arXiv subjects
Publications and source records attributed to V. S. Fadin.
We calculate the effective vertices for the quark-antiquark and the quark-antiquark-gluon production in the virtual photon - Reggeized gluon interaction. The last vertex is considered at the Born level; for the first one the one-loop corrections are obtained. These vertices have a number of applications; in particular, they are necessary for calculation of the virtual photon impact factor in the next-to-leading logarithmic approximation.
The method of calculation of effective vertices of interaction of the Reggeized gluon and quark with particles in QCD in the next-to-leading order is developed. The method is demonstrated in the case of already known vertices of both gluon-gluon and quark-quark transitions in the scattering of gluons and quarks on the Reggeized gluon. It is used for the calculation of the gluon-quark transition in the scattering on the Reggeized quark.
Representation of non-forward scattering amplitudes in the BFKL approach is discussed and the results obtained in the next-to leading order are briefly reviewed.
We reformulate the so-called ``strong bootstrap'' conditions for the gluon Reggeization in the next-to-leading approximation (NLA), firstly suggested by Braun and Vacca, using a different approach, which is not based on properties of the eigenstates of the NLA octet BFKL kernel. We write the second strong bootstrap condition for the NLA octet impact factors in a form which makes clear their dependence on the process. According to this condition, the NLA octet impact factors must be given by the product of the corresponding Reggeon interaction vertices with a universal coefficient function. This function can be used also in the formulation of the first strong bootstrap condition for the NLA BFKL kernel in the octet state.
In order to check the compatibility of the gluon Reggeization in QCD with the $s$-channel unitarity, the one-loop correction to the Reggeon-Reggeon-gluon vertex must be known at arbitrary space-time dimension $D$. We obtain this correction from the gluon production amplitude in the multi-Regge kinematics and present an explicit expression for it in terms of a few integrals over the transverse momenta of virtual particles. The one-gluon contribution to the non-forward BFKL kernel at arbitrary $D$ is also obtained.
Recently the non-forward BFKL kernel for interaction of two Reggeized gluons in the antisymmetric colour octet state in the $t$-channel was obtained in the next-to-leading order. It gives the possibility to check in this order the bootstrap condition for this kernel, appearing as the requirement of the compatibility of gluon Reggeization with the $s$-channel unitarity.
At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the double logarithmic effects to both non-radiative processes and to processes accompanied by soft gauge boson emission. In all cases the Sudakov double logarithms are found to exponentiate. We also discuss double logarithmic effects of a non-Sudakov type which appear in Regge-like processes.
We calculate in the next-to-leading approximation the non-forward gluon impact factors for arbitrary color state in the $t$-channel. In the case of the octet state we check the so-called "second bootstrap condition" for the gluon Reggeization in QCD, using the integral representation for the impact factors. The condition is fulfilled in the general case of an arbitrary space-time dimension and massive quark flavors for both helicity conserving and non-conserving parts.
We calculate in the next-to-leading approximation the non-forward quark impact factors for both singlet and octet color representation in the $t$-channel. The integral representation of the octet impact factor in the general case of arbitrary space-time dimension and massive quark flavors is used to check the so-called "second bootstrap condition" for the gluon Reggeization at the next-to-leading logarithmic approximation in perturbative QCD. We find that it is satisfied for both helicity conserving and non-conserving parts. The integrations are then performed for the explicit calculation of the impact factors in the massless quark case.
We calculate the quark part of the kernel of the generalized non-forward BFKL equation at non-zero momentum transfer $t$ in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in the Reggeon-Reggeon collisions. The results obtained can be used for an arbitrary representation of the colour group in the $t-$channel. Using the results for the adjoint representation, we demonstrate explicitly the fulfillment of the ``bootstrap'' condition for the gluon Reggeization in the next-to-leading logarithmic approximation in the part concerning the quark contribution.
We demonstrate, to next-to-leading order accuracy, the cancellation of the infrared singularities in the impact factors which arise in the QCD description of high energy processes A + B -> A' + B' of colourless particles. We study the example where A is a virtual photon in detail, but show that the result is true in general.
The representation of the total cross section at high energy $\sqrt s$ in the next-to-leading $\ln s$ approximation is given with definition of the impact factors and explicit expression for the BFKL kernel. The estimate of the Pomeron intercept and the next-to-leading contributions to anomalous dimensions near $j=1$ are presented.
I discuss radiative corrections to the BFKL equation for high energy cross sections in perturbative QCD. Due to the gluon Reggeization in the next-to-leading $\ln s$ approximation, the form of the BFKL equation remains unchanged and the corrections to the BFKL kernel are expressed in terms of the two-loop contribution to the gluon Regge trajectory, the one-loop correction to the Reggeon-Reggeon-gluon vertex and the contributions from two-gluon and quark-antiquark production in Reggeon-Reggeon collisions. I present the results of the calculation of the BFKL kernel in the next-to leading logarithmic approximation, the estimate of the Pomeron shift and the next-to-leading contribution to the anomalous dimensions of twist-2 operators near $j=1$.
The generalization of the BFKL equation for the case of non-forward scattering is considered. The kernel of the generalized equation in the next-to-leading approximation is expressed in terms of the gluon Regge trajectory and the effective vertices for particle production in Reggeon collisions. The ``bootstrap'' equations for the gluon Reggeization are presented.
We find one-loop correction to the integral kernel of the BFKL equation for the total cross section of the high energy scattering in QCD and calculate the next-to-leading contribution to anomalous dimensions of twist-2 operators near $j=1$.
The quark-antiquark contribution to the BFKL kernel is calculated. Using the effective vertex for the $q\bar q$ pair production in the Reggeon-Reggeon collision we find this contribution by integrating the square of this vertex over relative transverse momenta and fractions of longitudinal momenta of produced particles.
To find the region of applicability of the leading log(1/x) approximation for parton distributions in the small x region and to fix the argument of the QCD running coupling it is necessary to know radiative corrections to the kernel of the BFKL equation. The next-to-leading corrections to the BFKL kernel are expressed in terms of the two-loop correction to the gluon Regge trajectory, one-loop correction to the Reggeon-Reggeon-gluon vertex, and contributions from two-gluon and quark-antiquark production in the quasi-multi-Regge kinematics. We calculate differential and total cross sections of the two gluon production. Differential cross section can be applied for description of two jet production in the quasi-multi-Regge kinematics; the total cross section defines corresponding correction to the BFKL kernel. To escape the infrared divergencies we use dimensional regularization of the Feynman integrals.
The study of an intermediate mass Higgs boson, via the process gamma-gamma -> H -> bbbar from an initiallypolarized J_z = 0 state, has been advocated as an important feasible goal of a future photon linear collider. The crucial argument was the m_b^2/s suppression of the background process gamma-gamma (J_z = 0) -> bbbar. We critically review the contribution of the radiative background processes (in which the m_b^2/s suppression is absent) to the quasi-two-jet-like events with at least one, but preferably two, tagged energetic b jets. Within a complete study of the radiative processes, we find that a sizeable background contribution can come from the helicity-violating gamma-gamma (J_z = 0) -> bbbar process accompanied by soft gluon emission. These latter radiative corrections contain a new type of double logarithmic (DL) terms. We clarify the physical nature of these novel DL corrections. Despite the fact that the one-loop DL terms are comparable or even larger than the Born term, fortunately we find that the calculation of the cross section in the two-loop approximation is sufficient for a reliable evaluation of the background to the Higgs signal.