Study of vector boson decay and determination of the Standard Model parameters at hadronic colliders Page: 4 of 27
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2. Specifying the Standard Model
The Standard Model parameters are the fermion masses, the SU(2) and U(l) cou-
pling constants, the scaler Higgs vacuum expectation value, and the Higgs self coupling.
In a traditional transformation to a physically observable basis, the Higgs parameters
become the universal Fermi constant, Gp, and the Higgs mass, Mh, and the couplings
become the fine structure constant, a, and the sine of the Weinberg angle, sin 0w- The
advantage of this parameterization is obviously the precision with which a and Gf are
known from measurements of g-2 and the muon lifetime, and the accessibility of sin Sy/
via low energy neutral current experiments.
Problems arise, however, when higher order corrections are included. Sin^w is
defined by a variety of tree levei diagrams; when higher order diagrams are added, each of
these different processes yields a different value of sin To further obscure the matter,
the corrections depend on the fermion masses, and thus the unknown Mtop.
In order to compare the results of different measurements of sin it has become
customary to adopt, as a standard, the “on-shell” renormalization convention of Marciano
and Sirlin, where
”*j ** -1 - 9 «
is true to all orders, and radiative corrections are absorbed entirely into the vector boson
masses, such that
(1 — Ar)sin2#w (1 — Ar) sin2 8yr cos3
where A encompasses the well measured quantities
37.2805 ± 0.0003
and Ar encompasses the boson self-energy corrections. These corrections again depend
somewhat strongly on the fermion masses, particularly the unknown Mtopt and weakly on
The historical utility of this scheme was its use as a renormalization standard by
which different low energy neutral current experiments could recalculate and compare
their different measurements of sin Oyf. Viewed in a contemporary light, however, it
suggests a more contemporary basis. First, it is obvious from Eq. 1 that Mj; and Mw
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Amidei, D. Study of vector boson decay and determination of the Standard Model parameters at hadronic colliders, article, January 11, 1991; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1100190/m1/4/: accessed March 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.