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- 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).
- 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.
- 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.