Effects of CPT and Lorentz invariance violation on pulsar kicks

Abstract

The breakdown of Lorentz's and CPT invariance, as described by the Extension of the Standard Model, gives rise to a modification of the dispersion relation of particles. Consequences of such a modification are reviewed in the framework of pulsar kicks induced by neutrino oscillations (activesterile conversion). A peculiar feature of the modified energy-momentum relations is the occurrence of terms of the form δΠ ·p, where δΠ accounts for the difference of spatial components of flavor depending coefficients which lead to the departure of the Lorentz symmetry, andp = p/p, being p the neutrino momentum. Owing to the relative orientation of p with respect to δΠ, the coupling δΠ ·p may induce the mechanism to generate the observed pulsar velocities. Topics related to the velocity distribution of pulsars are also discussed. PACS No.: 11.30.Cp, 11.30.Er, 97.60.Gb, 14.60.Pq The studies of a possible breakdown of the fundamental symmetries in physics represent a very active research area. As suggested by Kostelecký and Samuel, String/M theory provides a scenario in which a departure of the Lorentz invariance might manifest [1]. Recently, these investigations have been reconsidered in the context of D-branes [2], Loop Quantum Gravity [3][4][5], Non-Commutative Geometry [6], and through the spacetime variation of fundamental coupling constants [8]. For modern tests on Lorentz invariance, see [7] According to Ref.[1], Lorentz's invariance violation (due to non trivial solution of (open) string field theory) follows from the observation that the vacuum solution of the theory could spontaneously violate the Lorentz and CPT invariance, even though such symmetries are satisfied by the underlying theory. The breakdown of these fundamental symmetries occurs in the Extension of the Standard Model, and only operators of mass with dimension four or less [9,10] are involved in order that the standard model power-counting renormalizability is preserved. In a recent work by Kostelecký and Mewes [11], it has been studied the general formalism for violations of Lorentz and CPT symmetry in the neutrino sector. The generalized equation of motion for free fermions (neutrinos in our case) is given by (we shall use natural units c = 1 = )where the spinor ψ B contains all the fields and their conjugates, the indices A and B range over all 2N possibility {f, f C }, being f = e, µ, τ, . . . the neutrino flavors and f C A = C AB f B . C is the symmetric matrix with non zero components C f f C = 1. Γ ν AB and M AB are 4 × 4 matrices in the spinor space, and can be decomposed using the basis of γ matricesandThe coefficients a µAB , b µAB , c µν AB , . . . are constants and in general they are flavor depending, and, and H µν AB preserve the CPT invariance, while a µAB , b µAB , e µAB , f µAB violate CPT and Lorentz invariance. Finally m and m 5 are Lorentz and CPT conserving.The time evolution of neutrinos is governed by the effective Hamiltonianwhere (c L ) µν ab = (c + d) µν ab and (a L ) µ ab = (a + b) µ ab , the vector (ǫ + ) ν = 1 √ 2 (0, ǫ ...

Lorentz- andCPT-violating models for neutrino oscillations

“…Nonetheless, it suffices to reproduce the data for atmospheric neutrinos via Eq. (18). The other degree of freedom in the two coefficientsk (p) ,c (q) determines the onset of the Lorentz-violating seesaw.…”

“…The interferometric nature of particle oscillations suggests that sensitive neutrino or neutralmeson experiments might well yield the first detectable signals of tiny Lorentz violation. In the neutrino sector, recent SME-based phenomenological studies [8,9,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and methodologies for experimental analysis [34,35] have spurred searches for Lorentz and CPT violation by the LSND [36], Super-Kamiokande (SK) [37], MINOS [38,39], MiniBooNE [40], and IceCube collaborations [41]. Searches have also been performed with neutral mesons [42,43], and recent D0 results suggest some evidence for anomalous CP violation [44] that could be attributed to Lorentz and CPT violation [45].…”

Perturbative Lorentz andCPTviolation for neutrino and antineutrino oscillations

“…A few consider also anisotropic effects [13,[34][35][36][37][38]. Here, we treat the general case, allowing all components of (a L ) α ab and (c L ) αβ ab to be nonzero.…”

Modern Tests of Lorentz Invariance

“…29It has recently been suggested that Lorentz violation might play a role in the formation of the pulsar itself, specifically in large pulsar anomalous velocities [192]. …”