Abstract
We describe a new approach towards the development of an entirely on-shell description of the bosonic electroweak sector of the Standard Model and the Higgs mechanism. We write down on-shell three particle amplitudes consistent with Poincaré invariance and little group covariance. Tree-level, four particle amplitudes are determined by demanding consistent factorization on all poles and correct UV behaviour. We present expressions for these 2 → 2 scattering amplitudes using massive spinor helicity variables. We show that on-shell consistency conditions suffice to derive relations between the masses of the W±, Z , the Weinberg angle and the couplings. This provides a completely on-shell description of the Higgs mechanism without any reference to the vacuum expectation value of the Higgs field.
Highlights
Quantum fields, path integrals and Lagrangians have been a cornerstone of 20th century theoretical physics
We describe a new approach towards the development of an entirely on-shell description of the bosonic electroweak sector of the Standard Model and the Higgs mechanism
We have presented a completely on-shell description of the higgs mechanism within the Standard Model
Summary
Path integrals and Lagrangians have been a cornerstone of 20th century theoretical physics. The forbidding complexity of the Feynman diagram based calculation of tree level gluon scattering amplitudes is understood to be an artifact of the unphysical degrees of freedom introduced by gauge redundancy These unphysical degrees of freedom are necessary to package the physical degrees of freedom into local quantum fields in a manner consistent with Poincare invariance [3]. The simplicity of these amplitudes fueled the development of a variety of “on-shell” techniques for computing scattering amplitudes involving massless particles. We will discover that demanding that these amplitudes have a well defined high energy limit imposes constraints on the structure of the theory
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