ALGORITHMIC CALCULATION OF TWO-LOOP FEYNMAN DIAGRAMS

J. Fleischer; O. V. Tarasov

Home/Archive/arXiv

arXiv · hep-ph/9502257

ALGORITHMIC CALCULATION OF TWO-LOOP FEYNMAN DIAGRAMS

J. Fleischer·O. V. Tarasov

View original source ↗Read source document ↗Export metadata ↓

Abstract

In a recent paper \cite{ft} a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero. It was demonstrated that by a certain conformal mapping and subsequent resummation by means of Padé approximants it is possible to obtain high precision numerical values of the Feynman integrals in the whole cut plane. The real problem in this approach is the calculation of the Taylor coefficients for the arbitrary mass case. Since their analytic evaluation by means of CA packages uses enormous CPU and yields very lengthy expressions, we develop an algorithm with the aim to set up a FORTRAN package for their numerical evaluation. This development is guided by the possibilities offered by the formulae manipulating language FORM \cite{FORM}.

Explore related subjects

hep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

J. Fleischer, O. V. Tarasov. 1995-02-08. ALGORITHMIC CALCULATION OF TWO-LOOP FEYNMAN DIAGRAMS. https://arxiv.org/abs/hep-ph/9502257

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Covariant reggeization framework for diffraction. Part I: Hadronic tensors in Minkovsky space-time of any dimension

In this paper we consider the general structure of irreducible tensor representations of the Poincaré group of arbitrary space-time dimension $D$ with multiple sets of Lorentz indices and different ways to construct them from basic elements (Lorentz vectors and the metric tensor). Then we apply the same methods to obtain the expansion of general hadronic tensors in terms of these irreducible tensors. We propose to use an effective approach in hadronic diffraction, which was usually called covariant reggeization, and obtain basic functions and tensors to calculate all the diffractive cross-sections.

hep-ph↗

arXiv2026

Extraction of the pion-nucleon coupling constant using the effective-range expansion with the left-hand cut

We apply the generalized effective-range expansion of Phys. Rev. Lett. 135, 011903(2025), which incorporates the left-hand cut from one-pion exchange, to low-energy neutron-proton scattering in the $^1S_0$ and $^3S_1$ channels. The amplitude zero for the center-of-mass momentum near 0.35 GeV in the $^1S_0$ channel is naturally accommodated within this framework. We extract the pole position, scattering length, effective range, and the pseudoscalar pion-nucleon coupling constant $g_{πN}^2/(4π)$ at different expansion orders. The low-energy parameters are stable and consistent with established values, while $g_{πN}^2/(4π)$ exhibits larger uncertainties. The extraction of $g_{πN}^2/(4π)$ is data-driven, relying on the analytic constraints from the left-hand cut and phase-shift data within the one-pion-exchange approximation. Despite larger uncertainties compared to high-precision extractions, the consistency with established values demonstrates that this framework can probe the left-hand-cut singularity.

hep-ph↗

arXiv2026

Sexaquarks and $H$ dibaryons in the $uuddss$ system: a comparison within a constituent quark model

We study the $uuddss$ multiquark within a constituent quark model framework, solving the corresponding nonrelativistic Schrodinger equation by means of a diffusion Monte Carlo (DMC) method. The total wavefunction is written as the product of a radial component and an exact spin-color-flavor state, restricted to isospin $I$=0. For this isospin, all allowed flavor wave functions are included. We explore two distinct constructions of the six-quark system. In the first one, corresponding to a sexaquark, all six quarks are treated as indistinguishable and the wave function is fully antisymmetric with respect to the exchange of any two quarks. In the second one, corresponding to the $H$ dibaryon, the system is partitioned into two sets of three quarks, effectively mimicking a baryon-baryon-like configuration including hidden color terms in which antisymmetry is imposed only within each three-quark cluster. Only when the system is forced into a baryon-baryon-like configuration, and for certain values of the spin, color and flavor quantum numbers, do we obtain states with masses close to, but above, the two-baryon threshold. Those states are characterized by two loosely bound three-quark clusters separated from one another by a distance of $\sim$ 2.5 fm. The remaining structures are compact objects irrespectively of their internal wavefunction.

hep-ph↗