1,535 research outputs found
Considerations Concerning the Radiative Corrections to Muon Decay in the Fermi and Standard Theories
The FAC, PMS, and BLM optimization methods are applied to the QED corrections
to the muon lifetime in the Fermi V-A theory. The FAC and PMS scales are close
to m_e, while the BLM scale nearly concides with the geometric average
\sqrt{m_e m_\mu}. The optimized expressions are employed to estimate the third
order coefficient in the \alpha(m_\mu) expansion and the theoretical error of
the perturbative series. Using arguments based on effective field theory and a
simple examination of Feynman diagrams, it is shown that, if contributions of
O(\alpha m_\mu^2/M_W^2) are neglected, the corrections to muon decay in the SM
factorize into the QED correction of the Fermi V-A theory and the electroweak
amplitude g^2/(1-\Delta r), both of which are strictly scale-independent. We
use the results to clarify how the QED corrections to muon decay and the Fermi
constant G_F should be used in the SM, and what is the natural choice of scales
if running couplings are employed.Comment: 11 pages, latex, no figures To be published in Nucl. Phys.
Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions
For moments of leptoproduction structure functions we show that all
dependence on the renormalization and factorization scales disappears, provided
that all the ultraviolet logarithms involving the physical energy scale Q are
completely resummed. The approach is closely related to Grunberg's method of
Effective Charges. A direct and simple method for extracting the universal
dimensional transmutation parameter of QCD from experimental data is advocated.Comment: 16 pages, no figure
Nonperturbative Contributions in an Analytic Running Coupling of QCD
In the framework of analytic approach to QCD the nonperturbative
contributions in running coupling of strong interaction up to 4-loop order are
obtained in an explicit form. For all they are shown to be
represented in the form of an expansion in inverse powers of Euclidean momentum
squared. The expansion coefficients are calculated for different numbers of
active quark flavors and for different number of loops taken into
account. On basis of the stated expansion the effective method for precise
calculation of the analytic running coupling can be developed.Comment: 9 pages, LaTeX, 1 table, 1 eps figur
Infrared renormalons and analyticity structure in pQCD
Relation between the infrared renormalons, the Borel resummation
prescriptions, and the analyticity structure of Green functions in perturbative
QCD (pQCD) is investigated. A specific recently suggested Borel resummation
prescription resulted in the Principal Value and an additional power-suppressed
correction that is consistent with the Operator Product Expansion. Arguments
requiring the finiteness of the result for any power coefficient of the leading
infrared renormalon, and the consistency in the case of the absence of that
renormalon, require that this prescription be modified. The apparently most
natural modification leads to the result represented by the Principal Value.
The analytic structure of the amplitude in the complex coupling plane, obtained
in this way, is consistent with that obtained in the literature by other
methods.Comment: 6 pages, revtex4, 1 eps-figure; improved version - the paragraph
containing Eqs.(18) and (19) is new, as well as the next paragraph; the Title
modified; some references added; version to appear in Phys. Rev.
Various versions of analytic QCD and skeleton-motivated evaluation of observables
We present skeleton-motivated evaluation of QCD observables. The approach can
be applied in analytic versions of QCD in certain classes of renormalization
schemes. We present two versions of analytic QCD which can be regarded as
low-energy modifications of the ``minimal'' analytic QCD and which reproduce
the measured value of the semihadronic tau decay ratio r{tau}. Further, we
describe an approach of calculating the higher order analytic couplings Ak
(k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling
A1(Q^2). This approach can be easily applied in any version of analytic QCD. We
adjust the free parameters of the afore-mentioned two analytic models in such a
way that the skeleton-motivated evaluation reproduces the correct known values
of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given
point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the
Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation
approach, in the three analytic versions of QCD. We compare with the results
obtained in the ``minimal'' analytic QCD and with the evaluation approach of
Milton et al. and Shirkov.Comment: 30 pages, 14 eps-figures; v3: parameters of the analytic QCD models
M1 and M2 were refined, the numerical results modified accordingly, new
paragraph at the end of Sec.II and at the end of Sec.III, discussion of
Figs.4 extended, references added; version to appear in PR
Relating Physical Observables in QCD without Scale-Scheme Ambiguity
We discuss the St\"uckelberg-Peterman extended renormalization group
equations in perturbative QCD, which express the invariance of physical
observables under renormalization-scale and scheme-parameter transformations.
We introduce a universal coupling function that covers all possible choices of
scale and scheme. Any perturbative series in QCD is shown to be equivalent to a
particular point in this function. This function can be computed from a set of
first-order differential equations involving the extended beta functions. We
propose the use of these evolution equations instead of perturbative series for
numerical evaluation of physical observables. This formalism is free of
scale-scheme ambiguity and allows a reliable error analysis of higher-order
corrections. It also provides a precise definition for as the pole in the associated 't Hooft scheme. A concrete application to
is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages,
DOE/ER/40322-17
The Meson Production in Proton-Proton Collisions in Next-To-Leading Order and Infrared Renormalons
In this article, we investigate the next-to-leading order contribution of the
higher-twist Feynman diagrams to the large- inclusive pion production
cross section in proton-proton collisions and present the general formulae for
the higher-twist differential cross sections in the case of the running
coupling and frozen coupling approaches. We compared the resummed
next-to-leading order higher-twist cross sections with the ones obtained in the
framework of the frozen coupling approach and leading-twist cross section. The
structure of infrared renormalon singularities of the higher twist subprocess
cross section and it's resummed expression (the Borel sum) are found. It is
shown that the resummed result depends on the choice of the meson wave
functions used in the calculations. We discuss the phenomenological
consequences of possible higher-twist contributions to the meson production in
proton-proton collisions in next-to-leading order at RHIC.Comment: 33 pages, 15 figures, 4 table
Experimental determination of the effective strong coupling constant
We present a first attempt to experimentally extract an effective strong
coupling constant that we define to be a low Q2 extension of a previous
definition by S. Brodsky et al. following an initial work of G. Grunberg. Using
Jefferson Lab data and sum rules, we establish its Q2-behavior over the
complete Q2-range. The result is compared to effective coupling constants
inferred from different processes and to calculations based on Schwinger-Dyson
equations, hadron spectroscopy or lattice QCD. Although the connection between
the experimentally extracted effective coupling constants and the calculations
is not established it is interesting to note that their behaviors are similar.Comment: Published in Physics Letters B 650 4 24
Scale-independent mixing angles
A radiatively-corrected mixing angle has to be independent of the choice of
renormalization scale to be a physical observable. At one-loop in MS-bar, this
only occurs for a particular value, p*, of the external momentum in the
two-point functions used to define the mixing angle: p*^2=(M1^2+M2^2)/2, where
M1, M2 are the physical masses of the two mixed particles. We examine two
important applications of this to the Minimal Supersymmetric Standard Model:
the mixing angle for a) neutral Higgs bosons and b) stops. We find that this
choice of external momentum improves the scale independence (and therefore
provides a more reliable determination) of these mixing angles.Comment: 14 pages, 11 ps figures Version to appear in PR
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