Regge Behavior Research Articles

From Regge behavior to DGLAP evolution

We study the interface between Regge behavior and DGLAP evolution in a non-perturbative model for the nucleon structure function based on a multipole pomeron exchange. This model provides the input for a subsequent DGLAP evolution that we calculate numerically. The soft input and its evolution give a good fit to the experimental data in the whole available range of x and Q^2.

Erratum to: “Perturbative evolution and Regge behaviour”

Erratum to: “Perturbative evolution and Regge behaviour”

Reggeon exchange from AdS/CFT

Using the AdS/CFT correspondence in a confining background and the worldline formalism of gauge field theories, we compute scattering amplitudes with an exchange of quark and antiquark in the t-channel corresponding to reggeon exchange. It requires going beyond the eikonal approximation, which was used when studying pomeron exchange. The wordline path integral is evaluated through the determination of minimal surfaces and their boundaries by the saddle-point method at large gauge coupling g 2 N c . We find a Regge behaviour with linear Regge trajectories. The slope is related to the q q ̄ static potential and is four times the pomeron slope obtained in the same framework. A contribution to the intercept, related to the Lüscher term, comes from the fluctuations around the minimal surface.

Glueball as a bound state in the self-dual homogeneous vacuum gluon field

Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex p^2-plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the selfdual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless 0(++) two-glouon state from the QCD generating functional in the one-gluon exchange approximation. The mass of this bound state is defined by the Bethe-Salpeter equation. The glueball mass varies in the region 1470{Mev} - 1600{Mev} for QCD coupling constant in the region 0.2 - 0.5 if the gluon condensate is 0.012 Gev^4.

Valence quark distributions in mesons in generalized QCD sum rules

The method for calculation of valence quark distributions at intermediate x is presented. The imaginary part of the virtual photon forward scattering amplitude on the quark current with meson quantum number is considered. The initial and final virtualities ${p}_{1}^{2}$ and ${p}_{2}^{2}$ of the currents are assumed to be large, negative, and different, ${p}_{1}^{2}\ensuremath{\ne}{p}_{2}^{2}.$ The operator product expansion (OPE) in ${p}_{1}^{2}{,p}_{2}^{2}$ up to dimension 6 operators is performed. Double dispersion representations in ${p}_{1}^{2}{,p}_{2}^{2}$ of the amplitude in terms of physical state contributions are used. Setting them equal to those calculated in QCD by OPE, the desired sum rules for quark distributions in mesons are found. The double Borel transformations are applied to the sum rules, destroying nondiagonal transition terms, which deteriorated the accuracy in the previous calculations of quark distributions in the nucleon. Leading-order perturbative corrections are taken into account. Valence quark distributions in the pion and longitudinally and transversally polarized $\ensuremath{\rho}$ mesons are calculated at intermediate $x, 0.2\ensuremath{\lesssim}x\ensuremath{\lesssim}0.7$ and normalization points ${Q}^{2}=2\ensuremath{-}4 {\mathrm{GeV}}^{2}$ with no fitting parameters. The use of the Regge behavior at small x and quark counting rules at large x allows one to find the first and the second moments of valence quark distributions. The obtained quark distributions may be used as an input for evolution equations. In the case of the pion the quark distribution is in agreement with those found from the data on the Drell-Yan process. The quark distributions in transversally and longitudinally polarized $\ensuremath{\rho}$ mesons are essentially different.

Regge behaviour of structure function and gluon distribution at low-x in leading order

We present a method to find the gluon distribution from the $F_2$ proton structure function data at low-x assuming the Regge behaviour of the gluon distribution function at this limit. We use the leading order (LO) Altarelli–Parisi (AP) evolution equation in our analysis and compare our result with those of other authors. We also discuss the limitations of the Taylor expansion method in extracting the gluon distribution from the $F_2$ structure function used by those authors.

Scale anomaly and “soft” pomeron in QCD

We propose a new non-perturbative approach to hadronic interactions at high energies and small momentum transfer, which is based on the scale anomaly of QCD and emphasizes the role of semi-classical vacuum fields. We find that the hadron scattering amplitudes exhibit Regge behavior and evaluate the intercept alpha(0) of the corresponding trajectory. Both the intercept and the scale for the slope of the trajectory appear to be determined by the energy density of non-perturbative QCD vacuum (the gluon condensate). Numerically, we find Delta = alpha(0) - 1 = 0.08 -0.1, consistent with the values ascribed phenomenologically to the ``soft'' Pomeron. For arbitrary numbers of colors N_c and flavors N_f, Delta is found to be proportional to (N_f/N_c)^2; however, in the large N_c (N_f fixed) limit, Delta \sim N_c^0.

Total hadronic cross-section of photon-photon interactions at OPAL

The total hadronic cross-section σ γγ for the interaction of real photons, γγ → hadrons, is extracted from measurement of the cross-section of the process e + e − → e + e −γ ∗γ ∗ → e + e − + hadrons using a luminosity function for the photon flux and form factors for extrapolating to Q 2 = 0. The data was taken with the OPAL detector at LEP at e +e − centre-of-mass energies √ s ee = 161 GeV, 172 GeV and 183 GeV. In the energy range 10 ≤ W ≤ 110 GeV the total hadronic γγ cross-section σ γγ is consistent with the Regge behaviour of the total cross-section observed in γp and hadron-hadron interactions.

PROTON STRUCTURE FUNCTIONS FROM CHIRAL DYNAMICS AND QCD CONSTRAINTS

The spin fractions and deep inelastic lepton structure functions of the proton are analyzed using chiral field theory involving Goldstone bosons. A detailed comparison with recent chiral models sheds light on their successful description of the spin fractions of the proton as being due to neglecting helicity nonflip chiral transitions. This approximation is valid for zero mass but not for constituent quarks. Since the chiral spin fraction models with the pure spin-flip approximation reproduce the measured spin fractions of the proton, axialvector constituent-quark-Goldstone boson couplings are found to be inconsistent with the proton spin data. Initial quark valence distributions are then constructed using quark counting constraints at Bjorken x→1 and Regge behavior at x→0. Sea quark distributions predicted by chiral field theory on this basis have the correct order of magnitude and shape. The spin fractions also agree with the data.

Bethe-Salpeter Approach for Mesons in the Pion Channel within the Dual Ginzburg-Landau Theory

We develop a formalism for the study of mesons with the Bethe-Salpeter (BS) equation using the dual Ginzburg-Landau (DGL) theory. We introduce a new method to solve the BS equation by using the expansion method with momentum square at zero momentum. We apply this formalism to mesons in the pion channel with parity Π = −(−) J and charge conjugation C = −Π. Due to the confinement property of the gluon propagator in the DGL theory, we find the Regge behavior, M 2 ∝ J; that is, the mass square is proportional to the

Interpolating between soft and hard dynamics in deep inelastic scattering

An explicit model for the proton structure function is suggested, interpolating between low-\(Q^2\) vector meson dominance and Regge behavior, on the one hand, and the high-\(Q^2\) solution of the Gribov-Lipatov-Altarelli-Parisi evolution equation, on the other hand. The model is fitted to the experimental data in a wide range of the kinematical variables with emphasis on the low-x HERA data. The boundaries, transition region and interface between various regimes are quantified.

Total hadronic cross-section for photon-photon interactions at LEP

The total hadronic cross-section σ γγ for the interaction of real photons, γγ → hadrons, is extracted from a measurement of the cross-section of the process e + e − → e + e −γ ∗γ ∗ → ( e + e − + hadrons) using a luminosity function for the photon flux and form factors for extrapolating to Q 2 = 0. The data was taken with the OPAL detector at LEP at e +e − centre-of-mass energies √ s ee = 161 GeV and 172 GeV. In the energy range 10 ≤ W ≤ 110 GeV the total hadronic γγ cross-section σ γγ is consistent with the Regge behaviour of the total cross-section observed in γp and hadron-hadron interactions.

Interpolating between soft and hard dynamics in deep inelastic scattering

An explicit model for the proton structure function interpolating between low- (VMD and Regge behavior)and high-$Q^2$ (GLAP evolution) is suggested. The model is fitted to the experimental data in a wide range of the kinematical variables with emphasis on the low-$x$ HERA data. The boundaries, transition region and interface between various regimes are quantified.

PROTON STRUCTURE FUNCTIONS FROM CHIRAL DYNAMICS AND QCD CONSTRAINTS

The spin fractions and deep inelastic lepton structure functions of the proton are analyzed based on chiral field theory invloving Goldstone bosons. A detailed comparison with several recent chiral models sheds light on their successful description of the spin fractions of the proton as being due to neglecting quark masses. Initial quark valence distributions at a higher scale than Λ QCD are constructed using quark counting constraints at large Bjorken x→1 and Regge behavior at small x. Reasonable strange quark distributions are then predicted by chiral field theory. The spin fractions also agree with the data.

Regge behaviour from an environmentally friendly renormalization group

The asymptotic behaviour of cubic field theories is investigated in the Regge limit using the techniques of environmentally friendly renormalization, environmentally friendly in the present context meaning asymmetric in its momentum dependence. In particular we consider the crossover between large and small energies at fixed momentum transfer for a model scalar theory of the type phi^2 psi. The asymptotic forms of the crossover scaling functions are exhibited for all two particle scattering processes in this channel to one loop in a renormalization group improved perturbation theory.

Light-cone wavefunctions at small x

There exist an infinite number of exact small momentum fraction-$x$ boundary conditions on light-cone wavefunctions of bound states in gauge theory. They are necessary for finite expectation values of the invariant mass operator and relate components of the wavefunction from different Fock sectors. We illustrate their consequences by analyzing the small-$x$ quark Regge behavior of a heavy large-$N$ meson, finding power-law rise of unpolarized distributions. The polarized distribution changes sign and then vanishes with minus the unpolarized Regge intercept.

Cross section of hadron production in γγ collisions at LEP

The reaction e + e − → e + e − γ ∗ γ ∗ → e + e − hadrons is analysed using data collected by the L3 detector during the LEP runs at s = 130−140 GeV and s = 161 GeV . The cross sections σ(e + e − → e + e − hadrons) and σ(γγ → hadrons) are measured in the interval 5 ≤ W γγ ≤ 75 GeV. The energy dependence of the σ(γγ → hadrons) cross section is consistent with the universal Regge behaviour of total hadronic cross sections.

Determination of the Bjorken sum and strong coupling from polarized structure functions

We present an NLO perturbative analysis of all available data on the polarized structure function g 1 ( x, Q 2) with the aim of making a quantitative test of the validity of the Bjorken sum rule, of measuring α s and of deriving helicity fractions. We take particular care over the small x extrapolation, since it is now known that Regge behaviour is unreliable at perturbative scales. For fixed α 5, we find that if all the most recent data are included g A = 1.19 ± 0.09, confirming the Bjorken sum rule at the 8% level. We further show that the value of α s is now reasonably well constrained by scaling violations in the structure function data, despite the fact that it cannot yet be reliably fixed by the value of the Bjorken sum: our final result is a s ( m z ) = −0.008 +0.010. We also confirm earlier indications of a sizeable positive gluon polarization in the nucleon.

Measurement of the neutron spin structure function g n1 with a polarized 3He internal target

Results are reported from the HERMES experiment at HERA on a measurement of the neutron spin structure function g 1 n ( x, Q 2) in deep inelastic scattering using 27.5 GeV longitudinally polarized positrons incident on a polarized 3He internal gas target. The data cover the kinematic range 0.023 < × < 0.6 and 1 (GeV/ c) 2 < Q 2 < 15 (GeV/ c) 2. The integral ∫ 0.6 0.023 g 1 n ( x) dx evaluated at a fixed Q 2 of 2.5 (GeV/ c) 2 is −0.034 ± 0.013(stat.)±0.005(syst.). Assuming Regge behavior at low x, the first moment Г n 1 = ∫ 1 0 g 1 n ( x) dx is −0.037 ± 0.013(stat.)±0.005(syst.)±0.006(extrapol.).

Simple Amplitudes for ϕ3 Feynman ladder graphs

Recently, we proposed a new approach for calculating Feynman graphs amplitude using the Gaussian representation for propagators which was proven to be exact in the limit of graphs having an infinite number of loops. Regge behavior was also found in a completely new way and the leading Regge trajectory calculated. Here we present symmetry arguments justifying the simple form used for the polynomials in the Feynman parameters [Formula: see text], where [Formula: see text] is the mean-value for these parameters, appearing in the amplitude for the ladder graphs. (Taking mean-values is equivalent to the Gaussian representation for propagators.)