Compton scattering off massive fundamental bosons of pure spin 1

Abstract

Relativistic particles with spins J > 0 are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of space-time provides not one but an infinity of such representations which are equivalent for free particles but yield different electromagnetic couplings upon gauging; thus the challenge is to develop criteria which allow us to select those of them which relate to physically detectable particles. We here take the position that the unitarity of the Compton scattering cross sections in the ultrarelativistic limit, when predicted by a consistent method for a spin-1 description, could provide such a criterion. We analyze the properties of massive fundamental spin-1 bosons transforming as antisymmetric tensors of second rank, (1, 0) ⊕ (0, 1). For this purpose, we employ the Poincaré covariant projector method, which provides consistent, gauge invariant, causal, and representation specific Lagrangians. This formalism yields a twofold extension of the Proca Lagrangian for the description of spin-1 bosons, first from an in-built g = 1 value of the gyromagnetic ratio to an unspecified general g = 1, and then from, single-parity, to parity-doublet degrees of freedom. We find different results for Compton scattering in these theories and track the differences to the lack of universality of the vector-antisymmetric-tensor equivalence theorem which is specific only to Proca's framework, and valid for g = 1, while it is violated within the more general Poincaré covariant projector formalism. Our main result is that a finite Compton scattering differential cross section in the ultrarelativistic limit requires us to consider the contributions of both parities in (1, 0) ⊕ (0, 1). On that basis, we conclude that massive spin-1 bosons transforming as antisymmetric tensors are physical parity doublets.

Bosonic and fermionic Weinberg-Joos (j,0) ⊕ (0,j) states of arbitrary spins as Lorentz tensors or tensor-spinors and second-order theory

“…This representation is equipped by separate Lorentz and Dirac indexes and provides a comfortable tool in calculations of scattering cross sections by means of the symbolic software package FeynCalc. A similar experience has been made in [17] regrading spin-1 transforming as (1, 0) ⊕ (0, 1), where the calculation of Compton scattering could not be tackled in terms of sixdimensional spinors and was instead easily executed in the anti-symmetric tensor-basis. We here specifically worked out the Compton scattering off 3 2 , 0 ⊕ 0, 3 2 and reported in eq.…”

“…The interest in such a study is motivated by the observation that distinct representation spaces of the Lorentz algebra so(1, 3) describe particles of different physical properties. For example, due to the representation dependence of the boost operator, the electromagnetic quadrupole and octupole moments of fundamental particles with spin-Same holds valid regarding spin-1 in the four-vector, 1 2 , 1 2 , versus the antisymmetric tensor, (1, 0) ⊕ (0, 1) [17]. In view of the expected production of new particles in the experiments run by the Large Hadron Collider it is important to have at ones disposal a reliable and comfortable to deal with universal calculation scheme for high spins transforming in carrier spaces of the Lorentz algebra different from the totally symmetric tensors of common use, the Weinberg-Joos states being the prime candidates.…”

Corrigendum to “Comparative Aspects of Spin-Dependent Interaction Potentials for Spin-1/2 and Spin-1 Matter Fields”

“…We recall that, in the vector field representation, eqs. (20) and (34), we have obtained the following polarization-dependence:…”

Covariant basis induced by parity for the(j,0)⊕(0,j)representation

“…Indeed, this problem has been studied in Ref. [40] for j ¼ 1 under the assumption that the most general tensor is given by Eq. (87) for j ¼ 1.…”

“…Since all the components c i have a second time derivative either in the free or in the interacting case, as discussed in [40] for the case j ¼ 1, this formalism actually describes the dynamics of a degenerate parity doublet. As pointed out by Weinberg [15], when the field is built as in Eq.…”