Isospin breaking in low-energy charged pion–kaon elastic scattering

We use chiral perturbation theory to evaluate the scattering amplitude for the process at leading and next-to-leading orders in the chiral counting and in the presence of isospin breaking effects. We also discuss the influence of the latter on the combination of the -wave scattering lengths which is relevant for the 2S–2P energy level shift of atoms. Received: 19 November 2001 / Revised version: 21 December 2001 / Published online: 5 April 2002     

Large N_ c in chiral perturbation theory

The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are chosen suitably, the known large counting rules of QCD can unambiguously be translated into corresponding counting rules for the effective coupling constants. As an application, we demonstrate that the Kaplan–Manohar transformation is in conflict with these rules and is suppressed to all orders in . The anomalous dimension of the axial singlet current generates an additional complication: The corresponding external field undergoes nonmultiplicative renormalization. As a consequence, the Wess–Zumino–Witten term, which accounts for the U(3)U(3) anomalies in the framework of the effective theory, contains pieces that depend on the running scale of QCD. The effect only shows up at nonleading order in , but requires specific unnatural parity contributions in the effective Lagrangian that restore renormalization group invariance. Received: 14 July 2000 / Published online: 27 October 2000     

The Gribov–Zwanziger action in the presence of the gauge invariant,nonlocal mass operator Tr∫d<Superscript>4</Superscript>xF<Subscript>μν</Subscript>(D<Superscript>2</Superscript>)<Superscript>-1</Superscript>F<Subscript>μν</Subscript> in the Landau gauge

We prove that the nonlocal gauge invariant mass dimension 2 operator F_μν(D²)^-1F_μν can be consistently added to the Gribov–Zwanziger action, which implements the restriction of the path integral’s domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov–Taylor identity. PACS 11.15.-q; 11.15.Tk     

Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms. Received: 23 July 1999 / Published online: 14 October 1999     

Conformal invariance in perturbation theory

Asymptotic conformal invariance is proved to be true at all orders in perturbation theory. The correct Ward Identities for broken conformal invariance are derived: they are the extension of the Callan Symanzik equation from scale to conformal transformations.     

A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant d=4 operator F _{μ ν} ²(x) to all orders of perturbation theory in pure Yang–Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other d=4 gauge variant operators, which we identify explicitly. We determine the mixing matrix Z to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix Γ derived from Z. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.     

Running Coupling Expansion for the Renormalized Φ 4 4 Trajectory from Renormalization Invariance

We formulate a renormalized running coupling expansion for theΒ-function and the potential of the renormalized Φ⁴-trajectory on four-dimensional Euclidean space-time. Renormalization invariance is used as a first principle. No reference is made to bare quantities. The expansion is proved to be finite to all orders of perturbation theory. The proof includes a large-momentum bound on the connected free propagator amputated vertices.     

Renormalization of Wilson operators in the light-cone gauge

We test the renormalization of Wilson operators and the Mandelstam–Leibbrandt gauge in the case when the sides of the loop are parallel to the vectors used in the M–L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M–L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M–L gauge for loops containing spacelike lines. Received: 31 May 2000 / Published online: 23 January 2001     

Renormalization of gauge theories

Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semisimple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independent from the parameters which define the gauge function.     

Baryon form factors in chiral perturbation theory

We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the charge radius and the – transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory. Received: 25 October 2000 / Published online: 23 January 2001     

Calculation of hyperfine splitting in mesons using configuration interaction approach

The spin–spin mass splitting of light, heavy and mixed mesons are described within a good accuracy in the potential model with screened potential. We conclude that the long-range part of the potential cannot be pure scalar and that a vector–scalar mixture is favored. Excellent spin–spin splittings of heavy quarkonia are obtained with the same parameters as the ones which give the correct average mass spectrum. The results are obtained by going beyond the usually used perturbation method, namely using a configuration interaction approach. Received: 19 September 2000 / Revised version: 19 April 2001 / Published online: 3 August 2001     

One-loop leading logarithms in electroweak radiative corrections

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we prove the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft–Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredients we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory. Received: 4 May 2001 / Published online: 6 July 2001     

Photon sector of quantum electrodynamics at high temperature in two spatial dimensions

The photon sector of quantum electrodynamics (QED) in two spatial dimensions is analyzed at high temperature to all orders of perturbation theory. Imaginary-time formalism is used. The photon self-energy and propagator at finite temperature with vanishing frequency is calculated to the second order of perturbation theory. Based upon the latter, an improved perturbation theory which incorporates Debye screening is formulated. By virtue of the latter and gauge invariance, infrared finitness holds. The temperature dependence of any contribution to the connected Green's functions in the improved perturbation theory is analyzed systematically. At very high temperature, the photon sector becomes equivalent to a very massive scalar boson field plus a massless electromagnetic field and both become decoupled: all connected Green's functions containing, at least, one closed fermion loop with four or more vertices are shown to tend to zero.     

Radiative decays of mesons in the NJL model

We revisit the theoretical predictions for anomalous radiative decays of pseudoscalar and vector mesons. Our analysis is performed in the framework of the Nambu–Jona–Lasinio model, introducing adequate parameters to account for the breakdown of chiral symmetry. The results are comparable with those obtained in previous approaches. Received: 14 September 2000 / Revised version: 1 March 2001 / Published online: 8 June 2001     

Non-commutative Lorentz symmetry and the origin of the Seiberg–Witten map

We show that the non-commutative Yang–Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The non-commutative Yang–Mills action is invariant under combined conformal transformations of the Yang–Mills field and of the non-commutativity parameter . The Seiberg–Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action. Received: 6 November 2001 / Published online: 5 April 2002     

Phase-Averaged Transport¶for Quasi-Periodic Hamiltonians

For a class of discrete quasi-periodic Schr?dinger operators defined by covariant representations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is proven. This result is established under a Diophantine condition on the incommensuration parameter. The relevant class of operators is distinguished by invariance with respect to symmetry automorphisms of the rotation algebra. It includes the critical Harper (almost-Mathieu) operator. As a by-product, a new solution of the frame problem associated with Weyl–Heisenberg–Gabor lattices of coherent states is given. Received: 30 May 2001 / Accepted: 2 January 2002     

Quantum scale invariance,cosmological constant and hierarchy problem

We construct a class of theories which are scale-invariant on quantum level in all orders of perturbation theory. In a subclass of these models scale invariance is spontaneously broken, leading to the existence of a massless dilaton. The applications of these results to the problem of stability of the electroweak scale against quantum corrections, to the cosmological constant problem and to dark energy are discussed.     

Results for all reactions e^+ e^- \rightarrow 4{\rm f}, 4{\rm f}\gamma with nonzero fermion masses

We accomplish our efforts to obtain predictions for all four–fermion final states of –annihilation and the corresponding bremsstrahlung reactions which are possible in the framework of the Standard Model. For this purpose we have developed a program ee4 . Our predictions are valid for fermions of arbitrary masses and we can obtain results for total cross sections without any collinear cut. Keeping exact fermion masses is of course required for top quark production. We give a detailed phenomenological analysis of fermion mass effects and real photon radiation for all channels of four–fermion production at LEP-II and next linear collider energies. Received: 2 October 2001 / Revised version: 2 January 2002 / Published online: 1 March 2002