Very Special Relativity Research Articles

Light-light scattering in Very Special Relativity Quantum Electrodynamics and cosmic anisotropies

We consider scattering of light by light in Very Special Relativity (VSR) Quantum Electrodynamics (QED) with a non-zero photon mass. In order to preserve gauge invariance and Sim(2) symmetry we made use of a recently introduced infrared regularization of VSR theories. Additionally, we show that all one loop diagrams with any number of photon external legs and zero fermion legs reduce to the standard QED result with the effective electron mass, as required by unitarity. It follows that the Euler-Heisenberg Lagrangian is the same as in QED. The total cross section of scattering of light by light exhibits tiny anisotropies that could be detected at cosmological scales. In particular, they should be looked at the Cosmic Microwave Background (CMB) Radiation for low photon frequencies.

Duality between the Maxwell-Chern-Simons and self-dual models in very special relativity

This work investigates the classical and quantum duality between the SIM(1)-Maxwell-Chern-Simons (MCS) model and its self-dual counterpart. Initially, we focus on free-field cases to establish equivalence through two distinct approaches: comparing the equations of motion and utilizing the master Lagrangian method. In both instances, the classical correspondence between the self-dual and MCS dual fields undergoes modifications due to very special relativity (VSR). Specifically, the duality is established when the associated VSR-mass parameters are identical, and the dual field is introduced through a non-local VSR correction. Furthermore, we analyze the duality when the self-dual model is minimally coupled to fermions. As a result, we demonstrate that Thirring-like interactions, corrected for non-local VSR contributions, are included in the MCS model. Additionally, we establish the quantum equivalence of the models by performing a functional integration of the fields and comparing the resulting effective Lagrangians.

Renormalization of Very Special Relativity gauge theories

Mandelstam-Leibbrandt (ML) regularization of Very Special Relativity (VSR) amplitudes in momentum space depends on two fixed null vectors nμ, {overline{n}}_{mu } besides external momenta. ML is known to preserve gauge invariance and naive power counting. The second null vector {overline{n}}_{mu } destroys the Sim(2) symmetry of the VSR model. We devise a systematic procedure to take the {overline{n}}_{mu } → 0 limit to recover the lost Sim(2) symmetry. The procedure produces Sim(2) and gauge invariant loop amplitudes. We show how to use this method to remove unphysical terms from the Non Relativistic Potential of Very Special Relativity Quantum Electrodynamics (VSR QED) with a massive photon. Then we compute the one loop renormalization of VSR QED. Finally we derive the anomalous magnetic moment of the electron, modified by neutrino and photon mass; and comments on the phenomenological implications.

Induced non-Abelian Chern–Simons effective action in very special relativity

In this paper, we study the one-loop induced effective action for a non-Abelian gauge field in the very special relativity (VSR) framework in a $$(2+1)$$ -dimensional spacetime. We show that there are new graphs contributing to the amplitudes of gluon n-point functions, e.g. $$\langle GG\rangle $$ , $$\langle GGG \rangle $$ and $$\langle GGGG \rangle $$ , originating from the non-local couplings generated in VSR. Using the one-loop analysis of the relevant graphs, we evaluate the VSR corrections to the induced kinetic term of the non-abelian gauge field action in three dimensions. Next, by applying the Ward identity, we determine the general tensorial structure for the amplitude of $$\langle GG\rangle $$ in VSR, which is valid at any order of the loop analysis. Moreover, we discuss the leading VSR corrections to the non-abelian Chern–Simons and Yang–Mills action through the analysis of $$\langle GG\rangle $$ , $$\langle GGG \rangle $$ and $$\langle GGGG \rangle $$ . In order to highlight the VSR effects, we present the VSR modification of non-Abelian Chern–Simons effective action and then obtain the equation of motion for the non-Abelian gauge field. As a result, we observe that the well-known pure gauge solution does not hold in the presence of VSR effects.

Very special linear gravity: A gauge-invariant graviton mass

Linearized gravity in the Very Special Relativity (VSR) framework is considered. We prove that this theory allows for a non-zero graviton mass mg without breaking gauge invariance nor modifying the relativistic dispersion relation. We find the analytic solution for the new equations of motion in our gauge choice, verifying as expected the existence of only two physical degrees of freedom. Finally, through the geodesic deviation equation, we confront some results for classic gravitational waves (GW) with the VSR ones: we see that the ratios between VSR effects and classical ones are proportional to (mg/E)2, E being the energy of a graviton in the GW. For GW detectable by the interferometers LIGO and VIRGO this ratio is at most 10−20. However, for GW in the lower frequency range of future detectors, like LISA, the ratio increases significantly to 10−10, that combined with the anisotropic nature of VSR phenomena may lead to observable effects.

Temperature effects for $$e^-+e^+\rightarrow \mu ^-+\mu ^+$$ scattering in very special relativity

The electron-positron scattering process is investigated in the context of very special relativity (VSR). This theory assumes that the true symmetry of nature is not the full Lorentz group, but some of its subgroups, such as the subgroups $SIM(2)$ and $HOM(2)$. In this context, the cross-section for electron-positron scattering at finite temperature is calculated. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. Our result shows that the cross-section is changed due to both effects, the VSR contributions and temperature effects. An estimated value for the VSR parameter using experimental data available in the literature is discussed.

Casimir effect in Very Special Relativity at finite temperature

Recently a great deal of interest in field theories formulated in a Lorentz violating framework has been developed. Here the Very Special Relativity (VSR) is considered. The main aspect in the VSR proposal is that laws of physics are invariant under the subgroups of the Poincaré group preserving the basic elements of special relativity. An important point is that the photon acquires a mass. In this context, the energy–momentum tensor for the electromagnetic field is calculated. From this, the Stefan–Boltzmann law and Casimir effect at finite temperature in VSR are obtained. The effects of temperature are introduced using the Thermo Field Dynamics (TFD) formalism. A comparative analysis with the Casimir effect for the standard electromagnetic case is developed.

Very special relativity induced phase due to neutrino magnetic moment in neutrino oscillation

In Very Special Relativity (VSR), the neutrino mass term is coupled with the VSR preferred axis, and hence Lorentz violating in nature. Beyond standard model physics predicts neutrino magnetic moment which is linearly proportional to the mass eigenstates of the neutrinos. We report an additive kinematic phase in the neutrino flavor oscillation due to the neutrino magnetic moment in the VSR framework. This phase is proportional to the coupling between the VSR preferred axis with the external magnetic field as well as the spin of the neutrino. Furthermore, we predict time variation in the neutrino oscillation with a period of one sidereal day.

Prospects of charged lepton flavor violation in very special relativity

Within very special relativity (VSR), neutrino mass term is non-local, Lorentz violating and does not need additional new fields beyond the standard model (SM). We can extend the SM by adding such VSR invariant mass terms for all the fermions. Gauging VSR mass term for standard model fermions induce charge lepton flavor violating (CLFV) processes, e.g., $$\mu \rightarrow e \gamma $$ , $$\mu \rightarrow eee$$ , and $$\tau \rightarrow \mu \mu \mu $$ , etc., which are absent in the SM at the tree level. We develop a procedure to calculate the three-body decay process for VSR framework and apply it to calculate the branching ratio of various CLFV processes. We also have revisited $$(g-2)_ \ell $$ in the context of VSR that put stringent constraint over the same flavor fermion photon interaction.

Bhabha scattering in very special relativity at finite temperature

In this paper the differential cross section for Bhabha scattering in the very special relativity (VSR) framework is calculated. The main characteristic of the VSR is to modify the gauge invariance. This leads to different types of interactions appearing in a non-local form. In addition, using the Thermo Field Dynamics formalism, thermal corrections for the differential cross section of Bhabha scattering in VSR framework are obtained.

Tree-level processes in very special relativity

In this paper we discuss the Bhabha and Compton scattering for the quantum electrodynamics defined in the framework of very special relativity (VSR). The main aspect of the VSR setting is that it admits different types of interactions appearing in a nonlocal form due to the modified gauge invariance. We explore the richness of these new couplings in the evaluation of the differential cross-section for these tree-level processes. We assess the behavior of the leading VSR Lorentz violation modifications by considering some special limits for the Bhabha and Compton cross-section expressions.

Lorentz-violating gaugeon formalism for rank-2 tensor theory

We develop a BRST symmetric gaugeon formalism for the Abelian rank-2 antisymmetric tensor field in the Lorentz-breaking framework. The Lorentz-breaking is achieved here by considering a proper subgroup of Lorentz group together with translation. In this scenario, the gaugeon fields together with the standard fields of the Abelian rank-2 antisymmetric tensor theory get mass. In order to develop the gaugeon formulation for this theory in very special relativity (VSR), we first introduce a set of dipole vector fields as a quantum gauge freedom to the action. In order to quantize the dipole vector fields, the VSR-modified gauge-fixing and corresponding ghost action are constructed as the classical action is invariant under a VSR-modified gauge transformation. Further, we present a Type I gaugeon formalism for the Abelian rank-2 antisymmetric tensor field theory in VSR. The gauge structures of Fock space constructed with the help of BRST charges are also discussed.

Thermal effects of very special relativity quantum electrodynamics

In this paper we compute the high-temperature effective Lagrangian for the quantum electrodynamics defined in the framework of Very Special Relativity (VSR). The main aspect of the VSR setting is that it modifies the gauge invariance, admitting now different types of interactions appearing in a nonlocal form. In order to explore the richness of these new couplings, we employ the usual Matsubara imaginary-time formalism to evaluate the effective Lagrangian at one and two-loop order. We illustrate the leading VSR Lorentz violation modifications by computing high-temperature internal energy density and establishing a comparison with the expected contribution.

Photon mass in very special relativity

In Very Special Relativity (VSR) a gauge invariant photon mass is allowed. We explore some consequences of keeping this parameter not zero. VSR-Maxwell equations are presented. In addition, we show modifications to the Feynman rules keeping the photon mass and we apply it in the computation of the electron self energy, whose result is free from infrared divergences. A computation of the Coulomb scattering is developed and a small signal of the privileged direction predicted in the theory is present at tree level. Radiative corrections are computed and the photon mass cancels due to soft photon emission as in the standard case.

Schwinger model à la Very Special Relativity

In this work, we show that Lorentz invariant theories in 1+1 dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in the presence of a mass term coming from the VSR invariant terms but without standard Lorentz invariant mass. Furthermore, it is shown that both the vector current as well as the axial current are modified with respect to the free case when the fermion is coupled to an external electromagnetic field due to the nonlocal operator present in the theory. The axial anomaly is computed, and we found the same standard topological invariant with a modification in the coefficient.

Inferring the covariant \u0398-exact noncommutative coupling in the top quark pair production at linear colliders

A novel non-minimal interaction of neutral right-handed fermion and abelian gauge field in the covariant Θ-exact noncommutative standard model (NCSM) which is invariant under Very Special Relativity (VSR) Lorentz subgroup, opens an avenue to study the top quark pair production at linear colliders. Here the non-minimal coupling is denoted as κ and the noncommutative (NC) scale Λ. In this work, we consider two types of analysis, one is without considering helicity basis technique and another, considering helicity of the initial and final state particles. Further, the realistic electron and positron beam polarization are taken into account to measure the NC parameters. In the first case, when κ is positive and certain values of Λ, we found that a specific threshold value of machine energy (optimal energy in the units of GeV) sqrt{s_0}left(simeq 2.52 varLambda +39right) may be quite useful to look for the signature of the spacetime noncommutativity with unpolarized beam. The statistical χ2 analysis of the azimuthal anisotropy which is due to broken rotational invariance about the beam axis, is quite possible when κ takes negative value 0 > κ > −0.596 which persuade a lower limit on NC scale Λ (1.0 to 2.4 TeV) at κmax = −0.296 with 95% C.L according to luminosity ranging from 100 fb−1 to 1000 fb−1 at machine energy sqrt{s}=1.4 TeV and 3.0 TeV. In another case, we perform detailed analysis for the polarized and unpolarized electron-positron beam to probe spacetime noncommutativity in light of following observables like azimuthal anisotropy, helicity correlation, and top quark helicity left-right asymmetry. The polarization of the initial beam {Pe− , Pe+ } = {−0.8, 0.3}({−0.8, 0.6}) enhances the ranges of lower limit on Λ, i.e. 1.13 to 2.80 TeV at κmax alongside the κmax enhanced into −0.5445 (−0.607) 95%C.L accord with luminosity and machine energy. Finally, we studied the intriguing mixing of the UV and the IR by invoking a specific structure of noncommutative anti-symmetric tensor Θμν which is invariant under translational T (2) VSR Lorentz subgroup.

Berwald spacetimes and very special relativity

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.

A Study of Gaugeon Formalism for QED in Lorentz Violating Background

At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus argued that some subgroup of proper Lorentz group could stand consistent and might possibly help us to circumvent this problem. It is this subgroup that goes by the name of Very Special Relativity (VSR). Apart from violating rotational symmetry, VSR is believed to preserve the very tenets of special relativity. The gaugeon formalism due to type-I Yokoyama and type-II Izawa are found to be invariant under BRST symmetry. In this paper, we analyze the scope of this invariance in the scheme of VSR. Furthermore, we will obtain VSR modified Lagrangian density using path integral derivation. We will explore the consistency of VSR with regard to these theories.

Phenomenological implications of very special relativity

We discuss several phenomenological implications of Very Special Relativity (VSR). It is assumed that there is a small violation of Lorentz invariance and the true symmetry group of nature is a subgroup called SIM(2). This symmetry group postulates the existence of a fundamental or preferred direction in space-time. We study its implications by using an effective action which violates Lorentz invariance but respects VSR. We find that the problem of finding the masses of fundamental fermions is in general intractable in the presence of VSR term. The problem can be solved only in special cases which we pursue in this paper. We next determine the signal of VSR in torsion pendulum experiment as well as clock comparison experiment. We find that VSR predicts a signal which is different from other Lorentz violating theories and hence a dedicated data analysis is needed in order to impose reliable limits. Assuming that signal is absent in data we determine the limits that can be imposed on the VSR parameters. We also study the implications of VSR in particle decay experiments taking the charged pion and kaon decay as an example. The effective interaction between the charged pion and the final state leptons is related to the fundamental VSR mass terms through a loop calculation. We also predict a shift in the angular dependence of the decay products due to VSR. In particular we find that these no longer display azimuthal symmetry with respect to the momentum of the pion. Furthermore the azimuthal and polar angle distributions show time dependence with a period of a sidereal day. This time dependence provides us with a novel method to test VSR in future experiments.

Axion mass bound in very special relativity

In this paper we propose a very special relativity (VSR)-inspired description of the axion electrodynamics. This proposal is based upon the construction of a proper study of the SIM(2)–VSR gauge-symmetry. It is shown that the VSR nonlocal effects give a health departure from the usual axion field theory. The axionic classical dynamics is analyzed in full detail, first by a discussion of its solution in the presence of an external magnetic field. Next, we compute photon–axion transition in VSR scenario by means of Primakoff interaction, showing the change of a linearly polarized light to a circular one. Afterwards, duality symmetry is discussed in the VSR framework.