Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.Comment: 25 pages, OUT--4102--43, BI--TP/92--5

NONSTANDARD GAUGE-BOSON SELF-INTERACTIONS WITHIN A GAUGE-INVARIANT MODEL

GROSSE-KNETTER C, KUSS I, Schildknecht D. NONSTANDARD GAUGE-BOSON SELF-INTERACTIONS WITHIN A GAUGE-INVARIANT MODEL. ZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS. 1993;60(2):375-388.We examine dimension-six extensions of the standard electroweak Lagrangian which are invariant under local SU(2)L x U(1)Y-transformations. The dimension-four trilinear and quadrilinear effective interactions of the vector bosons with one another are found to coincide with the vector boson interactions previously derived from global SU(2) weak isospin symmetry broken by electromagnetism. Supplementing the model by a well-known dimension-six single-parameter quadrupole interaction leads to the most general vector boson self-couplings that can be obtained by addition of dimension-six terms to the standard Lagrangian. We examine in some detail another SU(2)L x U(1)Y-symmetric interaction which contains W3B mixing and modifies both vector boson self-couplings and fermionic interactions. Independently of being strongly constrained by the LEP 1 data, the addition of this interaction to the above-mentioned non-standard ones does not change the form of the trilinear and quadrilinear non-standard self-couplings of the vector bosons. Therefore, while being interesting in itself with respect to LEP 1 physics, this term is irrelevant with respect to the phenomenology of the vector-boson self-interactions