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Register a new userThe Gottfried sum rule: theory vs experiment
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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.
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We report on recent work concerning the effect which the change in vacuum structure (negative energy Dirac sea), in the presence of a confining scalar field, has on the nucleon structure functions and parton distributions. Using the Dirac equation in 1+1 dimensions, we show that distortions in the Dirac sea are responsible for part of the violation of the Gottfried sum rule -- i.e., part of the flavor asymmetry in the proton sea. Our basic argument is that, even if isospin is an exact symmetry, the presence of a confining potential changes the vacuum structure, and inevitably leads to a violation of SU(2) flavour symmetry in a hadron with a different number of valence $u$ and $d$ quarks. The same mechanism also leads to a prediction for $Deltabar{u}$ and $Deltabar{d}$.
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 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.
We derive a new QCD sum rule for $D(0^+)$ which has only the $Dpi$ continuum with a resonance in the hadron side, using the assumption similar to that has been successfully used in our previous work to the mass of $D_s(0^+)(2317)$. For the value of the pole mass $M_c=1.38 $ GeV as used in the $D_s(0^+)$ case we find that the mass of $D(0^+)$ derived from this sum rule is significantly lower than that derived from the sum rule with the pole approximation. Our result is in agreement with the experimental dada from Belle.
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.
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