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Register a new userDistortions in the negative energy Dirac sea: violation of the Gottfried sum rule and $Deltabar{u}$ in proton
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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 $Deltabar{d}$.
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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.
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.
The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $m_{QED}^{p-n}=0.58pm 0.16,mbox{MeV}$.
We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.
We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark $XYZ$-like states at lowest order (LO) of perturbative (PT) QCD and up to $d=8$ condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the $XYZ$-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11 to 14 and compared, in Section 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the $XZ$ observed states are compatible with (almost) pure $J^{PC}=1^{+pm}, 0^{++}$ molecule or/and four-quark states. The ones of the $1^{-pm}, 0^{-pm}$ molecule / four-quark states are about 1.5 GeV above the $Y_{c,b}$ mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary $D,B$ mesons ($f_{DD}approx 10^{-3}f_D$) and may behave numerically as $1/ bar m_b^{3/2}$ (resp. $1/ bar m_b$) for the $1^{+},0^{+}$ (resp. $1^{-}, 0^{-}$) states which can stimulate further theoretical studies of these decay constants.
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