1,721,276 research outputs found
The Abelian embedding formulation of the Stuckelberg model and its power-counting renormalizable extension
No full textWe elucidate the geometry of the polynomial formulation of the non-abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent BRST differential exists allowing to implement the constraint on the sigma field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-abelian gauge fields. As all versions of the Stueckelberg theory, also the abelian embedding formulation yields a non power-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the abelian embedding formalism
Scalar resonances in the non-linearly realized electroweak theory
No full textWe introduce a physical scalar sector in a SU(2)⊗U(1) electroweak theory in which the gauge group is realized non linearly. By invoking theoretical as well as experimental constraints, we build a phenomenologically viable model in which a minimum of four scalar resonances appear, and the mass of the CP even scalar is controlled by a vacuum expectation value; however, the masses of all other particles (both matter as well as vector boson fields) are unrelated to spontaneous symmetry breaking and generated by the Stückelberg mechanism. We evaluate in this model the CP-even scalar decay rate to two photons and use this amplitude to perform a preliminary comparison with the recent LHC measurements. As a result, we find that the model exhibits a preference for a negative Yukawa coupling between the top quark and the CP-even resonance
Canonical Transformations and Renormalization Group Invariance in the presence of Non-trivial Backgrounds
No full textAll orders symmetric subtraction of the nonlinear sigma model in D=4
No full textThe symmetric subtraction of the nonlinear sigma model in D=4 is performed to all orders in the loop expansion by enforcing the functional equation associated with the invariance of the Haar measure under local left multiplication. This equation encodes a powerful hierarchy allowing one to fix all amplitudes involving at least one pion field in terms of those only containing insertions of the flat connection and the nonlinear sigma model constraint (ancestor amplitudes)
The hierarchy principle and the large mass limit of the linear sigma model
No full textIn perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs, at one loop level, on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use of the normalization conditions of the linear theory, in order to exploit the functional equation and the complete set of local solutions of its linearized form
Path-integral over non-linearly realized groups and hierarchy solutions
No full textThe technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group
Physical Unitarity for Massive Non-abelian Gauge Theories in the Landau Gauge: Stueckelberg and Higgs
No full textWe discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor identities should be respected!) and we devote the paper to the study of the space of the unphysical modes. We find that the theory is unitary only under the hypothesis that the 1-PI two-point function of the vector mesons has no poles (at p^2=0). This normalization condition might be rather crucial in the very definition of the theory. With all these provisos the theory is unitary. The proof of unitarity is given both in a form that allows a direct transcription in terms of Feynman amplitudes (cutting rules) and in the operatorial form. The same arguments and conclusions apply verbatim to the case of non-abelian gauge theories where the mass of the vector meson is generated via Higgs mechanism. To the best of our knowledge, there is no mention in the literature on the necessary condition implied by physical unitarity
A Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group
No full textWe propose a subtraction scheme for a massive Yang-Mills theory realized via a nonlinear representation of the gauge group (here SU(2)). It is based on the subtraction of the poles in D-4 of the amplitudes, in dimensional regularization, after a suitable normalization has been performed. Perturbation theory is in the number of loops and the procedure is stable under iterative subtraction of the poles. The unphysical Goldstone bosons, the Faddeev-Popov ghosts and the unphysical mode of the gauge field are expected to cancel out in the unitarity equation. The spontaneous symmetry breaking parameter is not a physical variable. We use the tools already tested in the nonlinear sigma model: hierarchy in the number of Goldstone boson legs and weak power-counting property (finite number of independent divergent amplitudes at each order). It is intriguing that the model is naturally based on the symmetry SU(2)_L local times SU(2)_R global. By construction the physical amplitudes depend on the mass and on the self-coupling constant of the gauge particle and moreover on the scale parameter of the radiative corrections. The Feynman rules are in the Landau gauge
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