Probing Lorentz violation effects via a laser beam interacting with a high-energy charged lepton beam

Eur. Phys. J. C (2019) 79:224 https://doi.org/10.1140/epjc/s10052-019-6716-5 Regular Article - Theoretical Physics Probing Lorentz violation effects via a laser beam interacting with a high-energy charged lepton beam Seddigheh Tizchang1,a , Rohoollah Mohammadi2,3,b , She-Sheng Xue4,c 1 School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran 2 Iranian National Museum of Science and Technology (INMOST), P.O. Box 11369-14611, Tehran, Iran 3 School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran 4 ICRANet and Department of Physics, University of Rome“Sapienza”, P.le A. Moro 5, 00185 Rome, Italy Received: 16 November 2018 / Accepted: 22 February 2019 © The Author(s) 2019 Abstract In this work, the conversion of linear polarization of a laser beam to circular one through its forward scattering by a TeV order charged lepton beam in the presence of Lorentz violation correction is explored. We calculate the ratio of circular polarization to linear one (Faraday conversion phase φFC ) of the laser beam interacting with either electron or the muon beam in the framework of the quantum Boltzmann equation. Regarding the experimentally available sensitivity to the Faraday conversion φFC  10−3 − 10−2 , we show that the scattering of a linearly polarized laser beam with energy k0 ∼ 0.1 eV and an electron/muon beam with flux ¯e,μ ∼ 1010 /1012 TeV cm−2 s−1 places an upper bound on the combination of lepton sector Lorentz violation coefficients cμν components (cT T +1.4 c(T Z ) +0.25(c X X +cY Y + 2 c Z Z ). The obtained bound on the combination for the electron beam is at the 4.35 × 10−15 level and for the muon beam at the 3.9 × 10−13 level. It should be mentioned that the laser and charged lepton beams considered here to reach the experimentally measurable φFC are currently available or will be accessible in the near future. This study provides a valuable supplementary to other theoretical and experimental frameworks for measuring and constraining Lorentz violation coefficients. 1 Introduction Usually, radiation can be both linearly and circularly polarized. It is well known that when an initially unpolarized photon scatters off a free electron through Compton scattering, it results in linear polarization but not circular polarization a e-mail: b e-mail: c e-mail: 0123456789().: V,-vol of the scattered radiation. However, it is shown that Compton scattering in the presence of external background fields, similar to strong magnetic fields [1–4] or theoretical (nontrivial) backgrounds such as non-commutativity in spacetime [2,5,6] and Lorentz symmetry violation [2], can produce circular polarization. Moreover, nonlinear effects such as the nonlinear Euler–Heisenberg effect can cause converting of photons from linear polarization to circular polarization [3,7,8]. In this paper, we consider Compton scattering through the collision of laser photons and high-energy charged lepton beams in the presence of Lorentz violation (LV) effects to study the generation of circular polarization in an Earth-based laboratory. Lorentz symmetry is a fundamental symmetry of the standard model in flat space-time and quantum field theory. However, it can be violated by an underlying theory at the Planck scale [9,10]. There are many theories in which the Lorentz symmetry is violated spontaneously, such as string theory [11–13], quantum gravity [14– 17] and non-commutative space-time [18–20]. Meanwhile, it is also possible to study LV in a general model-independent way in the context of effective field theory known as the Standard Model extension (SME). In the SME Lagrangian, the observer Lorentz symmetry (i.e. change of coordinate) is obeyed, while the particle Lorentz symmetry (i.e. boosts on particles and not on background fields) is violated [21,22]. The SME contains all feasible Lorentz breaking operators created by known fields of the standard model of dimension three or more. These operators are contracted with coefficients representing backgrounds and preferred directions in space-time [21,23,24] and can describe a small Lorentz symmetry violation at available energies. Generally, the number of coefficients is infinite. By the way, it is possible to choose a minimal subset of the SME with finite coefficients. The minimal SME contains renormalizable operators which are invariant under the gauge group of the standard model, 123 224 Page 2 of 9 Eur. Phys. J. C (2019) 79:224 SU (3) × SU (2) × U (1). In recent years, new studies have provided new types of constraints on the LV parameters [25– 29]. Among them astrophysical [30–32] and Earth [33–35] systems have shown stronger bounds on the LV parameters [36]. Observation of circularly polarized photons in lepton and photon scattering can be a proof of LV and might result in new physics beyond the standard model. In contrast, constraints on circular polarization might improve the available bounds on the parameters of the SME. The paper is organized as follows: in Sect. 2 we briefly introduce the Stokes parameter formalism and the generalized Boltzmann equation. In Sect. 3 we study the effect of LV on the collision of the relativistic lepton beam (electron/muon) and the laser. In Sect. 4 we give the value of the FC phase of the laser beam through this interaction. Finally, we discuss the results in the last section. polarized [37]. Now the phase difference (φ = φR − φL ) results in mixing between the U and V Stokes parameters, known as Faraday conversion (FC). The evolution of the Stokes parameter V given by this mechanism is obtained [1,39]: 2 Stokes parameters and quantum Boltzmann equation D̂i j (p) = (2π )3 2 p 0 δ (3) (0)ρi j (p). Normally, the polarization of a laser beam can be described by the well-known Stokes parameters coming in four dimensions, I , Q, U and V . I denotes the intensity of the laser beam, V shows the difference between left- and right-circular polarization Q and U indicate the linear polarization. Q is defined by the intensity difference between the polarized components of the electromagnetic wave in the direction of the x and y axes. U quantifies the discrepancy between 45◦ and 135◦ counted from the positive x axis, to the reference plane [37].The linear polarization can also be shown by vector P ≡ Q 2 + U 2 [38]. The Stokes parameters can be specified by a superposition of two opposite, right- and lefthand circular polarization contributions, (R̂) and (L̂): In order to figure out the time evolution of the density matrix (Stokes parameters), it is convenient to use the Heisenberg equation E L = E 0L cos[ω0 t − φL ], E R = E 0R cos[ω0 t − φR ]. (1) dφ FC , (4) dt where φFC is the FC phase. Generally, light traversing a relativistic plasma undergoes both FC and FR. Let us consider an ensemble of photons which is described by the density matrix ρi j ≡ (|i ><  j |/trρ). The densit (...truncated)