Properties of effective massive Yang-Mills theory in the limit of vanishing vector boson mass

Two-loop corrections to the pole mass of the vector boson and the pole masses and the magnetic moments of fermions are calculated in the framework of an effective field theory of massive Yang-Mills fields interacting with fermions. It is shown that the limit of vanishing vector boson mass is finite for all these quantities. Implications of the obtained results are discussed.Comment: 12 pages, 4 figure

Once more on the Higgs decay into two photons

We comment on the recently reiterated claim that the contribution of the W-boson loop to the Higgs boson decay into two photons leads to different expressions in the $R_\xi$ gauge and the unitary gauge. By applying a gauge-symmetry preserving regularization with higher-order covariant derivatives we reproduce once again the "classical" gauge-independent result.Comment: 6 pages, 1 figur

Cusps in K --> 3 pi decays

The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.Comment: 14 pages, 3 figures, uses Elsevier styl

Vacuum energy in the effective field theory of general relativity

In the framework of an effective field theory of general relativity a model of scalar and vector bosons interacting with the metric field is considered. It is shown in the framework of a two-loop order calculation that for the cosmological constant term which is fixed by the condition of vanishing vacuum energy the graviton remains massless and there exists a self-consistent effective field theory of general relativity coupled to matter fields defined on a flat Minkowski background. This result is obtained under the assumption that the energy-momentum tensor of the gravitational field is given by the pseudotensor of Landau-Lifshitz's classic textbook. Implications for the cosmological constant problem are also briefly discussed.Comment: 11 pages, 4 figure

Chiral unitary meson-baryon dynamics in the presence of resonances: Elastic pion-nucleon scattering

We develop a novel approach to chiral meson-baryon dynamics incorporating unitarity constraints and explicit resonance fields. It is based on the most general structure of any pion-nucleon partial wave amplitude neglecting the unphysical cuts as derived from the N/D method. This amplitude is then matched to the one-loop heavy baryon chiral perturbation theory result at third order and to tree level exchanges of baryon- and meson states in the s,t and u channels. This generates the left-hand cuts. The unitarization procedure does not involve form factors or regulator functions. The resonance parameters are determined from fits to the S- and P-wave pion-nucleon partial wave amplitudes for energies up to 1.3 GeV. In particular, the $\Delta (1232)$ is accurately reproduced whereas scalar and vector meson couplings are less precisely pinned down. We also obtain a satisfactory description of the $\pi$N threshold parameters. Further extensions of this method to coupled channels and the three-flavor case are briefly discussed.Comment: 23 pp, LaTeX2e, 10 fig

Triviality of quantum electrodynamics revisited

Quantum electrodynamics is considered to be a trivial theory. This is based on a number of evidences, both numerical and analytical. One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling. We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections, the Landau pole is removed. Therefore, we conclude that the conjecture, that for reasons of self-consistency, QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.Comment: 3 pages, 2 figure

Derivation of spontaneously broken gauge symmetry from the consistency of effective field theory II: Scalar field self-interactions and the electromagnetic interaction

We extend our study of deriving the local gauge invariance with spontaneous symmetry breaking in the context of an effective field theory by considering self-interactions of the scalar field and inclusion of the electromagnetic interaction. By analyzing renormalizability and the scale separation conditions of three-, four- and five-point vertex functions of the scalar field, we fix the two couplings of the scalar field self-interactions of the leading order Lagrangian. Next we add the electromagnetic interaction and derive conditions relating the magnetic moment of the charged vector boson to its charge and the masses of the charged and neutral massive vector bosons to each other and the two independent couplings of the theory. We obtain the bosonic part of the Lagrangian of the electroweak Standard Model as a unique solution to the conditions imposed by the self-consistency conditions of the considered effective field theory.Comment: 11 pp, 3 fig

Near threshold ppbar enhancement in the J/psi -> omega ppbar decay

The near-threshold behavior of the ppbar invariant mass spectrum from the J/psi -> omega ppbar decay reported recently by the BES Collaboration is analyzed. Contrary to the statement made by the BES Collaboration itself our study demonstrates that there is indeed a noticeable enhancement in the ppbar invariant mass spectrum near threshold. Moreover, this enhancement is nicely reproduced by the final state interaction in the relevant 11S0 ppbar partial wave as given by the Julich nucleon--antinucleon model. Therefore, and again contrary to the statement by the BES Collaboration, their new data on J/psi -> omega ppbar decay in fact strongly support the FSI interpretation of the ppbar enhancement, seen also in other decay reactions.Comment: 3 pages, 2 figure

Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.Comment: 6 pages, no figure

Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering

We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covered by the Wilsonian renormalization group approach. In the framework of pionless effective field theory, also extended by the inclusion of a long-range interaction of separable type, we demonstrate that Weinberg's power counting scheme is consistent in the sense that it leads to a systematic order-by-order expansion of the scattering amplitude.Comment: 23 pages, 2 figure