2,679 research outputs found
Isospin Breaking Effects in the Extraction of Isoscalar and Isovector Spectral Functions From
We investigate the problem of the extraction of the isovector and isoscalar
spectral functions from data on , in the presence of
non-zero isospin breaking. It is shown that the conventional approach to
extracting the isovector spectral function in the resonance region, in
which only the isoscalar contribution associated with is
subtracted, fails to fully remove the effects of the isoscalar component of the
electromagnetic current. The additional subtractions required to extract the
pure isovector and isoscalar spectral functions are estimated using results
from QCD sum rules. It is shown that the corrections are small () in
the isovector case (though relevant to precision tests of CVC), but very large
() in the case of the contribution to the isoscalar spectral
function. The reason such a large effect is natural in the isoscalar channel is
explained, and implications for other applications, such as the extraction of
the sixth order chiral low-energy constant, , are discussed.Comment: minor changes to introduction, section 2. In Press Phys. Rev.
New high order relations between physical observables in perturbative QCD
We exploit the fact that within massless perturbative QCD the same Green's
function determines the hadronic contribution to the decay width and the
moments of the cross section. This allows one to obtain relations
between physical observables in the two processes up to an unprecedented high
order of perturbative QCD. A precision measurement of the decay width
allows one then to predict the first few moments of the spectral density in
annihilations integrated up to with high accuracy.
The proposed tests are in reach of present experimental capabilities.Comment: 7 pages, Latex, no figure
Test of the Running of in Decays
The decay rate into hadrons of invariant mass smaller than
can be calculated in QCD assuming global
quark--hadron duality. It is shown that this assumption holds for
~GeV. From measurements of the hadronic mass distribution, the
running coupling constant is extracted in the range
0.7~GeV. At , the result is
. The running of is in good
agreement with the QCD prediction.Comment: 9 pages, 3 figures appended; shortened version with new figures, to
appear in Physical Review Letters (April 1996
Remark on the perturbative component of inclusive -decay
In the context of the inclusive -decay, we analyze various forms of
perturbative expansions which have appeared as modifications of the original
perturbative series. We argue that analytic perturbation theory, which combines
renormalization-group invariance and -analyticity, has significant merits
favoring its use to describe the perturbative component of -decay.Comment: 5 pages, ReVTEX, 2 eps figures. Revised paper includes clarifying
remarks and corrected references. To be published in Phys. Rev.
The Physics of Hadronic Tau Decays
Hadronic tau decays represent a clean laboratory for the precise study of
quantum chromodynamics (QCD). Observables (sum rules) based on the spectral
functions of hadronic tau decays can be related to QCD quark-level calculations
to determine fundamental quantities like the strong coupling constant,
parameters of the chiral Lagrangian, |V_us|, the mass of the strange quark, and
to simultaneously test the concept of quark-hadron duality. Using the best
available measurements and a revisited analysis of the theoretical framework,
the value alpha_s(m_tau) = 0.345 +- 0.004[exp] +- 0.009[theo] is obtained.
Taken together with the determination of alpha_s(m_Z) from the global
electroweak fit, this result leads to the most accurate test of asymptotic
freedom: the value of the logarithmic slope of 1/alpha_s(s) is found to agree
with QCD at a precision of 4%. In another approach, the tau spectral functions
can be used to determine hadronic quantities that, due to the nonperturbative
nature of long-distance QCD, cannot be computed from first principles. An
example for this is the contribution from hadronic vacuum polarization to
loop-dominated processes like the anomalous magnetic moment of the muon. This
article reviews the measurements of nonstrange and strange tau spectral
functions and their phenomenological applications.Comment: 89 pages, 32 figures; final version accepted for publication by
Reviews of Modern Physic
Is there evidence for dimension-two corrections in QCD two-point functions?
The ALEPH data on the (non-strange) vector and axial-vector spectral
functions, extracted from tau-lepton decays, is used in order to search for
evidence for a dimension-two contribution, , to the Operator Product
Expansion (other than quark mass terms). This is done by means of a
dimension-two Finite Energy Sum Rule, which relates QCD to the experimental
hadronic information. The average is
remarkably stable against variations in the continuum threshold, but depends
rather strongly on . Given the current wide spread in the values
of , as extracted from different experiments, we would
conservatively conclude from our analysis that is consistent with zero.Comment: A misprint in Eq. (14) has been corrected. No other changes. Paper to
appear in Phys. Rev.
Bilocal expansion of the Borel amplitude and the hadronic tau decay width
The singular part of Borel transform of a QCD amplitude near the infrared
renormalon can be expanded in terms of higher order Wilson coefficients of the
operators associated with the renormalon. In this paper we observe that this
expansion gives nontrivial constraints on the Borel amplitude that can be used
to improve the accuracy of the ordinary perturbative expansion of the Borel
amplitude. In particular, we consider the Borel transform of the Adler function
and its expansion around the first infrared renormalon due to the gluon
condensate. Using the next-to-leading order Wilson coefficient of the gluon
condensate operator, we obtain an exact constraint on the Borel amplitude at
the first IR renormalon. We then extrapolate, using judiciously chosen
conformal transformations and Pade approximants, the ordinary perturbative
expansion of the Borel amplitude in such a way that this constraint is
satisfied. This procedure allows us to predict the coefficient
of the Adler function, which gives a result consistent with the estimate by
Kataev and Starshenko using a completely different method. We then apply this
improved Borel amplitude to the tau decay width, and obtain the strong coupling
constant . We then compare this result with those of
other resummation methods.Comment: 30 pages, 4 eps-figures, revtex; version as appears in PRD; no major
changes; more careful rounding of some number
The Adler Function for Light Quarks in Analytic Perturbation Theory
The method of analytic perturbation theory, which avoids the problem of
ghost-pole type singularities and gives a self-consistent description of both
spacelike and timelike regions, is applied to describe the "light" Adler
function corresponding to the non-strange vector channel of the inclusive decay
of the lepton. The role of threshold effects is investigated. The
behavior of the quark-antiquark system near threshold is described by using a
new relativistic resummation factor. It is shown that the method proposed leads
to good agreement with the ``experimental'' Adler function down to the lowest
energy scale.Comment: 13 pages, one ps figure, REVTe
Decay constants, light quark masses and quark mass bounds from light quark pseudoscalar sum rules
The flavor and pseudoscalar correlators are investigated using
families of finite energy sum rules (FESR's) known to be very accurately
satisfied in the isovector vector channel. It is shown that the combination of
constraints provided by the full set of these sum rules is sufficiently strong
to allow determination of both the light quark mass combinations ,
and the decay constants of the first excited pseudoscalar mesons in
these channels. The resulting masses and decay constants are also shown to
produce well-satisfied Borel transformed sum rules, thus providing non-trivial
constraints on the treatment of direct instanton effects in the FESR analysis.
The values of and obtained are in good agreement with the
values implied by recent hadronic decay analyses and the ratios obtained
from ChPT. New light quark mass bounds based on FESR's involving weight
functions which strongly suppress spectral contributions from the excited
resonance region are also presented.Comment: 28 pages, 10 figure
Testing QCD with Hypothetical Tau Leptons
We construct new tests of perturbative QCD by considering a hypothetical tau
lepton of arbitrary mass, which decays hadronically through the electromagnetic
current. We can explicitly compute its hadronic width ratio directly as an
integral over the e^+ e^- annihilation cross section ratio, R_{e^+e^-}.
Furthermore, we can design a set of commensurate scale relations and
perturbative QCD tests by varying the weight function away from the form
associated with the V-A decay of the physical tau. This method allows the wide
range of the R_{e^+e^-} data to be used as a probe of perturbative QCD.Comment: 4 pages, 4 figure
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