Diffraction and an infrared finite gluon propagator

Abstract

We discuss some phenomenological applications of an infrared finite gluon propagator characterized by a dynamically generated gluon mass. In particular we compute the effect of the dynamical gluon mass on pp andpp diffractive scattering. We also show how the data on γp photoproduction and hadronic γγ reactions can be derived from the pp andpp forward scattering amplitudes by assuming vector meson dominance and the additive quark model. I. A QCD-INSPIRED EIKONAL MODEL WITH A GLUON DYNAMICAL MASSNowadays, several studies support the hypothesis that the gluon may develop a dynamical mass [1,2]. This dynamical gluon mass, intrinsically related to an infrared finite gluon propagator [3], and whose existence is strongly supported by recent QCD lattice simulations [4]), has been adopted in many phenomenological studies [5,6,7]. Hence it is natural to correlate the arbitrary mass scale that appears in QCD-inspired models with the dynamical gluon one, obtained by Cornwall [1] by means of the pinch technique in order to derive a gauge invariant Schwinger-Dyson equation for the gluon propagator. This connection can be done building a QCD-based eikonal model where the onset of the dominance of gluons in the interaction of high-energy hadrons is managed by the dynamical gluon mass scale.A consistent calculation of high-energy hadron-hadron cross sections compatible with unitarity constraints can be automatically satisfied by use of an eikonalized treatment of the semihard parton processes. In an eikonal representation, the total cross sections is given bywhere s is the square of the total center-of-mass energy and χ(b, s) is a complex eikonal function:In terms of the proton-proton (pp) and antiproton-proton (pp) scatterings, this combination reads χp p pp (b, s) = χ + (b, s) ± χ − (b, s). Following the Ref.[8], we write the even eikonal as the sum of gluon-gluon, quark-gluon, and quark-quark contributions:Here W (b; µ) is the overlap function at impact parameter space and σ ij (s) are the elementary subprocess cross sections of colliding quarks and gluons (i, j = q, g). The overlap function is associated with the Fourier transform of a dipole form factor, W (b; µ) = (µ 2 /96π) (µb) 3 K 3 (µb), where K 3 (x) is the modified Bessel function of second kind. The odd eikonal χ − (b, s), that accounts for the FIG. 1: The χ 2 /DOF as a function of dynamical gluon mass mg.difference between pp andpp channels, is parametrized aswhere m g is the dynamical gluon mass and the parameters C − and µ − are constants to be fitted. The factor Σ is defined as Σ ≡ 9πᾱ 2 s (0)/m 2 g , with the dynamical coupling constantᾱ s set at its frozen infrared value. The eikonal functions χ qq (b, s) and χ qg (b, s), needed to describe the lower-energy forward data, are simply parametrized with terms dictated by the Regge phenomenology [8]; the gluon term χ gg (b, s), that dominates the asymptotic behavior of hadron-hadron total cross sections, is written asHere F gg (τ ) ≡ [g ⊗ g](τ ) is the convoluted structure function for pair gg, C ′ is a normalizatio...

THE SMALL x BEHAVIOR OF THE GLUON STRUCTURE FUNCTION FROM TOTAL CROSS-SECTIONS

“…In this model (henceforth referred to as DGM model) the onset of the dominance of semihard gluons in the interaction of high-energy hadrons is managed by the dynamical gluon mass m g [11] (intrinsically related to an infrared finite gluon propagator, [12]) whose existence is strongly supported by recent QCD lattice simulations [13] as well as by phenomenological results [6,11,14,15,16,17]; for recent reviews on the phenomenology of massive gluons see Ref. [18] and references therein. In the DGM model the infrared coupling constant is also a function of the dynamical gluon mass [11].…”

A brief summary of d = 3 NAGTs

“…Chapter 6 gives a value 0.5. We can also compare this result to phenomenological determinations [29,30,31] of α s (q 2 0) 0.7 ± 0.3 coming from studies of infrared-sensitive scattering data. But in the real world to which these data apply, there are three families of light quarks, so we have to modify the FSE estimate.…”

Hybrid meson interpretation of the exotic resonance π_{1}(1600)

“…Therefore the infrared finiteness of the effective charge can be considered as one of the manifestations of the phenomenon of dynamical gluon mass generation. Phenomenology sensitive to infrared properties of QCD gives: α s (0) ≃ 0.7 ± 0.3 [61][62][63], while the phenomenological evidences for the strong coupling constant freezing in the infrared are much more numerous, as with the models where a static potential is used to compute the hadronic spectra make use of a frozen coupling constant at long distances, for more details see for example the Ref. [64].…”