Search results for "Background field method"
showing 10 items of 24 documents
Charge radius of the neutrino
2000
Using the pinch technique we construct at one-loop order a neutrino charge radius, which is finite, depends neither on the gauge-fixing parameter nor on the gauge-fixing scheme employed, and is process independent. This definition stems solely from an effective proper photon-neutrino one-loop vertex, with no reference to box or self-energy contributions. The role of the $\mathrm{WW}$ box in this construction is critically examined. In particular it is shown that the exclusion of the effective $\mathrm{WW}$ box from the definition of the neutrino charge radius is not a matter of convention but is in fact dynamically realized when the target fermions are right-handedly polarized. In this way …
Pinch technique self-energies and vertices to all orders in perturbation theory
2003
The all-order construction of the pinch technique gluon self-energy and quark-gluon vertex is presented in detail within the class of linear covariant gauges. The main ingredients in our analysis are the identification of a special Green's function, which serves as a common kernel to all self-energy and vertex diagrams, and the judicious use of the Slavnov-Taylor identity it satisfies. In particular, it is shown that the ghost-Green's functions appearing in this identity capture precisely the result of the pinching action at arbitrary order. By virtue of this observation the construction of the quark-gluon vertex becomes particularly compact. It turns out that the aforementioned ghost-Green…
New Schwinger-Dyson equations for non-Abelian gauge theories
2008
We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the sta…
On dynamical gluon mass generation
2007
The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is so…
Pinch technique at two loops: The case of massless Yang-Mills theories
2000
The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less Yang-Mills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quit…
Charge and magnetic moment of the neutrino in the background field method and in the linear R-xi(L) gauge
1999
We present a computation of the charge and the magnetic moment of the neutrino in the recently developed electro-weak Background Field Method and in the linear $R_{\xi}^L$ gauge. First, we deduce a formal Ward-Takahashi identity which implies the immediate cancellation of the neutrino electric charge. This Ward-Takahashi identity is as simple as that for QED. The computation of the (proper and improper) one loop vertex diagrams contributing to the neutrino electric charge is also presented in an arbitrary gauge, checking in this way the Ward-Takahashi identity previously obtained. Finally, the calculation of the magnetic moment of the neutrino, in the minimal extension of the Standard Model…
Connection between the pinch technique and the background field method
1995
The connection between the pinch technique and the background field method is further explored. We show by explicit calculations that the application of the pinch technique in the framework of the background field method gives rise to exactly the same results as in the linear renormalizable gauges. The general method for extending the pinch technique to the case of Green's functions with off-shell fermions as incoming particles is presented. As an example, the one-loop gauge independent quark self-energy is constructed. We briefly discuss the possibility that the gluonic Green's functions, obtained by either method, correspond to physical quantities.
Gluon mass and freezing of the QCD coupling
2007
Infrared finite solutions for the gluon propagator of pure QCD are obtained from the gauge-invariant non-linear Schwinger-Dyson equation formulated in the Feynman gauge of the background field method. These solutions may be fitted using a massive propagator, with the special characteristic that the effective mass employed drops asymptotically as the inverse square of the momentum transfer, in agreement with general operator-product expansion arguments. Due to the presence of the dynamical gluon mass the strong effective charge extracted from these solutions freezes at a finite value, giving rise to an infrared fixed point for QCD.
Pinch technique to all orders
2002
The generalization of the pinch technique to all orders in perturbation theory is presented. The effective Green's functions constructed with this procedure are singled out in a unique way through the full exploitation of the underlying Becchi-Rouet-Stora-Tyutin symmetry. A simple all-order correspondence between the pinch technique and the background field method in the Feynman gauge is established. Comment: 10 pages, 4 figures; one reference added, typos corrected; final version to match the pubblished one
One-loop renormalization of Resonance Chiral Theory: scalar and pseudoscalar resonances
2005
We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its beta-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite.