Unraveling duality violations in hadronic tau decays Page: 3 of 20
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Ever since the seminal work of Ref. , it has been recognized that hadronic tau decays
provide an excellent experimental setting for extracting precise values of Standard Model
parameters such as the strong coupling constant a, , the strange quark mass m, , and
the CKM matrix element V.S, .
The importance of a precise determination of QCD parameters can hardly be overempha-
sized, both in order to test the validity of the Standard Model as well as to constrain physics
beyond the Standard Model. In particular, as has a special status as the coupling constant
of QCD. The current world average value as given by Ref.  is
a,(M ) = 0.1189 0.0010 . (1.1)
Methods to determine a, include, among others, deep inelastic scattering, the e+e- cross
section, the Z width, and the lattice. What is special about the determination from tau
decays is that it extracts a, at a remarkably low energy scale (m = 1.777 GeV), but still
high enough for perturbation theory to be applicable and non-perturbative effects to be small.
Because of asymptotic freedom, the relative error on as gets reduced by roughly a factor of
three after evolving it from the tau mass to the Z mass. Recently, Ref.  performed an
analysis based on the ALEPH data collected at LEP, quoting as the final value
a, (m2) = 0.345 0.004exp 0.009th , (1.2)
which, extrapolated to the Z mass, gives
a,(M ) = 0.1215 0.0004exp 0.0010th 0.0005evoi (1.3)
= 0.1215 0.0012 .
A somewhat more conservative estimate was given in Ref. :
a,(m ) = 0.340 0.005exp 0.014th , (1.4)
as(Mf) = 0.1209 0.0006exp 0.0016th 0.0005evoi
= 0.1209 0.0018 .
These results are compatible with the OPAL value of a,(MZ) = 0.1219 0.0010exp
0.0017th  .
The results in (1.3), together with the lattice result 
as(Mf) = 0.1170 0.0012 , (1.5)
are the most precise determinations of the strong coupling constant to date. Remarkably,
they differ from each other by 2.7 standard deviations. In fact, as emphasized by Bethke ,
these two values extracted from tau decay and the lattice differ from the world average com-
puted with all the other measurements by +1.8 and -1.6 standard deviations, respectively.
Given the relevance of these measurements, we think it is timely to assess the validity of the
theoretical assumptions that go into the estimates of systematic errors in both cases. Our
aim in this paper is to do this for the result extracted from tau data.
We may subdivide the systematic uncertainties in the tau determination of the strong
coupling according to three (not mutually independent) categories:
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Cata, Oscar; Cata, Oscar; Golterman, Maarten & Peris, Santiago. Unraveling duality violations in hadronic tau decays, article, March 3, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc899116/m1/3/: accessed September 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.