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Register a new userRegge trajectories of Excited Baryons, quark-diquark models and quark-hadron duality
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The parton model relations in conjunction with quark-hadron duality in deep inelastic scattering suggests an asymptotic dominance of quark-diquark type of baryonic excited states with a radial Regge uniformly distributed mass squared spectrum $M_{n}^2 = mu^2 n + M_0^2$. We argue that this points to a lineary quark-diquark confining potential. We analyze the radial ($n$) and angular-momentum ($J$) Regge trajectories for all light-quark states with baryon number one listed in the 2016 edition of the Particle Data Tables. The parameters of the mass squared trajectories are obtained by linear regression assuming $Delta M_n^2 sim M_n Gamma_n $ weighted with the width $Gamma_n$ of the resonance and the error analysis is carried out accordingly.
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Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10; {mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.
We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality violating contributions. Starting with the assumption that for QCD at $N_c=infty$ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite $N_c$.
An exhaustive number of QCD finite energy sum rules for $tau$-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension $d=2$ condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions $d=6$ and $d=8$, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic $tau$-decay in the kinematic region above $ssimeq2.2$ GeV$^{2}$ for these kernels.
New measurements of the spin structure functions of the proton and deuteron g1p(x,Q2) and g1d(x,Q2) in the nucleon resonance region are compared with extrapolations of target-mass-corrected next-to-leading-order (NLO) QCD fits to higher energy data. Averaged over the entire resonance region (W<2 GeV), the data and QCD fits are in good agreement in both magnitude and Q2 dependence for Q2>1.7 GeV2. This global duality appears to result from cancellations among the prominent local resonance regions: in particular strong sigma{3/2} contributions in the Delta(1232) region appear to be compensated by strong sigma{1/2} contributions in the resonance region centered on 1.5 GeV. These results are encouraging for the extension of NLO QCD fits to lower W and Q2 than have been used previously.
The vector and axial-vector ALEPH hadronic spectral functions from $tau$-decay are used to probe potential quark-hadron duality violations (DV). This is done in the framework of finite energy QCD sum rules (FESR). A pinched integration kernel is introduced in the FESR in order to (a) quench potential duality violations on the real axis in the complex squared energy $s$-plane, and (b) effectively extend the analysis well beyond the kinematical $tau$-decay end-point where there is no longer data, i.e. in the range $s = 3 - 10 ,{mbox{GeV}}^2$. In the vector channel this procedure is supplemented with actual data from $e^+ e^-$-annihilation into hadrons, above the tau-decay kinematical end-point, with results fully supporting this extension. Very good agreement is obtained between data and two specific pinched FESR. Results from this analysis are confronted with those from a specific model of DV. As the sum rules are well satisfied in both cases within experimental errors, we conclude that possible DV must be buried under the experimental uncertainties. In other words, there seems to be no need for explicit models of DV in this case. Pinched kernels work as well, but with far less free parameters.
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