Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-09-04
Nucl.Phys. B553 (1999) 511-530
Physics
High Energy Physics
High Energy Physics - Phenomenology
21 pages, LaTeX, 6 ps figures
Scientific paper
10.1016/S0550-3213(99)00262-X
We consider the problem of improving the effective potential in mass independent schemes, as e.g. the $\MSbar$ or $\DRbar$ renormalization scheme, in the presence of an arbitrary number of fields with $\phi$-dependent masses $M_i(\phi_c)$. We use the decoupling theorem at the scales $\mu_i=M_i(\phi_c)$ such that the matching between the effective (low energy) and complete (high energy) one-loop theories contains no thresholds. We find that for any value of $\phi_c$, there is a convenient scale $\mu^*\equiv\min_i\{M_i(\phi_c)\}$, at which the loop expansion has the best behaviour and the effective potential has the least $\mu$-dependence. Furthermore, at this scale the effective potential coincides with the (improved) tree-level one in the effective field theory. The decoupling method is explicitly illustrated with a simple Higgs-Yukawa model, along with its relationship with other decoupling prescriptions and with proposed multi-scale renormalization approaches. The procedure leads to a nice suppression of potentially large logarithms and can be easily adapted to include higher-loop effects, which is explicitly shown at the two-loop level.
Casas Alberto J.
Clemente Vicente Di
Quiros Mariano
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