We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell ...amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the gauge invariance of light-front amplitudes, it is demonstrated that the Ward identities in this framework need additional instantaneous terms in the light-front graphs.
We review the methods of the computation of the scattering amplitudes in the light-front formalism. Basics of the light-front quantization, as well as helicity methods and different types of ...recursion relations for scattering amplitudes are reviewed. Computation of the wave-functions and fragmentation functions within the light-front theory are presented. Methods for obtaining off-shell scattering amplitudes are presented together with the new recursion relations which include the gauge invariant extensions of the off-shell amplitudes. Finally, relation between the formalism which makes use of the Wilson lines and light-front formalism is discussed.
We observe that the saturation model of deep inelastic scattering predicts a geometric scaling of the total gamma(*)p cross section in the region of small Bjorken variable x. The geometric scaling in ...this case means that the cross section is a function of only one dimensionless variable tau = Q(2)R(2)(0)(x), where the function R(0)(x) decreases with decreasing x. We show that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q(2). We suggest that the geometric scaling is more general than the saturation model.
Limiting fragmentation in proton–proton, deuteron–nucleus and nucleus–nucleus collisions is analyzed in the framework of the Balitsky–Kovchegov equation in high energy QCD. Good agreement with ...experimental data is obtained for a wide range of energies. Further detailed tests of limiting fragmentation at RHIC and the LHC will provide insight into the evolution equations for high energy QCD.
We investigate the effects of the saturation boundary on small-
x
evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL ...evolution are not cured by the presence of the saturation boundary. This indicates that a resummation of the higher order corrections is therefore needed also for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and we observe that the onset of the saturation corrections is delayed to higher rapidities. This seems to be related to the characteristic feature of the resummed splitting function which at moderately small values of
x
possesses a minimum.
We present results from the first next-to-leading-order (NLO) numerical analysis of forward hadron production in pA and dA collisions in the small-x saturation formalism. Using parton distributions ...and fragmentation functions at NLO, as well as the dipole amplitude from the solution to the Balitsky-Kovchegov equation with running coupling, together with the NLO corrections to the hard coefficients, we obtain a good description of the available RHIC data in dAu collisions. In the large p⊥ region beyond the saturation scale, we find that the NLO correction becomes dominant and negative, which indicates that other physics beyond NLO becomes important and should also be taken into account. Furthermore, we make predictions for forward hadron production in pPb collisions at the LHC. This analysis not only incorporates the important NLO corrections for all partonic channels, but also reduces the renormalization scale dependence and helps to significantly reduce the theoretical uncertainties. It therefore provides a precise test of saturation physics beyond the leading logarithmic approximation.
A
bstract
We perform the renormalization group improved collinear resummation of the photon-gluon impact factors. We construct the resummed cross section for virtual photon-photon (
γ
∗
γ
∗
) ...scattering which incorporates the impact factors and BFKL gluon Green’s function up to the next-to-leading logarithmic accuracy in energy. The impact factors include important kinematical effects which are responsible for the most singular poles in Mellin space at next-to-leading order. Further conditions on the resummed cross section are obtained by requiring the consistency with the collinear limits. Our analysis is consistent with previous impact factor calculations at NLO, apart from a new term proportional to
C
F
that we find for the longitudinal polarization. Finally, we use the resummed cross section to compare with the LEP data on the
γ
∗
γ
∗
cross section and with previous calculations. The resummed result is lower than the leading logarithmic approximation but higher than the pure next-to-leading one, and is consistent with the experimental data.
We perform the fit to the structure function
F
2
data from HERA including terms due to the resummation at small
x
. The equation for the unintegrated gluon density is solved, previously established ...within the renormalization group improved small
x
framework. We find very good description of the structure function
F
2
and its charm component
F
2
c
. The resulting unintegrated gluon density is found to be consistent with the calculations based on similar approaches available in the literature, with only slightly higher intercept value.
We analyze the possibilities for the study of inclusive diffraction offered by future electron-proton/nucleus colliders in the tera-electron-volt regime, the Large Hadron-electron Collider (LHeC) as ...an upgrade of the HL-LHC, and the Future Circular Collider in electron-hadron mode. Compared to ep collisions at HERA, we find an extension of the available kinematic range in x by a factor of order 20 and of the maximum Q2 by a factor of order 100 for LHeC, while the Future Circular Collider (FCC) version would extend the coverage by a further order of magnitude both in x and Q2. This translates into a range of the available momentum fraction of the diffractive exchange with respect to the hadron (ξ), down to 10−4–10−5 for a wide range of the momentum fraction of the parton with respect to the diffractive exchange (β). Using the same framework and methodology employed in previous studies at HERA, considering only the experimental uncertainties and not those stemming from the functional form of the initial conditions or other ones of theoretical origin, and under very conservative assumptions for the luminosities and systematic errors, we find an improvement in the extraction of diffractive parton densities from fits to reduced cross sections for inclusive coherent diffraction in ep by about an order of magnitude. For eA, we also perform the simulations for the Electron Ion Collider. We find that an extraction of the currently unmeasured nuclear diffractive parton densities is possible with accuracy similar to that in ep.
We investigate the prospects of the diffractive production of J/ψ mesons at a large momentum transfer |t| at the future Electron Ion Collider (EIC) in electron-proton collisions. In particular, we ...focus on the measurements of the rapidity gap size. The model used for the calculations is based on the diffractive exchange of the Balitsky-Fadin-Kuraev-Lipatov perturbative Pomeron. Calculations for the cross section and the estimates for the rates assuming integrated luminosity of 10 fb−1 are provided. Two experimental strategies were considered. First, measuring the rapidity gap size directly, by observing the activity in the forward part of the central detector, and second by putting a lower limit on the rapidity gap size in the case when the detector cannot measure forward activity. We find that it is possible to measure at the EIC the dependence of the cross section on rapidity gap interval up to four units in rapidity. This should allow us to measure the change of the cross section by a factor of 1.6 expected due to the BFKL exchange. This is possible with the present setup of the detector which projects the coverage up to 3.5 units of rapidity. We conclude however, that the extension of the detector up to higher rapidity, for example to 4.5 would be desirable and provide even better lever arm for testing rapidity gap physics at the EIC
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