- Initial hadrons are depicted by red, final hadrons in the beam fragmentation region are represented by blue, particles from soft and hard collisions are green and orange correspondingly, small disks are soft hadrons (blue, green and violet), large orange disks represent jets. Topology of hadron-hadron (p p, pbar p, pi p, pi pi, K p, p n) processes in the center-of-mass frame is represented by positions of initial and final particles on the theta (polar angle or pseudorapidity)-phi (azimuthal angle) plane.
-
Fig.1: elastic hadron-hadron cross-sections -
Fig.2: total hadron-hadron cross-section related to the elastic one via the optical theorem -
Fig.3: soft single dissociative (SD) process. M is the mass of the diffractively dissociated system of hadrons. M~1 GeV (low mass dissociation) and M>> 1 GeV (high mass dissociation) -
Fig.4: soft double dissociative (DD) process. M1,2 are masses of diffractively dissociated systems of hadrons. -
Fig.5: soft exclusive central diffractive (excl.CD), soft exclusive Double Pomeron Exchange (excl.DPE) process or soft Exclusive Double Diffractive Event (EDDE) in the literature. IPs and IR are soft pomeron and reggeon correspondingly. Mc< 3 GeV is the invariant mass of the central system. -
Fig.6: soft inclusive central diffraction with one hadron dissociated to the system of hadrons with mass M. -
Fig.7: soft inclusive central diffraction with both hadrons dissociated to systems of hadrons with masses M1,2. -
Fig.8: classification of central systems in the soft central diffraction (Reggeon-Reggeon fusion). a) exclusive process; b) soft inclusive process (total cross-section for soft Reggeon-Reggeon fusion). -
Fig.9: exclusive hard Single Diffraction. One of hadrons is scattered elastically and another one participates in the hard scattering. Mc> 3 GeV is the invariant mass of the central system produced in the hard scattering (heavy resonance or two jets, two electro-weak bosons and so on). MX is the mass of the hadron remnant from hard scattering. -
Fig.10: inclusive hard Single Diffraction. One of hadrons is dissociated diffractively and another one participates in the hard scattering. M is the invariant mass of the diffractively dissociated system of hadrons. -
Fig.11: hard exclusive Central Diffraction (hard EDDE or hard excl.DPE). Both hadrons are scattered elastically (or with low mass dissociation). Mc>3 GeV is the invariant mass of the central system of hadrons produced in the hard scattering (hard Reggeon-Reggeon fusion). -
Fig.12: hard inclusive Central Diffraction with Single Dissociation, where one hadron is dissociated (high mass dissociation) and another one is scattered elastically (or with low mass dissociation). -
Fig.13: hard inclusive Central Diffraction with Double Dissociation, where both hadrons are dissociated (high mass dissociation). -
Fig.14: classification of central systems in the hard central diffraction (hard Reggeon-Reggeon fusion). a) exclusive process; b) semi-inclusive process (exclusive part plus soft hadrons in the central region); c) inclusive process (total cross-section for hard Reggeon-Reggeon fusion). -
Fig.15: exclusive (hadron is scattered elastically) and inclusive (hadron is dissociated) photon-hadron scattering. -
Fig.16: soft exclusive (hadron is scattered elastically) and inclusive (hadron is dissociated) Vector Meson photoproduction (real photon) or electroproduction (virtual photon). Mass of the vector meson is of the order 1 GeV. -
Fig.17: hard exclusive (hadron is scattered elastically) and inclusive (hadron is dissociated) Vector Meson photoproduction (real photon) or electroproduction (virtual photon). Mass of the vector meson is much greater than 1 GeV. -
Fig.18: hard exclusive (hadron is scattered elastically) and inclusive (hadron is dissociated) dijet photoproduction (real photon) or electroproduction (virtual photon). Invariant mass of the dijet system and transverse momenta of jets are much greater than 1 GeV. -
Fig.19: unitarity relation for the soft central inclusive production. -
Fig.20: unitarity relation for the hard central inclusive production. -
Fig.21: unitarity relation for the photon-hadron scattering. -
Fig.22: possible processes in the singlet gluon-gluon fusion (from hard Pomeron-Pomeron fusion). a) dijet production; b) 3 jets production; c) two electro-weak vector bosons production; d) heavy quarkonia production; e) Higgs boson production; f) other resonances of the Standard Model or its extensions (glueball, Radion, Gravitons, SUSY particles, Unparticles and so on). -
Fig.23: processes with leading neutrons production. Single pion exchange: a) with total pi+ p scattering, b) with elastic pi+ p scattering, c) with inclusive pi+ p dijet production. Double pion exchange: d) with total pi+ pi+ scattering, e) with elastic pi+ pi+ scattering, f) with inclusive pi+ pi+ dijet production.
Calculations of distributions for diffractive processes can be done by several methods. The main problem is to find an adequate description of processes with different space-time scales. For "soft" processes (low transverse momentum transfer, small masses, large distances) we use the so called Regge-eikonal approach which was extended to the scattering of virtual particles. This model is nonperturbative and obtained from the basic principles. For "hard" processes (high transverse momentum transfer or large masses, small distances) like production of QCD jets and massive states we can use perturbative methods of Standard Model or its extensions. Perturbation theory of QCD (strong interactions) is based on the assumption that coupling constant is small in the kinematical region with high momentum transfer (asymptotic freedom).
Usually models that describe processes with different scales are mixtures of "soft" and "hard" methods that coincide at some intermetiate kinematical point, where both of them are still valid (boundary condition). Scattering amplitudes are consisted of two (or more) parts, and, finally should satisfy all the general principles.
Some authors try to improve perturbative calculations to reach the "soft" kinematical region and to understand the mechanism of confinement. They obtain different renorm-invariant partial sums of the perturbative expansion (DGLAP, BFKL, ...) which are applicable in a more wide kinematical region, including even the "soft" part. We can also make other expansions like semiclassical approach (for large number of colours in QCD) or Operator Product Expansion (OPE) with renormalization group improvements. The final answer is often very complicated and contains many parameters and functions (couplings, Regge trajectories, parton distributions). This tell us that the model is incomplete and needs further development. At present time we try to find an optimal phenomenological solution with minimal number of parameters and good statistical properties that describes data on all the above diffractive processes.
- Regge-eikonal approach for real and virtual particles (Regge poles, cuts, linear or nonlinear trajectories);
- Perturbative expansion in the QCD strong coupling;
- Operator Product Expansion (composite operators, parton distributions and coefficient functions);
- Semi-classical approach (expansion for large number of colours in QCD);
- Evolution equations, resummations (DGLAP, BFKL, ...);
- Elastic and total cross-sections (Figs.1,2) for p p, p pbar, pi p, K p scattering (description with nonlinear Regge-trajectories);
- EDDE (Figs. 5-8,11-13,14a,b), for all the hard subprocesses depicted in the Fig.22;
- Exclusive vector meson photo- and electroproduction (left pictures in Figs.16,17);
- Leading neutrons (with extraction of pi+ p and pi+ pi+ total and elastic cross-sections, Fig.23a,b,d,e);
- Froissar-Martin bound;
- Dispersion relations;
- RG equation;
- Energy-momentum sum rules;
- DGLAP evolution equation;
- Bethe-Salpeter equation;