Testing κ-Poincaré with neutral kaons

In recent work on experimental tests of quantum-gravity-motivated phenomenological models, a significant role has been played by the so-called “κ” deformations of Poincaré symmetries. Sensitivity to values of the relevant deformation length λ as small as 5 · 10m has been achieved in recent analyses comparing the structure of κPoincaré symmetries with data on the gamma rays we detect from distant astrophysical sources. We investigate violations of CPT symmetry which may be associated with κ-Poincaré in the physics of the neutral-kaon system. A simple estimate indicates that experiments on the neutral kaons may actually be more λ-sensitive than corresponding astrophysical experiments, and may already allow to probe values of λ of order the Planck length. Marie Curie Fellow of the European Union (address from February 2000: Dipartimento di Fisica, Universitá di Roma “La Sapienza”, Piazzale Moro 2, Roma, Italy) On leave of absence from Dipartimento di Scienze Fisiche, Universitá di Napoli, Mostra D’Oltremare, Pad. 19, Napoli, Italy. It has been recently realized [1, 2, 3] that observations of gamma rays from distant astrophysical sources can be used to set stringent bounds on the length parameter that characterizes “κ-Poincaré”, one of the most studied scenarios for the dimensionful quantum deformation of Poincaré symmetries, which has been developed most notably in Refs. [4, 5, 6]. This realization has attracted significant attention because the level of sensitivity of planned gamma-ray observatories (see, e.g., Refs. [7, 8]) should be sufficient to explore values of the length parameter as small as the Planck length (Lp ∼ 1.6 · 10m). Only very few other experimental contexts [9, 10, 11, 12] can achieve this type of “Planckian sensitivity”, and such sensitivity levels with respect to κ-Poincaré are especially meaningful in light of the fact that it appears likely [10, 13, 14, 15, 16, 17] that the space-time foam of quantum gravity would induce a dimensionful (although, of course, not necessarily “κ”) deformation of Poincaré symmetries. We are here interested in exploring the consequences of the fact that [18] the κ-Poincaré deformation would also induce a corresponding deformation of CPT invariance. There is a wide literature on the idea that ordinary CPT invariance might be violated by quantum-gravity effects (see, e.g., Refs. [9, 10, 19, 20, 21, 22]), but usually the relevant quantum-gravity scenarios are not developed to the point of allowing a definite prediction for the effects of violation of ordinary CPT invariance, and one is led to the use of multi-parameter phenomenological approaches. As observed in Ref. [18], in the κ-Poincaré framework it appears plausible that one should arrive at a definite prediction for all CPT violating effects parametrized only by the single length parameter λ characterizing the underlying non-commutative “κ-Minkowski” space-time [5] [x , t] = ıλ x c , [x , x] = 0 (1) where c is the conventional speed-of-light constant and j, k = 1, 2, 3. Such a single-parameter description of CPT violation within the κ-Poincaré framework however still requires [18] the development of several mathematical tools on the non-commutative κ-Minkowski space-time. Since it appears likely that a long time will be necessary for these technical developments to mature, in this Letter we present a simple heuristic estimate of κ-Poincaré-induced CPT violation in the neutral-kaon system. As already emphasized in Ref. [18], the neutral-kaon system, with its delicate balance of mass/length scales, can provide a natural context for setting bounds on λ through tests of CPT invariance. It is in fact well established [9, 19, 20, 21, 22] that observable properties of the neutral-kaon system are extremely sensitive to any deviation from ordinary CPT invariance. Our heuristic estimate is based on the κ-deformed dispersion relation [1, 4, 5, 6, 18]