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Register a new userFour-loop QCD analysis of the Bjorken sum rule vs data
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We study the polarized Bjorken sum rule at low momentum transfers in the range $0.22<Q<1.73 {rm GeV}$ with the four-loop N$^3$LO expression for the coefficient function $C_{rm Bj}(alpha_s)$ in the framework of the common QCD perturbation theory (PT) and the singularity-free analytic perturbation theory (APT). The analysis of the PT series for $C_{rm Bj}(alpha_s)$ gives a hint to its asymptotic nature manifesting itself in the region $Q<1$ GeV. It relates to the observation that the accuracy of both the three- and four-loop PT predictions happens to be at the same 10% level. On the other hand, the usage of the two-loop APT allows one to describe the precise low energy JLab data down to $Qsim 300$ MeV and gives a possibility for reliable extraction of the higher twist (HT) corrections. At the same time, above $Qsim 700$ MeV the APT two-loop order with HT is equivalent to the four-loop PT with HT compatible to zero and is adequate to current accuracy of the data.
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We have studied the charmonium and bottomonium hybrid states with various $J^{PC}$ quantum numbers in QCD sum rules. At leading order in $alpha_s$, the two-point correlation functions have been calculated up to dimension six including the tri-gluon condensate and four-quark condensate. After performing the QCD sum rule analysis, we have confirmed that the dimension six condensates can stabilize the hybrid sum rules and allow the reliable mass predictions. We have updated the mass spectra of the charmonium and bottomonium hybrid states and identified that the negative-parity states with $J^{PC}=(0, 1, 2)^{-+}, 1^{--}$ form the lightest hybrid supermultiplet while the positive-parity states with $J^{PC}=(0, 1)^{+-}, (0, 1, 2)^{++}$ belong to a heavier hybrid supermultiplet.
The in-medium masses of the bottomonium ground states [$1S$ ($Upsilon (1S), eta_b$) and $1P$ ($chi_{b0},chi_{b1}$)] are investigated in the magnetized vacuum (nuclear medium), using the QCD sum rule framework. In QCD sum rule approach, the mass modifications are calculated in terms of the medium modifications of the scalar and twist-2 gluon condensates, which are obtained in the nuclear medium, from the medium change of a scalar dilaton field, $chi$ within a chiral effective model. The in-medium masses of the bottomonium ground states are observed to decrease with increasing density. P-wave states are observed to have more appreciable mass-shifts than the S-wave states. In the present investigation, the effects of spin-mixing between 1S bottomonium states, $Upsilon(1S)$ and $eta_b$ are taking into account in presence of an external magnetic field. The contribution of magnetic fields are seen to be dominant via spin-magnetic field interaction effects, which leads to an appreciable rise and drop in the in-medium masses of the longitudinal component of vector $1S$ state ($Upsilon$) and pseudoscalar state ($eta_b$) respectively. For zero magnetic field, the effects of baryon density on the bottomonium ground states in isospin asymmetric nuclear medium are observed to be quite appreciable. These should have observable consequences for the production of the open and hidden bottom meson states resulting from high energy asymmetric nuclear collisions in facilities which probe high density baryonic matter. There is observed to be large contributions to the masses of the longitudinal component of the vector bottomonium state, $Upsilon (1S)$ and pesudoscalar state $eta_b$ in strong magnetic fields.
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A.L. Kataev (Institute for Particle Physics Phenomenology
, Universityn of Durham
, Durham
2003
The current status of theoretical QCD calculations and experimental measurements of the Gottfried sum rule are discussed. The interesting from our point of view opened problems are summarised. Among them is the task of estimating the measure of light-quark flavour asymmetry in possible future experiments.
We study the semileptonic branching fraction of $B$-meson into higher resonance of charmed meson $D^{**}$ by using the Bjorken sum rule and the heavy quark effective theory(HQET). This sum rule and the current experiment of $B$-meson semileptonic decay into $D$ and $D^*$ predict that the branching ratio into $D^{**}l u_l$ is about 1.7%. This predicted value is larger than the value obtained by the various theoretical hadron models based on the HQET.
In the present paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach up to ${cal O}(alpha_s^4)$-level still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate $alpha_s$-running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low $Q^2$-region, the effective momentum of the process is small and to have a reliable prediction, we adopt four low-energy $alpha_s$ models to do the analysis. Our predictions show that even though the high-twist terms are generally power suppressed in high $Q^2$-region, they shall have sizable contributions in low and intermediate $Q^2$ domain. By using the more accurate scheme-and-scale independent pQCD prediction, we present a novel fit of the non-perturbative high-twist contributions by comparing with the JLab data.
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