Implications of Kleinian relativity

Abstract

Inspired in metamaterials, we present a covariant mechanics for particles in Kleinian spacetime and show some of its effects, such as time contraction and length dilatation. We present the new expressions for relativistic momentum and energy for a point-like particle. To illustrate the new mechanics, we describe the particle motion under a uniform Newtonian gravitational field. We also revisit the free spin-half particle problem in Kleinian spacetime, discuss some quantum implications, like the constraint on the dispersion relation for Weyl fermions, and adapt a metamaterial analog system to Klein spacetime.

The REDTOP experiment: Rare $\eta/\eta^{\prime}$ Decays To Probe New Physics

“…Since the SM expectation for Br η ( ) → e + e − is still two orders of magnitude below current experimental sensitivity, there is significant room for New Physics contributions to this final state. REDTOP should have an expected sensitivity to Br η → e + e − with O(10 −10 ) precision, and to Br η → e + e − with O(10 −9 ) precision, which should lead to a sensitivity to a − η ( ) mixing angles of order θ aη ∼ O(10 −4 ) and θ aη ∼ O(10 −2 ), respectively (see [63], Sec. VIII, and Table XXXIV).…”

“…Low-energy strong interaction effects, however, introduce large uncertainties to the calculation of axio-hadronic η and η decays. In [63], this calculation was performed in the framework of Resonance Chiral Theory (RχT), an interpolating effective theory between the low-energy χPT framework and the microscopic QCD description. RχT encodes the most prominent features of nonperturbative strong dynamics by incorporating the low-lying QCD resonances and extending the principle of vector meson dominance [66].…”

“…• p + Li → η + X with η → π 0 π 0 a and a → e + e − • p + Li → η + X with η → π + π − a and a → e + e − Three separate sets with ∼350,000 events were generated, each corresponding to a benchmark parameter sets listed in Table I of Ref. [63]. A forth sample, with the parameters corresponding to the Standard Model prediction, was also generated.…”

Classical Kalb-Ramond field theory in curved spacetimes

“…The Kalb-Ramond fields can be obtained via tensor calculus (30) and (33), via ordinary vector formalism (37), ( 38) and ( 39), but in order to illustrate the power of exterior differential calculus, we will consider the static Kalb-Ramond field created by a localized source distribution in various spacetimes, assimilated to fixed backgrounds, using mainly Eqs. ( 21) and (24).…”

“…Other particular metrics not considered in this paper could also be of interest. Let us mention the case of Kleinian metrics with specific signature alterations leading to the emergence of two time components [36,37]. This may be of specific interest in the context of the identification of the 2-form R.…”