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We investigate enhanced EW corrections to inclusive hard processes in the TeV energy region with emphasis on the small-x situation, in which the hard scale Q is significantly smaller than the available energy sqrt{s}= Q/x. We first propose and justify a general factorization formula in which the (double-log) EW form factor at scale Q^2 is factorized from EW parton distribution functions, which satisfy evolution equations of DGLAP type. We then investigate the small-x behavior of the EW parton distributions including the novel ones for non-vanishing t-channel weak isospin T and we compare it with a BFKL-type approach. In either approach we find that large small-x corrections of order alpha_w log x log Q^2/M^2 (M being the EW symmetry breaking scale) are present only for T=2 and not for T=1. This implies that only transverse WW interactions (coupled to T=2) are affected, while the T=1 components feel just the form factor at scale Q^2.
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We investigate small$-x$ resummation effects in QCD coefficient functions for $Z_0g$ and $Wg$ fusion processes, and we compare them with the known ones of $gamma g$ type. We find a strong process dependence, that we argue to be due to the possible presence of collinear singularities for either small or large $k$ of the exchanged gluon. For top quark production, we find that the $ggra tbar{t}$ and $Z_0gra tbar{t}$ channels have larger resummation enhancements than the $Wgra tbar{t}$ one.
Recent data on the structure function F_2(x,Q^2) at small values of x are analysed and compared with theoretical expectations. It is shown that the observed rise at small x is consistent with a logarithmic increase, growing logarithmically also with Q^2. A stronger increase, which may be incompatible with unitarity when extrapolated to asymptotically small values of x, cannot be inferred from present data.
D.I.S. at small Bjorken $x$ is considered within the dipole cascade formalism. The running coupling in impact parameter space is introduced in order to parametrize effects that arise from emission of large size dipoles. This results in a new evolution equation for the dipole cascade. Strong coupling effects are analyzed after transforming the evolution equation in Borel ($b$) space. The Borel singularities of the solution are discussed first for the universal part of the dipole cascade and then for the specific process of D.I.S. at small $x$. In the latter case the leading infrared renormalon is at $b=1/beta_0$ indicating the presence of $1/Q^2$ power corrections for the small-$x$ structure functions.
We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of $alpha_s ln^2 (1/x)$ with $alpha_s$ the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small $x$, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-$x$ evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-$x$ asymptotics of the quark and gluon OAM distributions in the large-$N_c$ limit: begin{align} L_{q + bar{q}} (x, Q^2) = - Delta Sigma (x, Q^2) sim left(frac{1}{x}right)^{frac{4}{sqrt{3}} , sqrt{frac{alpha_s , N_c}{2 pi}} }, L_G (x, Q^2) sim Delta G (x, Q^2) sim left(frac{1}{x}right)^{frac{13}{4 sqrt{3}} , sqrt{frac{alpha_s , N_c}{2 pi}}} . end{align}
We present a global fit to HERA data on the reduced cross section measured in electron-proton collisions in the region of small Bjorken-$x$: $xle x_0=10^{-2}$ and moderate to high values of the virtuality $Q^2<Q^2_{max}=650$ GeV$^2$. The main dynamical ingredients in the fits are two recently proposed improved BK equations for the description of the small-$x$ evolution of the dipole scattering amplitude. These two new equations provide an all-order resummation of double collinear logarithms that arise beyond leading logarithmic accuracy. We show that a very good description of data is possible in both cases, provided the parent dipole or smallest dipole prescriptions are employed for the running of the coupling.
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