Abstract
Abstract
The one-loop beta functions for systems of Ns scalars and Nf fermions interacting via a general potential are analysed as tensorial equations in 4 − ε dimensions. Two distinct bounds on combinations of invariants constructed from the couplings are derived and, subject to an assumption, are used to prove that at one-loop order the anomalous dimensions of the elementary fields are universally restricted by γϕ ⩽ $$ \frac{1}{2} $$
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Nsε and γψ ⩽ Nsε. For each root of the Yukawa beta function there is a number of roots of the quartic beta function, giving rise to the concept of ‘levels’ of fixed points in scalar-fermion theories. It is proven that if a stable fixed point exists within a certain level, then it is the only such fixed point at that level. Solving the beta function equations, both analytically and numerically, for low numbers of scalars and fermions, well-known and novel fixed points are found and their stability properties are examined. While a number of fixed points saturate one out of the two bounds, only one fixed point is found which saturates both of them.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Cited by
2 articles.
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