# 11.11.2003 M.Kalmykov # format: MAPLE # We use the following notations # "pi" is Pi = 3.14.... # "mmH" is a square of Higgs-boson mass # "mmZ" is a square of Z-boson mass # "mmW" is a square of W-boson mass # "mmd1" is a square of d-quark mass # "mmd2" is a square of c-quark mass # "mmd3" is a square of b-quark mass # "mmu1" is a square of u-quark mass # "mmu2" is a square of s-quark mass # "mmu3" is a square of t-quark mass # "e" is a electric charge, so that e^2/(4*pi) \sim 1/137... # It is equal in our notations eP, eP:=137.036; # and we use the auxiliary parameter alpha, alpha:=1/(4*Pi*eP); # "s" is sin of Weinberg angle, s^2 = 1-mmW/mmZ \sim 1/4; # "mm" is a renormalization scale, mu^2. ###################################### # # Important notes: # ####################################### # # The result is expressible in terms of alpha(0). # To transfer it into alpha(M_Z) you can use the following expression: # (see, Eq.(5.3), (5.6) in Nucl.Phys. B 658 (2003) 49. # # alpha(M_Z) - alpha(0) := evalf( # alpha*(7*ln(mmW/mm)-2/3 - 4/3*( ln(mme1/mm) + ln(mme2/mm) + ln(mme3/mm) ) # - 16/9*ln(mmu3/mm) # - 44/9*(ln(mmW/mm) - 5/3) # ) # +HADRONS ); #where the value of HADRONS can be extracted from # F.Jegerlehner, hep-ph/0105283; HADRONS:=0.027572 # hep-ph/0310234; HADRONS:=0.027690