Pomeron Intercept Research Articles

THE SPIN CONTRIBUTION TO THE pp-TOTAL CROSS-SECTION AT HIGH ENERGY

The experimental data on the pp-total cross-sections including the spin-dependent parts are analyzed with the goal to determine the contribution of spin interactions at high energies. Based on the Regge model with cuts, the energy dependencies of such contributions are estimated for two spin-dependent terms: (1) the total spin dependent term, σ1 and (2) the spin projection dependent term, σ2. The estimates show that their contributions to the unpolarized total cross section, σ0, decrease with energy from several % around 2 GeV/c to 10-2% around 200 GeV/c. The assumption σ1= -σ2 does not seem to be correct, while the hypothesis 3 σ1=-σ2 is more preferable, especially in the measured energy interval 2-6 GeV. There is a clear indication that the spin effects are sensitive to the pomeron intercept at - t=0 (GeV/c)2. In order to pin down such effects the spin dependent total cross-sections must be measured with precisions better than 10 μb at 200 GeV/c.

A More Restrictive Upper Bound for the Bare Pomeron Intercept

By studying the properties of the modified Gribov-Levin-Ryskin evolution equation which incorporates both shadowing and antishadowing effects, the more restrict upper bound is set for the bare pomeron intercept in the case when gluons uniformly distribute within the proton.

Irreducible part of the next-to-leading BFKL kernel

On the basis of previous work by Fadin, Lipatov, and collaborators, and of our group, we extract the "irreducible" part of the next-to-leading (NL) BFKL kernel, we compute its (IR finite) eigenvalue function, and we discuss its implications for small-x structure functions. We find consistent running coupling effects and sizable NL corrections to the Pomeron intercept and to the gluon anomalous dimension. The qualitative effect of such corrections is to smooth out the small-x rise of structure functions at low values of Q2. A more quantitative analysis will be possible after the extraction of some additional, energy-scale dependent contributions to the kernel, which are not treated here.

Study of photon dissociation in diffractive photoproduction at HERA

Diffractive dissociation of quasi-real photons at a photon-proton centre of mass energy of W >> 200 GeV is studied with the ZEUS detector at HERA. The process under consideration is {gamma}{rho}{yields} XN, where X is the diffractively dissociated photon system of mass MX and N is either a proton or a nucleonic system with mass MN < 2 GeV. The cross section for this process in the interval 3 < MX < 24 GeV relative to the total photoproduction cross section was measured to be s{sup partial}D/s{sub tot} = 6.2 {+-}0.2 (stat) {+-}1.4 (syst)%. After extrapolating this result to the mass interval of mf2 < MX2 < 0.05W2 and correcting it for proton dissociation, the fraction of the total cross section attributed to single diffractive photon dissociation, {gamma}{rho}{yields}, is found to be s{sub SD}/s{sub tot} = 13.3 {+-}0.5 (stat){+-}3.6(syst)%. The mass spectrum of the dissociated photon system in the interval 8 < MX < 24 GeV can be described by the triple pomeron (PPP) diagram with an effective pomeron intercept of {alpha}{sub P}(0)=1.12{+-}0.04(stat) {+-}0.08(syst). The cross section for photon dissociation in the range 3 < MX < 8 GeV is significantly higher than that expected from the triple pomeron amplitudemore » describing the region 8 < MX < 24 GeV. Assuming that this discrepancy is due to a pomeron-pomeron-reggeon (PPR) term, its contribution to the diffractive cross section in the interval 3 < MX < 24 GeVis estimated to be f{sub PPR}=26{+-} 3(stat) {+-} 12(syst).« less

Diffraction dissociation in photoproduction at HERA

A study is presented of the process γp → XY, where there is a large rapidity gap between the systems X and Y. Measurements are made of the differential cross section as a function of the invariant mass M X of the system produced at the photon vertex. Results are presented at centre of mass energies of 〈W〉 = 187 GeV and 〈W〉 =231 GeV, both where the proton dominantly remains intact and, for the first time, where it dissociates. Both the centre of mass energy and the \(M_X^2\) dependence of HERA data and those from a fixed target experiment may simultaneously be described in a triple-Regge model. The low mass photon dissociation process is found to be dominated by diffraction, though a sizable subleading contribution is present at larger masses. The pomeron intercept is extracted and found to be αP(0) = 1.068 ± 0.016 (stat.) ± 0.022 (syst.) ± 0.041 (model), in good agreement with values obtained from total and elastic hadronic and photoproduction cross sections. The diffractive contribution to the process γp → Xp with \(M_X^2/{W^2} < 0.05\) is measured to be 22.2 ± 0.6 (stat.) ± 2.6 (syst.) ± 1.7 (model)% of the total γp cross section at 〈W〉 = 187 GeV.

Bounds on the soft pomeron intercept

The Donnachie-Landshoff fit of total cross sections has now become a standard reference for models of total, elastic and diffractive cross-sections. Adopting their philosophy that simple-pole exchanges should account for all data to present energies, we assess the uncertainties on their fits. Our best estimate for the pomeron intercept is 1.096 −0.009 +0.012, but several models have a good χ 2 for intercepts in the range [1.07,1.11].

A new determination of the soft pomeron intercept

Using Regge theory at Born level and with eikonalized amplitudes we obtain for the pomeron intercept the values 1.104 and 1.122, respectively, from global fits to total cross section and ϱ-value data for p ± p, π ± p and K ± p.

Hard diffraction in the QCD dipole picture

Using the QCD dipole picture of the BFKL pomeron, the gluon contribution to the cross-section for single diffractive dissociation in deep-inelastic high-energy scattering is calculated. The resulting contribution to the proton diffractive structure function integrated over t is given in terms of relevant variables, x P , Q 2, and β = x Bj x P . It factorizes into an explicit x P -dependent Hard Pomeron flux factor and structure function. The lux factor is found to have substantial logarithmic corrections which may account for the recent measurements of the Pomeron intercept in this process. The triple Pomeron coupling is shown to be strongly enhanced by the resummation of leading logs. The obtained pattern of scaling violation at small β is similar to that for F 2 at small x Bj .

T-channel approach to Reggeon interactions in QCD.

Starting from the multi-Regge effective action for high-energy scattering in QCD a $t$-channel approach can be developed which is similar to the approach by White based on general Regge arguments. The BFKL kernel of reggeized gluon interaction, contributions to the $2 \rightarrow 4 $ reggeized gluon vertex function and the one-loop correction to the BFKL kernel are considered. The conditions are discussed under which this approach can provide a simple estimante of the next-to-leading logarithmic corrections to the BFKL perturbative pomeron intercept.

Production of vector mesons by real and virtual photons at high energies

A model based on Reggeon field theory is used for the description of the photo- and electroproduction of vector mesons ( ϱ 0, ω, φ, J ψ ) on the proton. Its main feature is the dependence of the Pomeron intercept on the virtuality of the photon. The few parameters of the model were determined by fitting the total cross sections for real and virtual photons on the proton. This allows a parameter-free description of the energy dependence of vector meson production. Very good agreement with the existing high energy data is obtained.

The dipole picture of high energy scattering, the BFKL equation and many gluon compound states

The relationship and equivalence between the BFKL and dipole equation kernels are investigated by means of explicit calculations in light-cone perturbation theory. A dipole equation, equivalent to the usual equation, for interactions between four reggeized gluons is given in the large Nc limit. The leading trajectory of the four-gluon system is bounded by 2αp − 1 with αp the BFKL pomeron intercept.

Reggeized gluons with a running coupling constant

The equation for two reggeized gluons in the vacuum channel is generalized to take into account the running QCD coupling constant on the basis of the bootstrap condition for gluon reggeization. Both the gluon trajectory as a function of momentum and the interaction as a function of distance grow like log log in the ultraviolet. The resulting equation depends on the confinement region. With a simple parametrization of its influence by an effective gluon mass the pomeron intercept turns out to be much smaller than for a fixed coupling constant (the BFKL pomeron).

Pomeron with a running coupling constant: intercept and slope

The equation for two reggeized gluons with running QCD coupling constant, proposed earlier on the basis of the bootstrap condition, is investigated by the variational technique in the vacuum channel. The pomeron intercept and slope are calculated as a function of the infrared cutoff parameter m (“the gluon mass”). The intercept depends weakly on m staying in the region 0.3–0.5 for values of m in the range 0.3–1.0 GeV. The slope goes down from 5.0 GeV −2 to 0.08 GeV −2 in this range. The optimal value of m seems to lie in the region 0.6–0.8 GeV with the intercept 0.35 and slope 0.35-0.15. The character of the pomeron singularity: pole or cut, is also discussed.

A phenomenological model for the Pomeron intercept in quantum chromodynamics

The integral equation leading to the perturbative vacuum singularity (Lipatov pomeron) intercept in quantum chromodynamics is modified by replacing the massless gluon propagator by diverse expressions motivated by the inclusion of non-perturbative effects. It is found that with suitable values of the parameters in the modified gluon propagator it is possible to obtain a pomeron intercept equal to that of the usual non-perturbative one.

BFKL evolution and universal structure function at very small x

The Balitskii-Fadin-Kuraev-Lipatov (BFKL) and the Gribov-Lipatov-Dokshitzer-Altarelli-Parisi (GLDAP) evolution equations for the diffractive deep inelastic scattering at 1/ x ⪢ 1 are shown to have a common solution in the weak coupling limit: F 2 (x, Q 2) ∝ [αs(Q 2)] −y (1/x) Δ ▪ . The exponent γ and the pomeron intercept Δ ▪ are related by γΔ ▪ = 4 3 for the N ƒ = 3 active flavors. The existence of this solution implies that there is no real clash between the BFKL and GLDAP descriptions at very small x. We present derivation of this solution in the framework of our generalized BFKL equation for the dipole cross section, discuss conditions for the onset of the universal scaling violations and analyse the pattern of transition from the conventional Double-Leading-Logarithm approximation for the GLDAP evolution to the BFKL evolution at large 1/ x.

Unitarity Relations for Gluonic Pomeron

We discuss simple possible models of the gluonic pomeron by a gluon ladder and also its window corrections which lead to the cylinder configuration. Under the assumption of multiperipheral unitarity model and reggeized gluons and quarks, it is shown that a mechanism like the Lee-Veneziano model, which leads to the pomeron intercept αP(0) = 1, can be derived also for these new gluonic models, for the simple ladder and its window corrections individually. This suggests a solution of the pomeron puzzling.

Pomeron and odderon in high energypp and $$p\bar p$$ elastic scattering

High energypp and\(p\bar p\) data on elastic scattering and total cross sections are analyzed in a model including the pomeron, odderon and secondary reggeons. A dipole model is used for the pomeron and for the odderon. By construction, our (bare) pomeron ansatz produces a single dip, as observed experimentally. The model reproduces the logarithmically rising cross sections with a unit pomeron intercept, but better fits are obained when a small non-zero value of the parameter δ = αp (0) is allowed for. Predictions for the future accelerators (UNK, LHC, SSC) are given.

The pomeron as an expanding grey disk

In the crossing symmetric Reggeon calculus based on the 1N expansion, s-channel unitarity sum rules are written down explicitly to each order in 1N. Some of the lowest order sum rules are shown to imply a non-vanishing bare triple-Pomeron coupling at t = 0, irrespectively of the bare Pomeron intercept.

THE POMERON INTERCEPT REVISITED

We study the lattice approximation to Reggeon Field Theory. An approximate computation of the renormalized Pomeron intercept is proposed and shows that it is equal to one as required for the theory to be consistent with experimental results and with Froissart’s bound. A stricter derivation of this requirement is also given. At fixed impact parameter the cross section seems to be asymptotically bounded.

Bare pomeron in perturbative QCD and small x behavior of gluon distributions

The solution of the integral equation describing the bare pomeron in perturbative QCD with asymptotic freedom corrections taken into account is studied. Upper and lower bounds for the bare pomeron intercept are obtained in terms of the QCD coupling constant at some large scale. The intercept is substantially above unity. After the connection with the operator product expansion is discussed, it is shown that the behavior of parton distribution functions at small x is governed by the intercept of the bare pomeron. Thus they are steeper than 1/ x by a power of x.