PERT AND NON-PERT QCD EW AND SYMMETRY BREAKING BEYOND THE SM HEAVY FLAVOUR PHYSICS NEUTRINO AND NON ACCEL PHYSICS

Low x Dynamics

Alan Martin, James Stirling

Subleading log(1/x) contributions

A consistency condition (or kinematic constraint) was introduced which allows a major part of the subleading log(1/x) corrections to be incorporated in the BFKL equation in a straightforward manner. Phenomenologically, the inclusion of the consistency condition has the effect of stabilizing the solution of the BFKL equation, despite the known large next-to-leading log(1/x) contributions.

The unintegrated gluon distribution

A unified BFKL and DGLAP evolution equation was introduced which incorporated the above consistency constraint. The formalism was used to fit to deep inelastic scattering data and the unintegrated gluon distribution, h(x,k_t²), determined.

Recently the above analysis has been extended and the first realistic unintegrated gluon distribution has been obtained. The distribution f(x,k_t²,µ²) depends on two hard scales (k_t and the scale µ of the probe) and we have to deal with a complicated evolution equation. On the other hand the emissions are angular ordered and it turns out that the distribution can be obtained from the single scale evolution equation for h(x,k_t²), with the µ dependence determined at the last step of the evolution. Sample results are:

Skewed parton distributions

A general discussion can be found here and the application to diffractive vector meson electroproduction here. It was shown that these distributions are completely determined by the conventional parton distributions at small x. Indeed simple analytic formula were presented.

Forward jets and neutral pions in DIS events

Mueller originally emphasised that a study of deep inelastic (x,Q²) events containing a forward jet (x_j,k_t²) could directly probe BFKL dynamics if k_t²~Q², x_j is large and z=x/x_j is small. Our most recent phenomenological study can be found here, where the possibility of using forward neutral pions is also discussed.

Small x dynamics at hadron colliders

The production at hadron colliders of `Mueller-Navelet' jet pairs with modest p<sub>T</sub> and large rapidity separation Dy = |y<sub>1</sub>-y<sub>2</sub>| is another direct test of BFKL dynamics. The `naive' (or leading logarithm approximation) BFKL prediction is that the parton-level subprocess cross section should increase at large Dy as exp(aDy), mimicking the x^-a increase of the structure function F₂ at small x, see the figure below. A derivation of this result can be found here.

However, this increase is very difficult to observe in practice, since it is diluted by running coupling effects and kinematical constraints from phase space as controlled by the parton distributions. A Monte Carlo has been developed which correctly incorporates these effects. As can be seen from the figure bolow, at present (Tevatron) energies the effect on the Dy dependence of the hadron-level cross section is dramatic, overwhelming the naive BFKL result. Alternative methods of probing for BFKL physics have therefore been explored. The azimuthal decorrelation of the jet pair has been studied, as has the possibility of using two hadron collider energies to cancel the effects of the parton distributions. Whether or not BFKL physics is relevant for dijet production at Tevatron energies is still an open question. However the situation should become clearer at the LHC, where the higher collision energy weakens the impact of the kinematic constraints.

Words by Alan Martin, James Stirling