Behavior Of Perturbation Theory Research Articles

Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach

We study the large order behaviour in perturbation theory of the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. In particular, we consider their first infrared renormalons, for which we obtain their analytic structure with logarithmic accuracy and also an approximate determination of their normalization constant. Estimates of higher order terms of the perturbative series are given. The Renormalon subtracted scheme is worked out for these observables and compared with experimental data. Overall, good agreement with experiment is found. This allows us to obtain {\hat a}_0 and some higher-twist non-perturbative constants from experiment: {\hat a}_0=0.141\pm 0.089; f_{3,RS}(1 GeV)=-0.124^{+0.137}_{-0.142} GeV^2.

B→Xulbar nul decay distributions to order αs

An analytic result for the O(alpha_s corrections to the triple differential B -> X_u l nu decay rate is presented, to leading order in the heavy-quark expansion. This is relevant for computing partially integrated decay distributions with arbitrary cuts on kinematic variables. Several double and single differential distributions are derived, most of which generalize known results. In particular, an analytic result for the O(alpha_s) corrections to the hadronic invariant mass spectrum is presented. The effects of Fermi motion, which are important for the description of decay spectra close to infrared sensitive regions, are included. The behaviour of perturbation theory in the region of time-like momenta is also investigated

Ultraviolet renormalons in abelian gauge theories

We analyze the large-order behaviour in perturbation theory of classes of diagrams with an arbitrary number of chains (i.e. photon lines, dressed by vacuum polarization insertions). We derive explicit formulae for the leading and subleading divergence as n, the order in perturbation theory, tends to infinity, and a complete result for the vacuum polarization at the next-to-leading order in an expansion in l / N f, where N f is the number of fermion species. In general, diagrams with more chains yield stronger divergence. We define an analogue of the familiar diagrammatic R-operation, which extracts ultraviolet renormalon counterterms as insertions of higher-dimension operators. We then use renormalization group equations to sum the leading (in n/ N f ) k corrections to all orders in l INf and find the asymptotic behaviour in n up to a constant that must be calculated explicitly order by order in 1/ N f .

Deuteron Form Factor.

We obtain the perturbative QCD (PQCD) prediction for the leading twist deuteron form factor, treated as a pair of nucleons in nonrelativistic bound state. It is [lt]10[sup [minus]3] times experiment at [ital Q][sup 2]=4 GeV[sup 2], suggesting that PQCD is not relevant to the deuteron form factor at present values of [ital Q][sup 2], or that non-nucleon (e.g., hidden color'') degrees of freedom must be included for a correct description of the deuteron. The tree-level amplitude [similar to][ital eg][sup 10] and is the sum of several 10[sup 6] Feynman diagrams, making it an interesting case study in the behavior of perturbation theory.

Asymptotic behavior of perturbation theory for the electromagnetic current-current correlation function in QCD.

A simple and direct approach is used to examine the constraints imposed by asymptotic freedom and analytically on the large-order behavior of perturbaton theory for the current-current correlation function and its imaginary part which gives the {ital R} ratio in high-energy {ital e}{sup +-}{ital e{minus}} annihilation.

Asymptotics of the cut discontinuity and large order behaviour from the instanton singularity: The case of lattice Schr�dinger operators with exponential disorder

We discuss the relation between the singularity structure of the Borel transform, the asymptotics of the cut discontinuity and the large order behaviour of perturbation theory. In an explicit example — a tight binding model with exponential disorder — we show how to obtain the first instanton singularity from a cluster expansion in the Borel variable, and as an application we determine the exact decay of the density of states asE → ∞. The method opens some perspectives for similar problems arising from different models of Mathematical Physics.

Perturbation theory in large order for some elementary systems

AbstractReasons for understanding the general problem of perturbation theory in large order are discussed. It is shown that the behavior of perturbation theory in larger order is generally very simple because it reflects just the semiclassical content of the theory. Many simple examples are given, including some graph‐counting problems. The behavior of mass‐renormalized perturbation series for some very simple field‐theory models is examined. It is shown that mass renormalization hardly affects the large‐order behavior of a weak‐coupling perturbation series. However, in a strong‐coupling perturbation series mass renormalization has a dramatic effect.

Asymptotic estimates and borel resummation for a doubly anharmonic oscillator

The large-order behavior of perturbation theory for an oscillator with both quartic and sextic anharmonicity is examined. Two approaches are considered: an explicit double expansion in the two coupling constants and a single expansion in the number of loops. A two-variable extension of the Borel resummation technique is developed and applied to the double series, and the standard one-variable resummation technique is applied to the loop expansion. Numerical values for the ground-state energy are calculated in each case and the two procedures are compared.

Large-order behavior of perturbation theory and mass terms

The large-order behavior of perturbation theory of phi/sup 4/ theory in four dimensions in the presence of mass terms is estimated. A new scale comes into the coefficient functions. For mass m and order K this scale is m..sqrt..K.

Borel summability and the renormalization group

The assumptions and results of recent work by Lipatov and others on the behavior of perturbation theory at high orders are delineated and used in conjunction with the Callan-Symanzik equation. Some consequences related to Borel summability and scaling are obtained for $g{\ensuremath{\varphi}}^{4}$ field theory in four dimensions. Our main result is to show that the above work implies that for this theory a contradiction exists between Borel summability in which the Borel sum fully determines the Euclidean Green's functions in a fixed interval, $0<g<\ensuremath{\epsilon}$ and the existence of a nontrivial ultraviolet-stable fixed point for $0<g<\ensuremath{\infty}$.

The transformational behaviour of perturbation theories

The transformational behaviour of Hori's noncanonical perturbation theory (Hori 1971) as well as that of the theory of Krylov-Bogoliubof-Mitropolsky is studied. An integration procedure of the perturbation equations is based on the transformation properties that have been established.

Asymptotic behaviour of production amplitudes in perturbation theory: 6-Point production graphs

In this paper we study the production amplitudes asymptotic behaviour in perturbation theory for scalar particles inλΦ3 topology when the number of the external lines is 6. The choice of independent invariants is complicated by a geometric equation expressed by the annihilation of a Grammian. We give an asymptotic solution in some particular cases (quasi-elastic processes). Some Eden's and Tiktopoulos' theorems aboutC andD properties are generalized. The calculation is performed for energies going to infinity and momentum transfers small and fixed. This can be considered a particular way to approach the multiperipheral model. The two methods of λ-transform and Mellin transform are used. We found, as expected, in some cases a Regge asymptotic behaviour.

High-energy behaviour in perturbation theory

The high-energy behaviour due to contributions from the edge of the hypercontour of integration of a large class of Feynman graphs is determined. It is shown that the sum of the leading terms of graphs with a certain type of iterated structure has a high-energy behaviour consistent with Regge poles which tend tol = −1, −2, −3, ... as the coupling constant tends to zero. Expressions are obtained for the trajectories and residues of these associated Regge poles.