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Register a new userThe Gross-Llewellyn Smith sum rule up to ${cal O}(alpha_s^4)$-order QCD corrections
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In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the $mathcal{O}(alpha_s^4)$-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent fixed-order pQCD contribution for GLS sum rule, e.g. $S^{rm GLS}(Q_0^2=3{rm GeV}^2)|_{rm PMC}=2.559^{+0.023}_{-0.024}$, where the error is squared average of those from $Deltaalpha_s(M_Z)$, the predicted $mathcal{O}(alpha_s^5)$-order terms predicted by using the Pad{e} approximation approach. After applying the PMC, a more convergent pQCD series has been obtained, and the contributions from the unknown higher-order terms are highly suppressed. In combination with the nonperturbative high-twist contribution, our final prediction of GLS sum rule agrees well with the experimental data given by the CCFR collaboration.
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The order $alpha_s^2$ perturbative QCD correction to the Gottfried sum rule is obtained. The result is based on numerical calculation of the order $alpha_s^2$ contribution to the coefficient function and on the new estimate of the three-loop anomalous dimension term. The correction found is negative and rather small. Therefore it does not affect the necessity to introduce flavour-asymmetry between $bar{u}$ and $bar{d}$ antiquarks for the description of NMC result for the Gottfried sum rule.
We provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark $Q$. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known $overline{rm MS}$ mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the $overline{rm MS}$ mass concept to renormalization scales $ll m_Q$. The MSR mass depends on a scale $R$ that can be chosen freely, and its renormalization group evolution has a linear dependence on $R$, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the ${cal O}(Lambda_{rm QCD})$ renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the ${cal O}(Lambda_{rm QCD})$ renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.
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QCD one-loop corrections to the semileptonic process $e^+ e^- to mu^- bar u_mu u bar d$ are computed. We compare the exact calculation with a ``naive approach to strong radiative corrections which has been widely used in the literature and discuss the phenomenological relevance of QCD contributions for LEP2 and NLC physics.
We calculate the next-to-next-to-leading order ${cal O}(alpha_s^4)$ one-loop squared corrections to the production of heavy-quark pairs in the gluon-gluon fusion process. Together with the previously derived results on the $q bar{q}$ production channel the results of this paper complete the calculation of the one-loop squared contributions of the next-to-next-to-leading order ${cal O}(alpha_s^4)$ radiative QCD corrections to the hadroproduction of heavy flavors. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in dimensional regularization.
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