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- Cosmic-ray fermion decay by emission of on-shell W bosons with CPT violationPublication . Colladay, D.; Noordmans, J. P.; Potting, RobertusWe study CPT and Lorentz violation in the electroweak gauge sector of the Standard Model in the context of the Standard-Model Extension. In particular, we consider the Lorentz-violating and CPT-odd Chern-Simons like parameter for the W boson, which is thus far unbounded by experiment. We demonstrate that any nonzero value of this parameter implies that, for sufficiently large energies, one of the polarization modes of the W boson propagates with spacelike four-momentum. In this scenario, an emission of W bosons by ultra-high-energy cosmic rays is possible. We calculate the induced fermion energy-loss rate, and we deduce the first limit on the pertinent Lorentz-and CPT-violating parameter that couples to the W boson. Consistency between the quantum description in various reference frames is preserved by using a recently formulated covariant quantization procedure for massive photons and applying it to the W bosons.
- Cherenkov radiation with massive, CPT-violating photonsPublication . Colladay, Don; McDonald, Patrick; Potting, RobertusThe source of CPT violation in the photon sector of the Standard Model Extension arises from a Chern-Simons-like contribution that involves a coupling to a fixed background vector field k(AF)(mu). These Lorentz- and CPT-violating photons have well-known theoretical issues that arise from missing states at low momenta when k(AF)(mu) is timelike. In order to make the theory consistent, a tiny mass for the photon can be introduced, well below current experimental bounds. The implementation of canonical quantization can then be implemented as in the CPT-preserving case by using the Stuckelberg mechanism. We explicitly construct a covariant basis of properly normalized polarization vectors at fixed three-momentum satisfying the momentum space field equations, in terms of which the vector field can be expanded. As an application of the theory, we calculate the Cherenkov radiation rate for the case of purely timelike k(AF)(mu) and find a radiation rate at high energies that has a contribution that does not depend on the mass used to regulate the photons.
- CPT and Lorentz violation in the electroweak sectorPublication . Colladay, D; Noordmans, Jacob; Potting, RobertusLong ago, Carroll, Field and Jackiw introduced CPT-violation in the photon sector by adding a dimension-3 gauge-invariant term parametrized by a constant four-vector parameter k(AF) to the usual (Maxwell) Lagrangian, deriving an ultra-tight bound from astrophysical data. Here, we will discuss recent work studying the extension of this term to the full electroweak gauge sector of the Standard Model. In the context of the Standard Model Extension, CPT and Lorentz violation arises from two gauge-invariant terms parametrized by the four vectors k(1) and k(2). First we will show how upon spontaneous breaking of the electroweak gauge symmetry these two terms yield Lorentz-violating terms for the photon and the W and Z bosons. As it turns out, the resulting modified dispersion relations for the W bosons yield spacelike momentum for one of its propagating modes at sufficiently large energy. This in turn allows for the possibility of Cherenkov-like W-boson emission by high-energy fermions such as protons, provoking their decay. Analysis of ultra-high-energy cosmic ray data allows for bounding the previously unbound parameter k(2), and, by combination with the ultra-tight bound on k(AF), the parameter k(1).
- Structural aspects of Lorentz-violating quantum field theoryPublication . Cambiaso, M; Lehnert, R; Potting, RobertusIn the last couple of decades the Standard Model Extension has emerged as a fruitful framework to analyze the empirical and theoretical extent of the validity of cornerstones of modern particle physics, namely, of Special Relativity and of the discrete symmetries C, P and T (or some combinations of these). The Standard Model Extension allows to contrast high-precision experimental tests with posited alterations representing minute Lorentz and/or CPT violations. To date no violation of these symmetry principles has been observed in experiments, mostly prompted by the Standard-Model Extension. From the latter, bounds on the extent of departures from Lorentz and CPT symmetries can be obtained with ever increasing accuracy. These analyses have been mostly focused on tree-level processes. In this presentation I would like to comment on structural aspects of perturbative Lorentz violating quantum field theory. I will show that some insight coming from radiative corrections demands a careful reassessment of perturbation theory. Specifically I will argue that both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted given that the asymptotic single-particle states can receive quantum corrections from Lorentz-violating operators that are not present in the original Lagrangian.
- CPT and Lorentz Violation in the Photon and Z-Boson SectorPublication . Colladay, Donald; Noordmans, Jacob; Potting, RobertusViolation of CPT and Lorentz symmetry in the photon sector is described within the minimal Standard-Model Extension by a dimension-3 Chern-Simons-like operator parametrized by a four-vector parameter k(AF) that has been very tightly bounded by astrophysical observations. On the other hand, in the context of the SU (2) x U (1) electroweak gauge sector of the Standard-Model Extension, CPT and Lorentz violation is described similarly, by dimension-3 operators parametrized by four-vector parameters k(1) and k(2). In this work, we investigate in detail the effects of the resulting CPT and Lorentz violation in the photon and Z-boson sectors upon electroweak-symmetry breaking. In particular, we show that, for the photon sector, the relevant Lorentz-violating effects are described at the lowest order by the kAF term, but that there are higher-order momentum-dependent effects due to photon-Z boson mixing. As bounds on CPT and Lorentz violation in the Z sector are relatively weak, these effects could be important phenomenologically. We investigate these effects in detail in this work.
- Covariant quantization of CPT-violating photonsPublication . Colladay, D.; McDonald, P.; Noordmans, J. P.; Potting, RobertusWe perform the covariant canonical quantization of the CPT - and Lorentz-symmetry-violating photon sector of the minimal Standard-Model Extension, which contains a general (timelike, lightlike, or spacelike) fixed background tensor k(AF)(u). Well-known stability issues, arising from complex-valued energy states, are solved by introducing a small photon mass, orders of magnitude below current experimental bounds. We explicitly construct a covariant basis of polarization vectors, in which the photon field can be expanded. We proceed to derive the Feynman propagator and show that the theory is microcausal. Despite the occurrence of negative energies and vacuum-Cherenkov radiation, we do not find any runaway stability issues, because the energy remains bounded from below. An important observation is that the ordering of the roots of the dispersion relations is the same in any observer frame, which allows for a frame-independent condition that selects the correct branch of the dispersion relation. This turns out to be critical for the consistency of the quantization. To our knowledge, this is the first system for which quantization has consistently been performed, in spite of the fact that the theory contains negative energies in some observer frames.
- Lorentz and CPT violationPublication . Potting, Robertus; Branco, GC; EmmanuelCosta, D; Felipe, RG; Joaquim, FR; Lavoura, L; PalomaresRuiz, S; Rebelo, MN; Romao, JC; Silva, JP; SilvaMarcos, JIDuring the past two decades there has been a growing interest in the possibility that Lorentz and/or CPT might not be exact symmetries of Nature. In this short review, we present the current state of affairs, addressing both theoretical and experimental/observational issues. We pay particular attention to the role that has been played by the so-called Standard Model Extension
- Cherenkov-like emission of Z bosonsPublication . Colladay, D.; Noordmans, Jacob; Potting, Robertus; Grzadkowski, B; Kalinowski, J; Krawczyk, MWe study CPT and Lorentz violation in the electroweak gauge sector of the Standard Model in the context of the Standard-Model Extension (SME). In particular, we show that any non-zero value of a certain relevant Lorentz violation parameter that is thus far unbounded by experiment would imply that for sufficiently large energies one of the helicity modes of the Z boson should propagate with spacelike four-momentum and become stable against decay in vacullin. In this scenario, Cherenkov-hike radiation of Z bosons by ultra-highenergy cosmic-ray protons becomes possible. We deduce a bound on the Lorentz violation parameter from the observational data on ultra-high energy cosmic rays.