Abstract
The renormalization in a Lorentz-breaking scalar-spinor higher-derivative model involving phi ^4 self-interaction and the Yukawa-like coupling is studied. We explicitly de-monstrate that the convergence is improved in comparison with the usual scalar-spinor model, so, the theory is super-renormalizable, with no divergences beyond four loops. We compute the one-loop corrections to the propagators for the scalar and fermionic fields and show that in the presence of higher-order Lorentz invariance violation, the poles that dominate the physical theory, are driven away from the standard on-shell pole mass due to radiatively induced lower dimensional operators. The new operators change the standard gamma-matrix structure of the two-point functions, introduce large Lorentz-breaking corrections and lead to modifications in the renormalization conditions of the theory. We found the physical pole mass in each sector of our model.
Highlights
At the same time, it is natural to consider one more aspect of studying the Lorentz-breaking extensions of the field theory models
Since the mass corrections are finite in both sectors, in some sense we are working in the scheme in which the finite parts of the renormalized mass correspond to the pole mass, and one can say that we are working in the on-shell subtraction scheme
We considered the Myers–Pospelov-like higher-derivative extensions of the Yukawa model which incorporates possible new physics from the Planck scale through dimension five operators coupled to a preferred four vector nμ which breaks the Lorentz symmetry
Summary
It is natural to consider one more aspect of studying the Lorentz-breaking extensions of the field theory models It consists in introducing essentially Lorentzbreaking terms, that is, those ones proportional to some constant vectors or tensors, involving higher derivatives. Up to now, the quantum impact of the Myers–Pospelov-like class of terms being introduced already at the classical level, where the higher-derivative additive term should carry a small parameter which can enforce large quantum corrections [30], almost was not studied except of the QED [31,32] and superfield case [33] The presence of such effect raises the question how to define correctly the physical parameters in the renormalized theory. We discuss our results, and in the Appendix A, Appendix B and Appendix C, we provide some details of the calculations
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