Tachyonic field theory and neutrino mass running

Abstract

Abstract:In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino.(ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations. PACS

From Generalized Dirac Equations to a Candidate for Dark Energy

“…Adding to the difficulties, we notice that recent experimental claims regarding the conceivable observation of highly superluminal neutrinos have turned out to be false. One may point out that a relative deviation v = c (1+δ) with δ ∼ 10 −5 at E ∼ 30 GeV, as claimed by some recent experimental collaborations, would correspond to a negative neutrino mass square in the order of ∼ −(100 MeV) 2 , if one assumes a Lorentz-invariant dispersion relation [34]. Still, there is at present no conclusive answer regarding the conceivable superluminality of at least one neutrino flavor [35][36][37][38][39], and it is intriguing that all available direct measurements of the neutrino mass square have resulted in negative expectation values, still compatible with zero within experimental uncertainty, whereas published experimental best estimates for the neutrino speed [40][41][42][43] have been superluminal, again still compatible with the speed of light within experimental error.…”

Dynamics of neutrino wave packet in the Tachyon-like Dirac equation

“…This suggests that such particles are theoretically possible but are unstable and do not decrease their energy by increasing their velocity, as the classical tachyon theory would predict [26]. This hypothesis has been deeply investigated by Jentschura [33], who proposed possible mechanisms of decay. The first validation test of the obtained solutions is represented by the study of the Zitterbewegung effect.…”

Production of tachyonic neutrino in matter

“…Moreover, as usually expected in pair creation, the module of the vector impulse is the same for both particles n andn. From the second equation of (20), we obtain the following:…”

“…Since b > 1 and q  cos 1, we can always find a superluminal velocity u t and an angle θ for which the product b q cos is unitary so that equation (21) is equal to the first equation of (20). Therefore, from a photon, it is always possible to create a/ n n tachyon pair, even in vacuum, due to the fact that, in the momentum-energy dispersion relation of a tachyon, the mass term is always negative.…”

“…The study of tachyons in the framework of quantum mechanics uses models developed in the last few decades that coherently extend the theory of relativity to superluminal motion. Some of these theories violate Lorentz invariance and describe tachyons as unstable particles that decay into ordinary (subluminal) particles [19,20]. Other models instead treat tachyons as stable particles that are parts of the real world [21,22].…”