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Regge-pole behavior from perturbative scalar-field theories

Journal Article · · Phys. Rev., D; (United States)
;
In the planar approximation, we consider the large-energy-s, fixed-transfer-t limit of the four-point vertex function. In phi/sup 3/ theory (6 space-time dimensions) and in phi/sup 4/ theory (4 space-time dimensions), for any essentially and crossed planar graph, we analytically calculate the coefficients of all powers of logarithms of s for the leading power of s. After summing the series in logarithms obtained when the four-point function is considered, we discuss the existence of Regge trajectories from a Riccati-type differential equation. In g (phi/sup 3/)/sub 6/ theory we find a discrete family of Regge-pole trajectories with g-dependent intercepts accumulating at ..cap alpha.. = -1. In g (phi/sup 4/)/sub 4/ theory the solution of the Riccati equation may be easily found if there exists a fixed point g = g*; the result then is a fixed g-independent cut and an infinite number of pole trajectories (the square-root branch point is above the intercepts at g = g*).
Research Organization:
Commissariat a l'Energie Atomique, Division de la Physique, Service de Physique Theorique, CEN-Saclay, Boite Postale n/sup o/ 2,91190 Gif-sur-Yvette, France
OSTI ID:
5866693
Journal Information:
Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 20:8; ISSN PRVDA
Country of Publication:
United States
Language:
English

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Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BETHE-SALPETER EQUATION
DIAGRAMS
DIFFERENTIAL EQUATIONS
EQUATIONS
FEYNMAN DIAGRAM
FIELD THEORIES
FUNCTIONS
INTEGRAL TRANSFORMATIONS
MATRICES
MELLIN TRANSFORM
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
REGGE POLES
REGGE TRAJECTORIES
RENORMALIZATION
RICCATI EQUATION
S MATRIX
SCALAR FIELDS
SPACE-TIME
TRANSFORMATIONS
ULTRAVIOLET DIVERGENCES
VERTEX FUNCTIONS