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Register a new userGauge dependence of the gauge boson projector
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The propagator of a gauge boson, like the massless photon or the massive vector bosons $W^pm$ and $Z$ of the electroweak theory, can be derived in two different ways, namely via Greens functions (semi-classical approach) or via the vacuum expectation value of the time-ordered product of the field operators (field theoretical approach). Comparing the semi-classical with the field theoretical approach, the central tensorial object can be defined as the gauge boson projector, directly related to the completeness relation for the complete set of polarisation four-vectors. In this paper we explain the relation for this projector to different cases of the $R_xi$ gauge and explain why the unitary gauge is the default gauge for massive gauge bosons.
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The measurement of anomalous gauge boson self couplings is reviewed for a variety of present and planned accelerators. Sensitivities are compared for these accelerators using models based on the effective Lagrangian approach. The sensitivities described here are for measurement of generic parameters kappa_v, lambda_v, etc., defined in the text. Pre-LHC measurements will not probe these couplings to precision better than O(1/10). The LHC should be sensitive to better than O(1/100), while a future NLC should achieve sensitivity of O(1/1000) to O(1/10000) for center of mass energies ranging from 0.5 to 1.5 TeV.
The Standard Model (SM) Higgs Lagrangian is straightforwardly rewritten into the {it scale-invariant} nonlinear sigma model $G/H=[SU(2)_L times SU(2)_R]/SU(2)_{V}simeq O(4)/O(3)$, with the (approximate) scale symmetry realized nonlinearly by the (pseudo) dilaton ($=$ SM Higgs). It is further gauge equivalent to that having the symmetry $O(4)_{rm global}times O(3)_{rm local}$, with $O(3)_{rm local}$ being the Hidden Local Symmetry (HLS). In the large $N$ limit of the scale-invariant version of the Grassmannian model $G/H=O(N)/[O(N-3)times O(3)] $ $simeq O(N)_{rm global}times [O(N-3)times O(3)]_{rm local}$, identical to the SM for $Nrightarrow 4$, we show that the kinetic term of the HLS gauge bosons (SM rho) $rho_mu$ of the $O(3)_{rm local}simeq [SU(2)_V]_{rm local}$ are dynamically generated by the nonperturbative dynamics of the SM itself. The dynamical SM rho stabilizes the skyrmion (SM skyrmion) $X_s$ as a dark matter candidate within the SM: The mass $M_{X_s} ={cal O}(10, {rm GeV})$ consistent with the direct search experiments implies the induced HLS gauge coupling $g_{_{rm HLS}}={cal O}(10^3)$, which realizes the relic abundance, $Omega_{X_s} h^2 ={cal O}(0.1)$. If instead $g_{_{rm HLS}}lesssim 3.5$ ($M_rho lesssim 1.2 $ TeV), the SM rho could be detected with narrow width $lesssim 100 ,{rm GeV}$ at LHC, having all the $a=2$ results of the generic HLS Lagrangian ${cal L}_A+ a {cal L}_V$, i.e., $rho$-universality, KSRF relations and the vector meson dominance, independently of $a$. There exists the second order phase phase transition to the unbroken phase having massless $rho_mu$ and massive $pi$ (no longer NG bosons), both becoming massless free particles just on the transition point (scale-invariant ultraviolet fixed point).The results readily apply to the 2-flavored QCD as well.
In principle, observables as for example the sphaleron rate or the tunneling rate in a first-order phase transition are gauge-independent. However, in practice a gauge dependence is introduced in explicit perturbative calculations due to the breakdown of the gradient expansion of the effective action in the symmetric phase. We exemplify the situation using the effective potential of the Abelian Higgs model in the general renormalizable gauge. Still, we find that the quantitative dependence on the gauge choice is small for gauges that are consistent with the perturbative expansion.
The perturbative effective potential suffers infrared (IR) divergences in gauges with massless Goldstones in their minima (like Landau or Fermi gauges) but the problem can be fixed by a suitable resummation of the Goldstone propagators. When the potential minimum is generated radiatively, gauge-independence of the potential at the minimum also requires resummation and we demonstrate that the resummation that solves the IR problem also cures the gauge-dependence issue, showing this explicitly in the Abelian Higgs model in Fermi gauge. In the process we find an IR divergence (in the location of the minimum) specific to Fermi gauge and not appreciated in recent literature. We show that physical observables can still be computed in this gauge and we further show how to get rid of this divergence by a field redefinition. All these results generalize to the Standard Model case.
We present the results obtained by the Triple Gauge Couplings working group during the LEP2 Workshop (1994-1995). The report concentrates on the measurement of $WWgamma$ and $WWZ$ couplings in $e^-e^+to W^-W^+$ or, more generally, four-fermion production at LEP2. In addition the detection of new interactions in the bosonic sector via other production channels is discussed.
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