Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-09-25
Phys.Lett. B446 (1999) 267-271
Physics
High Energy Physics
High Energy Physics - Phenomenology
latex2e, 5 pages, minor errors corrected and references updated
Scientific paper
10.1016/S0370-2693(98)01539-1
Within the context of massive N-component $\phi^4$ scalar field theory, we use asymptotic Pade-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant beta-function $\beta_g$, the anomalous mass dimension $\gamma_m$, the vacuum-energy beta-function $\beta_v$, and the anomalous dimension $\gamma_2$ of the scalar field propagator. These estimates are then compared with explicit calculations of the five-loop contributions to $\beta_g$, $\gamma_m$, $\beta_v$, and are seen to be respectively within 5%, 18%, and 27% of their true values for $N$ between 1 and 5. We then extend asymptotic Pade-approximant methods to predict the presently unknown six-loop contributions to $\beta_g$, $\gamma_m$, and $\beta_v$. These predictions, as well as the six-loop prediction for $\gamma_2$, provide a test of asymptotic Pade-approximant methods against future calculations.
Chishtie Farrukh
Elias Victor
~Steele ~G. T.
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