Exact relations between running of
αs and
α in

SQCD + SQED
A. L. Kataev+*, K. V. Stepanyantz×
+Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia
*Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
×Moscow State University, Physical Faculty, Department of Theoretical Physics, 119991 Moscow, Russia
Abstract
In
supersymmetric QCD and QED theory we derive the (all-order)
exact equations relating the renormalization group behaviour of
the strong and electromagnetic couplings and prove that they are valid in the combined
higher covariant derivative
regularized and minimal subtraction of logarithms renormalized
prescription. In particular, the β-function
of
supersymmetric QCD can be expressed in terms of the Adler D-function.
If all flavors have the same absolute value of the
electromagnetic charges, it is also possible to write a simple relation
between the β-functions for the strong and electromagnetic coupling
constants. In this particular case there is a special renormalization
group invariant relation.