In left-right symmetric models ͑LRSMs͒ the light neutrino masses arise from two sources: the seesaw mechanism and a vacuum expectation value of an SU(2) L triplet. If the left-right symmetry breaking v R is low, v R Շ15 TeV, the contributions to the light neutrino masses from both the seesaw mechanism and the triplet Yukawa couplings are expected to be well above the experimental bounds. We present a minimal LRSM with an additional U͑1͒ symmetry in which the masses induced by the two sources are below the eV scale and the twofold problem is solved. We further show that, if the U͑1͒ symmetry is also responsible for the lepton flavor structure, the model yields a small mixing angle within the first two lepton generations.
The method to obtain massive non-relativistic states from the Poincaré algebra is twofold. First, following İnönü and Wigner, the Poincaré algebra has to be contracted to the Galilean one. Second, the Galilean algebra has to be extended to include the central mass operator. We show that the central extension might be properly encoded in the non-relativistic contraction. In fact, any İnönü–Wigner contraction of one algebra to another corresponds to an infinite tower of Abelian extensions of the latter. The proposed method is straightforward and holds for both central and non-central extensions. Apart from the Bargmann (non-zero mass) extension of the Galilean algebra, our list of examples includes the Weyl algebra obtained from an extension of the contracted SO(3) algebra, the Carrollian (ultrarelativistic) contraction of the Poincaré algebra, the exotic Newton–Hooke algebra and some others.
This paper is dedicated to the memory of Laurent Houart (1967–2011).
The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m 2 /H 2 . In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.
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