All-order ? expansions of hypergeometric functions of one variable

We briefly sketch a proof concerning the structure of the all-order ɛ expansions of generalized hypergeometric functions with special sets of parameters.     

Field renormalization constant for unstable particles

A recently proposed normalization condition for the imaginary part of the self-energy of an unstable particle is shown to lead to closed, exact expressions for the renormalized self-energy and propagator, which are consequently free of ultraviolet divergences to all orders in perturbation theory. In turn, the corresponding closed expressions for the mass and field renormalization counterterms are necessary in some important cases to avoid power-like infrared divergences in high orders of perturbation theory. In the same examples, the width plays the rôle of an infrared cutoff, and, consequently, the field renormalization counterterm is not an analytic function of the coupling constant.     

Two-fold Mellin–Barnes transforms of Usyukina–Davydychev functions

In our previous paper (Allendes et al., 2013 [10]), we showed that multi-fold Mellin–Barnes (MB) transforms of Usyukina–Davydychev (UD) functions may be reduced to two-fold MB transforms. The MB transforms were written there as polynomials of logarithms of ratios of squares of the external momenta with certain coefficients. We also showed that these coefficients have a combinatoric origin. In this paper, we present an explicit formula for these coefficients. The procedure of recovering the coefficients is based on taking the double-uniform limit in certain series of smooth functions of two variables which is constructed according to a pre-determined iterative way. The result is obtained by using basic methods of mathematical analysis. We observe that the finiteness of the limit of this iterative chain of smooth functions should reflect itself in other mathematical constructions, too, since it is not related in any way to the explicit form of the MB transforms. This finite double-uniform limit is represented in terms of a differential operator with respect to an auxiliary parameter which acts on the integrand of a certain two-fold MB integral. To demonstrate that our result is compatible with original representations of UD functions, we reproduce the integrands of these original integral representations by applying this differential operator to the integrand of the simple integral representation of the scalar triangle four-dimensional integral J(1,1,1−ε)$J(1,1,1-\epsilon )$.     

Reconciling open-charm production at the Fermilab Tevatron with QCD

We study the inclusive hadroproduction of D0, D+, D*+, and D(s)+ mesons at next-to-leading order in the parton model of quantum chromodynamics endowed with universal nonperturbative fragmentation functions fitted to e+e- annihilation data from CERN LEP1. Working in the general-mass variable-flavor-number scheme, we resum the large logarithms through the evolution of the fragmentation functions and, at the same time, retain the full dependence on the charm-quark mass without additional theoretical assumptions. In this way, the cross section distributions in transverse momentum recently measured by the CDF Collaboration in run II at the Fermilab Tevatron are described within errors.     

Tevatron-hera colour-octet charmonium anomaly versus higher-order QCD effects

Approximately taking into account the higher-order effects due to multiple-gluon initial-state radiation, we extract from the latest Tevatron data of prompt hadroproduction the leading colour-octet matrix elements within the nonrelativistic-QCD (NRQCD) factorization formalism proposed by Bodwin, Braaten, and Lepage. We find that the matrix elements which describe the formation of mesons from colour-octet pairs in the angular-momentum states and , with , which are responsible for the excess of the predicted cross section of inelastic photoproduction over the existing HERA data at high values of the inelasticity variable , are significantly reduced. We conclude that it is premature to proclaim a discrepancy between the Tevatron and HERA measurements of inclusive production in the NRQCD framework. We also consider mesons originating from the radiative feed down of promptly produced mesons. Received: 10 March 1998 / Revised version: 22 April 1998 / Published online: 30 July 1998     

Prospects of measuring general Higgs couplings at e^+e^- linear colliders

We examine how accurately the general HZV couplings, with , may be determined by studying processes at future linear colliders. By using the optimal-observable method, which makes use of all available experimental information, we find out which combinations of the various HZV coupling terms may be constrained most efficiently with high luminosity. We also assess the benefits of measuring the tau-lepton helicities, identifying the bottom-hadron charges, polarizing the electron beam and running at two different collider energies. The HZZ couplings are generally found to be well constrained, even without these options, while the couplings are not. The constraints on the latter may be significantly improved by beam polarization. Received: 4 February 2000 / Published online: 6 April 2000