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Register a new userNon-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation
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Authors
Carlos Contreras
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In this paper, we use the re-summation procedure, suggested in Refs.cite{DIMST,SALAM,SALAM1,SALAM2}, to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce th non-linear corrections in the saturation region, which is based on the leading twist non-linear equation. In the kinematic region:$tau,equiv,r^2 Q^2_s(Y),leq,1$ , where $r$ denotes the size of the dipole, $Y$ its rapidity and $Q_s$ the saturation scale, we found that the re-summation contributes mostly to the leading twist of the BFKL equation. Assuming that the scattering amplitude is small, we suggest using the linear evolution equation in this region. For $tau ,>,1$ we are dealing with the re-summation of $Lb bas ,ln tauRb^n$ and other corrections in NLO approximation for the leading twist.We find the BFKL kernel in this kinematic region and write the non-linear equation, which we solve analytically. We believe the new equation could be a basis for a consistent phenomenology based on the CGC approach.
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In this paper we compare the experimental HERA data with the next-to-leading order approach (NLO) of Ref.[C.~Contreras, E.~Levin, R.~Meneses and M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029). This approach includes the re-summed NLO corrections to the kernel of the evolution equation, the correct asymptotic behaviour in the NLO at $tau = r^2 Q^2_s ,gg,1$; the impact parameter dependence of the saturation scale in accord with the Froissarrt theorem as well as the non-linear corrections. In this paper, we successfully describe the experimental data with the quality, which is not worse, than in the leading order fits with larger number of the phenomenological parameters. It is demonstrated, that the data could be described, taking into account both the diffusion on $ln(k_T)$, which stems from perturbative QCD, and the Gribovs diffusion in impact parameters. It is shown an ability to describe the data at rather large values of $alpha_S$.
In the paper we propose and solve analytically the non-linear evolution equation in the leading twist approximation for the Odderon contribution. We found three qualitative features of this solution, which differs the Odderon contribution from the Pomeron one :(i) the behaviour in the vicinity of the saturation scale cannot be derived from the linear evolution in a dramatic difference with the Pomeron case; (ii) a substantial decrease of the Odderon contribution with the energy; and (iii) the lack of geometric scaling behaviour. The two last features have been seen in numerical attempts to solve the Odderon equation.
We compute the hydrodynamic relaxation times $tau_pi$ and $tau_j$ for hot QCD at next-to-leading order in the coupling with kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds which apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.
We present new sets of fragmentation functions in next-to-leading order QCD that are determined from e+e- annihilation data of inclusive particle production. In addition to the O(alpha_s) unpolarized cross section the longitudinal cross section is also used to extract the gluon fragmentation function from e+e- annihilation data. As the O(alpha_s) vanishes for longitudinal polarized photons (or Z bosons), the O(alpha_s^2) corrections are required to reduce the scale ambiguities. Recently, P.J. Rijken and W.L. van Neerven presented the longitudinal coefficient functions to next-to-leading order. We confirm part of their results in this thesis and complete the calculation by the results for the color class C_F*T_R that must be included for a consistent comparison with LEP1 data. The complete set of coefficient functions is then used together with novel data from ALEPH to determine the fragmentation functions for charged hadrons. This set, and also sets for charged pions, kaons, and D^* mesons as well as neutral kaons published previously, can then be employed to test QCD in e+e- annihilation, photoproduction, gamma-gamma collisions, p-p_bar scattering and DIS. Finally, we suggest how the improved knowledge on the fragmentation in particular of the gluon could be used to determine the gluon and charm content of the photon.
Motivated by applications in thermal QCD and cosmology, we elaborate on a general method for computing next-to-leading order spectral functions for composite operators at vanishing spatial momentum, accounting for real, virtual as well as thermal corrections. As an example, we compute these functions (together with the corresponding imaginary-time correlators which can be compared with lattice simulations) for scalar and pseudoscalar densities in pure Yang-Mills theory. Our results may turn out to be helpful in non-perturbative estimates of the corresponding transport coefficients, which are the bulk viscosity in the scalar channel and the rate of anomalous chirality violation in the pseudoscalar channel. We also mention links to cosmology, although the most useful results in that context may come from a future generalization of our methods to other correlators.
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