-})/m_{\pi}(\mbox{av}) = (-2.9 \pm 2.0)\cdot 10^{-6}(mπ+−mπ−)/mπ(av)=(−2.9±2.0)⋅10−6, an improvement by two orders of magnitude.

Strong magnetic fields in gauge theories

The problem of photon propagation in a medium in presence of a strong magnetic field in the frame of quantum electrodynamics is discussed in the present paper, based on previous literature in this area. The breaking of the spatial symmetry by the magnetic field determine the existence of a set of basic vectors and tensors which must satisfy the gauge and CPT invariance of quantum electrodynamics. The charge symmetric and non-symmetric cases are discussed. In the second case the Faraday effect is produced. A chiral current arises, associated to a pseudovector eigenvector ofthe polarization operator (due to the breaking of the spatial symmetry by the external magnetic field), related to the so-called axial anomaly. The path integrals and functional derivation are widely used to obtain the self-energy and vertex operators, and the Dyson equations. The inadequate introduction of a chiral chemical potential in the standard model is discussed for the Weinberg-Salam model for electroweak interactions.

CP violation in mixing and oscillations in a toy model for leptogenesis with quasi-degenerate neutrinos

We study the sources of CP violation for baryogenesis models with quasi-degenerate neutrinos. Our approach is to use the renormalized propagator in a quantum field theory model of neutrino oscillations, paying close attention to unitarity requirements. From the probabilities of lepton number violating processes obtained in this way, we derive a source term for the time evolution of the lepton asymmetry. The source term has contributions that can be identified with CP violation from mixing, oscillations and interference between both. Given that this source term does not involve processes with unstable particles in the initial or final states, neither does it require to calculate number densities of neutrinos, no subtraction of real intermediate states must be performed. In equilibrium the source term is null, as demanded by unitarity and CPT invariance, due to a cancellation between the terms coming from CP violation in mixing and oscillations. The calculations are done in a simple scalar toy model, and the resummed propagator is diagonalized at first order in the decay widths over the mass difference. We also comment on the effect of the interference term, which is mild at the order we work, but seems to become more important with increasing degeneracy.

Phenomenological Effects of CPT and Lorentz Invariance Violation in Particle and Astroparticle Physics

It is well known that a fundamental theorem of Quantum Field Theory (QFT) set in flat spacetime ensures the CPT invariance of the theory. This symmetry is strictly connected to the Lorentz covariance, and consequently to the fundamental structure of spacetime. Therefore it may be interesting to investigate the possibility of departure from this fundamental symmetry, since it can furnish a window to observe possible effects of a more fundamental quantum gravity theory in a “lower energy limit”. Moreover, in the past, the inquiry of symmetry violations provided a starting point for new physics discoveries. A useful physical framework for this kind of search is provided by astroparticle physics, thanks to the high energy involved and to the long path travelled by particles accelerated by an astrophysical object and then revealed on Earth. Astrophysical messengers are therefore very important probes for investigating this sector, involving high energy photons, charged particles, and neutrinos of cosmic origin. In addition, one can also study artificial neutrino beams, investigated at accelerator experiments. Here we discuss the state of art for all these topics and some interesting new proposals, both from a theoretical and phenomenological point of view.

Tests of CPT invariance in gravitational waves with LIGO-Virgo catalog GWTC-1

A discovery of gravitational waves from binary black holes raises a possibility that measurements of them can provide strict tests of CPT invariance in gravitational waves. When CPT violation exists, if any, gravitational waves with different circular polarizations could gain a slight difference in propagating speeds. Hence, the birefringence of gravitational waves is induced and there should be a rotation of plus and cross modes. For CPT-violating dispersion relation $${\omega ^{2}=k^{2}}$$ ω 2 = k 2 $${\pm 2\zeta k^{3}}$$ ± 2 ζ k 3 , where a sign $${\pm }$$ ± denotes different circular polarizations, we find no substantial deviations from CPT invariance in gravitational waves by analyzing a compilation of ten signals of binary black holes in the LIGO-Virgo catalog GWTC-1. We obtain a strict constraint on the CPT-violating parameter, i.e., $$\zeta =0.14^{+0.22}_{-0.31}\times 10^{-15}\,\text {m}$$ ζ = 0 . 14 - 0.31 + 0.22 × 10 - 15 m , which is around two orders of magnitude better than the existing one. Therefore, this study stands for the up-to-date strictest tests of CPT invariance in gravitational waves.

Tests of the CPT Invariance at the Antiproton Decelerator of CERN

The Standard Model, the theory of particle physics is based on symmetries: both the structure of the composite particles and their interactions are derived using gauge invariance principles. Some of these are violated by the weak interaction like parity and CP symmetry, and even masses are created via spontaneous symmetry breaking. CPT invariance, the most essential symmetry of the Standard Model, states the equivalency of matter and antimatter. However, because of the lack of antimatter in our Universe it is continuously tested at CERN. We overview these experiments: measuring the properties of antiprotons as compared to those of the proton at the Antiproton Decelerator and also searching for antimatter in cosmic rays.

Estimation of antihydrogen properties in experiments with small signal deficit

For a class of precision CPT-invariance test measurements using antihydrogen, a deficit in the data indicates the presence of the signal. The construction of classical confidence intervals for the properties of the antiatoms from measurements may pose a challenge due to the limited statistics experimentally available. We use the Feldman–Cousins (Feldman and Cousins, Phys. Rev. D , 57 , 3873. ( doi:10.1103/PhysRevD.57.3873 )) method to estimate model parameters for such a low count rate measurement. First, we construct confidence intervals for the Poisson process with a known background and an unknown signal deficit. Then the generalized Monte Carlo version of the method is applied to the use case of the hyperfine transition frequency measurement of the ground-state antihydrogen atom, where the expected double-dip resonance line shape and the mean background is assumed to be known. We find that confidence intervals of the antihydrogen properties could be obtained already from low statistics data. We also discuss how the method may be extended to allow estimation of additional model parameters.

Can the universe be described by a wave function?

Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkhoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the “mostly empty” universe we observe around us cannot be described by an exact wave function [Formula: see text]. Rather, the weakly coupled particles we see are approximate quasiparticles arising as excitations of a “fuzz”. The “fuzz” does have an exact wave function [Formula: see text], but this exact wave function does not directly describe local particles. The argument proceeds by relating the cosmological setting to the black hole information paradox, and then using the small corrections theorem to show the impossibility of an exact wave function describing the visible universe.