Fermion helicity flip in weak gravitational fields.

The helicity flip of a spin2 Dirac particle interacting gravitationally with a scalar field is analyzed in the context of linearized quantum gravity. It is shown that massive fermions may have their helicity flipped by gravity, in opposition to massless fermions which preserve their helicity. 04.20.Cv, 04.60.+n Typeset using REVTEX 1 The behavior of a spinning particle in a gravitational field is a long standing problem [1,2], which has known recently a revival of interest. In particular, whether gravity flips or not the helicity of a spin2 Dirac particle has been examined lately in the semiclassical context [3,4]. Although a final answer will have to wait for a complete theory of quantum gravity, we believe the linearized quantum approach can shed new light on the subject. Our aim in this letter is to examine the problem of fermion helicity flip in this context. Namely, we calculate at tree level the helicity flip probability for a spin2 Dirac particle interacting via a graviton exchange with a massive scalar particle in Minkowski space. We conclude that only massive fermions can have their helicity flipped. The main virtue of our treatment is the fact that all concepts employed are simple, and widely used in field theory. The coupling of matter fields with gravity in the context of the linearized theory is obtained using weak field approximation. In this vein, the spacetime metric may be written as gμν = ημν +κhμν , where ημν is the Minkowski metric, κ ≡ √ 32πG = 8.211×10−19 GeV plays the role of a small coupling constant, and the perturbation hμν represents the graviton field which is supposed to be quantized in Minkowski space using Cartesian coordinates. Hence, it is the metric tensor ημν which will provide the canonical isomorphism between the vector space and the corresponding dual space. Next, by minimally coupling gravity to the scalar field φ [5], and to the fermionic field ψ [6], we obtain the following interaction actions to first order in κ Sφφh = ∫ dx κ 4 [