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 $Q>\Lambda$ 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 $n_f$ 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

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-$p_T$ 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

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.

Commensurate Scale Relations in Quantum Chromodynamics

We use the BLM method to show that perturbatively-calculable observables in QCD can be related to each other without renormalization scale or scheme ambiguity. We define and study the commensurate scale relations. We show that the commensurate scales satisfy the renormalization group transitivity rule which ensures that predictions in PQCD are independent of the choice of an intermediate renormalization scheme. We generalize the BLM procedure to higher order. The application of this procedure to relate known physical observables in QCD gives surprisingly simple results. In particular, the annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule for polarized electroproduction are related through simple coefficients, which reinforces the idea of a hidden symmetry between these two observables.Comment: 35 pages (RevTeX), one PostScript figure included at the end. SLAC-PUB-6481, UMD Preprint #94-13

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

Individual and collective stock dynamics: intra-day seasonalities

We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion kurtosis is a markedly decreasing function of the index return. This means that during large market swings, the idiosyncratic component of the stock dynamics becomes sub-dominant. In a nutshell, early hours of trading are dominated by idiosyncratic or sector specific effects with little surprises, whereas the influence of the market factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure

Test of the Running of αs\alpha_s in τ\tau Decays

The $\tau$ decay rate into hadrons of invariant mass smaller than $\sqrt{s_0}\gg\Lambda_{\rm QCD}$ can be calculated in QCD assuming global quark--hadron duality. It is shown that this assumption holds for $s_0>0.7$~GeV$^2$. From measurements of the hadronic mass distribution, the running coupling constant $\alpha_s(s_0)$ is extracted in the range 0.7~GeV$^2<s_0<m_\tau^2$. At $s_0=m_\tau^2$, the result is $\alpha_s(m_\tau^2)=0.329\pm 0.030$. The running of $\alpha_s$ 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

On parton distributions beyond the leading order

The importance of properly taking into account the factorization scheme dependence of parton distribution functions is emphasized. A serious error in the usual handling of this topic is pointed out and the correct procedure for transforming parton distribution functions from one factorisation scheme to another recalled. It is shown that the conventional $\overline{\rm {MS}}$ and DIS definitions thereof are ill-defined due to the lack of distinction between the factorisation scheme dependence of parton distribution functions and renormalisation scheme dependence of the strong coupling constant $\alpha_s$. A novel definition of parton distribution functions is suggested and its role in the construction of consistent next-to-leading order event generators briefly outlined.Comment: PRA-HEP-93/05, Latex, 10 pages and 2 Postscript figures appended at the end of this fil

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 $\tau$ decay width and the moments of the $e^+e^-$ 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 $\tau$ decay width allows one then to predict the first few moments of the spectral density in $e^+e^-$ annihilations integrated up to $s\sim m_\tau^2$ with high accuracy. The proposed tests are in reach of present experimental capabilities.Comment: 7 pages, Latex, no figure

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 $O(\alpha_s^4)$ 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 $\alpha_s(M_Z) =0.1193 \pm 0.0007_{exp.} \pm 0.0010_{EW+CKM} \pm 0.0009_{meth.} \pm 0.0003_{evol.}$. 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