QCD and rising cross sections

Towards a complete description of high-energy photoproduction

“…In order to agree with the average charged multiplicity o f minimum-bias events, one needs to set p ?min 1:3 GeV at 200 GeV and 1:45 GeV at 900 GeV. It is not clear whether the di erence is signi cant, but in the following we h a v e assumed a slow logarithmic variation p ?min = 1 : 3 + 0 : 15 ln(E cm =200) ln(900=200) : (15) Similar (constant) values have been determined when the increase of the pp total cross section with energy is interpreted as a consequence of the increasing minijet cross section [21]. This interpretation requires additional assumptions compared with a simple multiple interactions scenario, such a s (i) the value of soft (s) before unitarization, (ii) the shape of the hadronic wave function, and (iii) the matching with some di erent p h ysics in the low-energy region, where tot is decreasing with energy.…”

Scale dependence of nuclear gluon structure

“…next section). We shall use Qo = 2 GeV, since this is the lowest scale one can use when applying the parametrized parton distributions of Duke and Owens [32], and it satisfies the requirement of a perturbative scale [1,2,16,33]. Typically, for the measured points at small x the scales are less than 2 GeV, and at x~, 0.3 they are higher than that.…”

“…In onephoton exchange approximation, the differential cross section per nucleon of a deep inelastic charged lepton scattering from an unpolarized target A is given by (1), where the standard deep inelastic variables are x = XBj = Q 2 /(2Mv), y = vIE with E being the incident lepton energy and v the energy difference between the incident and scattered lepton in the laboratory frame. The squared 4-momentum of the virtual photon is denoted by q; = _Q2, the free mass of a nucleon in the target A by M and the ratio of the longitudinally and transversally polarized virtual photon absorption cross sections by R(x, Q2).…”

“…This is seen e.g. in the rapid rise of the total inelastic cross sections and in particle multiplicities [1][2][3]. With increasing energy, information on parton number densities at smaller and smaller x's is needed.…”

Modeling pion and proton total cross-sections at LHC

“…QCD provides an obvious mechanism for this rise through the increasing number of low-energy perturbative gluon-gluon collisions, producing the so called mini-jets [20]. How to link these cross-sections to the total crosssection, without violating unitarity, was first done in the mid 80s through the eikonal mini-jet model [21,22]. Mini-jet models are used in MonteCarlo simulation programs for very high energy collisions [23], although there are some unsolved problems concerning the elastic and diffractive components of the scattering, as recently summarized in [24].…”