Unitarity and the QCD-improved dipole picture

Abstract

As a consequence of QCD factorization theorems, a wide variety of inclusive and exclusive cross sections may be formulated in terms of a universal colour dipole cross section at small $x$. It is well known that for small transverse size dipoles this cross section is related to the leading-log gluon density. Using the measured pion-proton cross section as a guide, we suggest a reasonable extrapolation of the dipole cross section to the large transverse size region. We point out that the observed magnitude and small $x$ rise of the gluon density from conventional fits implies that the DGLAP approximation has a restricted region of applicability. We found that `higher twist' or unitarity corrections are required in, or close to, the HERA kinematic region, even for small `perturbative' dipoles for scattering at central impact parameters. This means that the usual perturbative leading twist description, for moderate virtualities, $1 < Q^2 < 10$ GeV$^2$, has rather large `higher twist' corrections at small $x$. In addition, for these virtualities, we also find sizeable contributions from large non-perturbative dipoles ($b \gsim 0.4$ fm) to $F_2$, and also to $F_L$. This also leads to deviations from the standard leading twist DGLAP results, at small $x$ and moderate $Q^2$. Our model also describes the low $Q^2$ data very well without any further tuning. We generalize the Gribov unitarity limit for the structure functions of a hadron target to account for the blackening of the interaction at central impact parameters and to include scattering at peripheral impact parameters which dominate at extremely large energies.Comment: Final version, 38 pages, 16 figures, 1 table. A successful comparison to all low Q^2 HERA data is included. The discussion has been completely rewritten and extended to include both a detailed comparison with other models for the dipole cross section and also a new section on the approach to the black limit in DIS, including various new predictions. 23 new references have been added and several figures change

Scattering of dark particles with light mediators

“…There is an extensive literature on the subject [39][40][41][42][43][44][45][46][47][48][49]. We will follow mostly Ref.…”

Deeply virtual Compton scattering and saturation approach

“…The main feature in a successful model is to be able to match the soft (low Q 2 ) and hard (large Q 2 ) regimes in a unified way. This has been achieved in models using Regge approach [4], QCD color transparency phenomena [5] and/or hybrid ones mixing nonperturbative functional approach and Regge phenomenology [6]. Phenomenological analysis including a parton saturation phenomenon at high energies has been considered, for instance in [7,8].…”

Revealing the Black-Body Regime of Small-xDeep-Inelastic Scattering through Final-State Signals

“…Numerical studies performed using Eqs. (1) and (2) have demonstrated that interactions at the upper range of HERA energies in gluon-induced processes may be fairly close to the BBL in a wide range of impact parameters (see, e.g., [8,10]). This is consistent with an analysis [11] of current fits to HERA diffractive data, which leads to diffractive gluon densities which are significantly larger than the quark ones (see also [12]).…”

“…It is essentially given by Eq. (10). Since the distributions in z (or equivalently u) do not depend on M, the jet distribution in z is given by…”