Quartic Mass Corrections to $R_{had}$

Abstract

The influence of nonvanishing quark masses on the total cross section in electron positron collisions and on the $Z$ decay rate is calculated. The corrections are expanded in $m^2/s$ and $\as$. Methods similar to those applied for the quadratic mass terms allow to derive the corrections of order $\as m^4/s^2$ and $\as^2m^4/s^2$. Coefficients which depend logarithmically on $m^2/s$ and which cannot be absorbed in a running quark mass arise in order $\as^2$. The implications of these results on electron positron annihilation cross sections at LEP and at lower energies in particular between the charm and the bottom threshold and for energies several GeV above the $b\bar{b}$ threshold are discussed.

17 pages, LaTex (uses epsf.sty, figures appended as uuencoded ps- and eps-files). A complete postscript file, including figures, is available via anonymous ftp at ttpux2.physik.uni-karlsruhe.de (129.13.102.139) as /pub/ttp94-08/ttp94-08.ps, Local preprint# TTP94-08

References in corpus (5)

• Heavy Quark Vacuum Polarisation to Three Loops
• The alpha_s^3 correction to Gamma (Z^0 -> hadrons)
• The ${\alpha }_s^3$ Corrections to the Effective Neutral Current and to the Z Decay Rate in the Heavy Top Quark Limit
• $R_{had}$ at the $B$-factory
• Flavour Singlet $\mathcal{O}({\alpha }_s^2{m}_b^2/m_t^2)$ Corrections to the Partial Decay Rate $\Gamma (Z\to b\bar{b})$

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