arXiv subjects
Publications and source records attributed to V. S. Fadin.
As is known from the classical theory of complex angular momenta, along with the Regge poles in the complex $j$ - plane should be cuts that are generated by the poles. In QCD, the cuts are generated by exchanges of the Reggeized gluons, whose properties are strikingly different from the properties of Reggeons in classical theory, which leads to peculiarities of the formation of the cuts. The talk is devoted to the discussion of these peculiarities.
It is shown that contrary to claims of Ref. [1] the formulated in the proper physical variables Low theorem [2] for soft photon emission does not require any modification. We also reject the criticism in Ref. [1] of the papers [3,4]. At the same time, we identify some inaccuracies in Ref. [3] in the presentation of the soft-photon theorem for the case of spin-one-half particles. We also point out shortcomings in consideration of the Low theorem in the classic textbooks [5,6].
The increasing accuracy of current and planned experiments to measure the anomalous magnetic moment of the muon requires more precision and reliability of its theoretical calculation. For this purpose, we calculate the differential cross section for the process of annihilation of an electron-positron pair into two photons, one of which is virtual, accompanied by the emission of soft photons, taking into account radiative corrections of the order $α^2$. The results obtained can be used to improve the accuracy of calculating the contribution of the hadron vacuum polarization to the muon anomalous moment. It is shown that all logarithmically amplified two-loop corrections can be easily found using modern theorems of soft and collinear factorizations and available one-loop results.
The structure function approach and the parton picture, developed for the theoretical description of the deep inelastic electron-proton scattering, also proved to be very effective for calculation of radiative corrections in Quantum Electrodynamics. We use them to calculate radiative corrections to the cross section of electron-proton scattering due to electron-photon interaction, in the experimental setup with the recoil proton detection, proposed by A.A. Vorobev to measure the proton radius. In the one-loop approximation, explicit expressions for these corrections are obtained for arbitrary momentum transfers. It is shown that, at momentum transfers small compared with the proton mass, various contributions to the corrections mutually cancel each other with power accuracy. In two loops, the corrections are obtained in the leading logarithmic approximation.
The largest radiative corrections to the cross section of electron-proton scattering at high energies are associated with emission of photons, real and virtual, by electron. They contain large logarithms coming from soft and collinear photons. Cancellation of the contributions of the soft photons to virtual and real corrections is well known. Less known is the fact that the contributions of the photons collinear to scattered electrons are also cancelled for the most of experiments. On the contrary, contributions of the photons collinear to initial electrons as a rule are not cancelled. It is shown, however, that these contributions are cancelled for the experimental set up suggested by A.A. Vorobev for measurement of proton radius.
Reggeon cuts in QCD amplitudes with negative signature are discussed. These cuts appear in the next-to-next-to-leading logarithmic approximation (NNLLA) and greatly complicate the derivation of the BFKL equation. Feynman diagrams responsible for appearance of these cuts are indicated and the cut contributions are calculated in the two- and three-loop approximation.
Peculiar properties of the BFKL approach in the next-to-next-to-leading logarithmic approximation (NNLLA) are discussed. In this approximation the scheme of derivation of the BFKL equation must be changed because of violation of the simple factorized form of amplitudes with multi-Reggeon exchanges and necessity to take into account imaginary parts of amplitudes in the unitarity relations.
Here we consider a contribution of Delta(1232) resonance to real photon radiative corrections for elastic $ep$-scattering. The effect is found to be small for past experiments to study unpolarized cross section as well as for the recent VEPP-3 experiment to investigate two-photon exchange effects by precision measurement of $e^\pm p$-scattering cross sections ratio.
We analyze a modification of the BFKL kernel for the adjoint representation of the colour group in the maximally supersymmetric (N=4) Yang-Mills theory in the limit of a large number of colours, related to the modification of the eigenvalues of the kernel suggested by S. Bondarenko and A. Prygarin in order to reach the Hermitian separability of the eigenvalues. We restore the modified kernel in the momentum space. It turns out that the modification is related only to the real part of the kernel and that the correction to the kernel can not be presented by a single analytic function in the entire momentum region, which contradicts the known properties of the kernel.
General expressions for the impact factors up to terms vanishing at the space-time dimension $D\rightarrow 4$ are presented. Their infrared behaviour is analysed and calculation of exact in $D\rightarrow 4$ asymptotics at small momenta of Reggeized gluons is discussed.
We perform an examination of discontinuities of multiple production amplitudes, which are required for further development of the BFKL approach. It turns out that the discontinuities of 2 $\to$ 2 + n amplitudes obtained in the BFKL approach contradict to the BDS ansatz for amplitudes with maximal helicity violation in N = 4 supersymmetric Yang-Mills theory with large number of colours starting with n = 2. Explicit expressions for the discontinuities of the 2 $\to$ 3 and 2 $\to$ 4 amplitudes in the invariant mass of pairs of produced gluons are obtained in the planar N=4 SYM in the next-to-leading logarithmic approximation. These expressions can be used for checking the conjectured duality between the light-like Wilson loops and the MHV amplitudes.
The proof of the multi-Regge form of multiple production amplitudes in the next-to-leading logarithmic approximation is presented for Yang-Mills theories with fermions and scalars in any representations of the colour group and with any Yukawa-type interaction. Explicit expressions for the Reggeized gauge boson trajectory, the Reggeon vertices and the impact factors are given. Fulfilment of the bootstrap conditions is proved.
In the BFKL approach, discontinuities of multiple production amplitudes in invariant masses of produced particles are discussed. It turns out that they are in evident contradiction with the BDS ansatz for $n$-gluon amplitudes in the planar $N$=4 SYM at $n\ge 6$. An explicit expression for the NLO discontinuity of the two-to-four amplitude in the invariant mass of two produced gluons is is presented.
This paper describes a new multipurpose event generator, ESEPP, which has been developed for the Monte Carlo simulation of unpolarized elastic scattering of charged leptons on protons. The generator takes into account the lowest-order QED radiative corrections to the Rosenbluth cross section including first-order bremsstrahlung without using the soft-photon or ultrarelativistic approximations. ESEPP can be useful for several significant ongoing and planned experiments.
It is shown that in the next-to-leading approximation of N=4 SUSY the BFKL equation for two-gluon composite states in the adjoint representation of the gauge group can be reduced to a form which is invariant under Moebius transformation in the momentum space. The corresponding similarity transformation of its integral kernel is constructed in an explicit way.
We present results for the NLO kernel of the BKP equations for composite states of three reggeized gluons in the Odderon channel, both in QCD and in N=4 SYM. The NLO kernel consists of the NLO BFKL kernel in the color octet representation and the connected $3\to3$ kernel, computed in the tree approximation.
As it was recently shown, the colour singlet BFKL kernel, taken in Moebius representation in the space of impact parameters, can be written in quasi-conformal shape, which is unbelievably simple compared with the conventional form of the BFKL kernel in momentum space. It was also proved that the total kernel is completely defined by its Moebius representation. In this paper we calculated the difference between standard and quasi-conformal BFKL kernels in momentum space and discovered that it is rather simple. Therefore we come to the conclusion that the simplicity of the quasi-conformal kernel is caused mainly by using the impact parameter space.
We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group $SU(N_c)$ in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.