Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHyperasymptotics and quark-hadron duality violations in QCD
73
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 $N_c$.
rate research
Read More
We establish a holographic bottom-up model which covers both the baryonic and quark matter phases in cold and dense QCD. This is obtained by including the baryons using simple approximation schemes in the V-QCD model, which also includes the backreaction of the quark matter to the dynamics of pure Yang-Mills. We examine two approaches for homogeneous baryon matter: baryons as a thin layer of noninteracting matter in the holographic bulk, and baryons with a homogeneous bulk gauge field. We find that the second approach exhibits phenomenologically reasonable features. At zero temperature, the vacuum, baryon, and quark matter phases are separated by strongly first order transitions as the chemical potential varies. The equation of state in the baryonic phase is found to be stiff, i.e., the speed of sound clearly exceeds the value $c_s^2=1/3$ of conformal plasmas at high baryon densities.
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.
The origin of quark-hadron Duality Violations (DVs) can be related to the sigularities of the Laplace transform of the spectral function. With the help of rather generic properties of the large-$N_c$ approximation and a generalized form for the radial trajectories found in Regge Theory, we may locate these singularities in the complex plane and obtain an expression for the DVs which turns out to agree with general expectations. Using the two-point vector correlator as a test laboratory, we show how the usual dispersion relation may give rise to perturbation theory, the power corrections from the condensate expansion and DVs.
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.
Using data from the recent BONuS experiment at Jefferson Lab, which utilized a novel spectator tagging technique to extract the inclusive electron-free neutron scattering cross section, we obtain the first direct observation of quark-hadron duality in the neutron F_2 structure function. The data are used to reconstruct the lowest few (N=2, 4 and 6) moments of F_2 in the three prominent nucleon resonance regions, as well as the moments integrated over the entire resonance region. Comparison with moments computed from global parametrizations of parton distribution functions suggest that quark--hadron duality holds locally for the neutron in the second and third resonance regions down to Q^2 ~ 1 GeV^2, with violations possibly up to 20% observed in the first resonance region.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
