During the past few years, with the ongoing Run 3 of the LHC and its upcoming High-Luminosity upgrade, the need to study observables that can be both experimentally measured and theoretically predicted with high precision has grown. In particular, on the theory side, improvements of fixed-order perturbative predictions, resummation of logarithmic enhancements, and accurate determination of proton structure have become mandatory. With this thesis, we want to contribute to this effort. We aim to improve the present accuracy in the resummation of the logarithmic enhancements that arise in the coefficient function for partonic scattering, in the high-energy limit. At present, we know how to resum the Leading Logarithmic (LL) contributions to coefficient functions. We aim to extend this resummation to achieve the resummation for the Next-to-Leading Logarithmic (NLL) contributions and this thesis takes a first step in this direction. High-energy (or small-$x$) resummation of LL terms in the coefficient function is based on the so-called $k_t$-factorization theorem, which allows us to separate the coefficient function into two parts. The first one is the so-called off-shell coefficient function, which is similar to the usual coefficient function but is computed with the incoming gluon off-shell. If this coefficient function is computed in a physical gauge, it is free from small-$x$ logarithms. The second is the evolution factor, $\mathcal{U}$, which resums the logarithmic contributions in the coefficient function. To extend this procedure to resum NLL contribution we have to work on these two elements. In this thesis, we take a first step in the direction of this resummation by presenting the light-cone gauge calculation for the off-shell coefficient function for a specific process, the Higgs-induced Deep-Inelastic Scattering (HDIS). Thanks to the work described in this thesis, we have been able to clarify several technical and conceptual aspects of calculations in the light-cone gauge, which because of its complexity, is not commonly used. In particular, we present two prescriptions to regularise the spurious infra-red singularities due to the gauge choice and a general method to compute non-covariant loop integrals. We also discuss in detail the renormalization procedure in this gauge, which is highly nontrivial due to the non-covariant nature of the gauge choice. Our approach and presentation differ from what can be found in the literature because our focus is always on computing off-shell scattering amplitudes.
Towards the resummation of high-energy next-to-leading logarithms in QCD
RINAUDO, ANNA
2024-06-14
Abstract
During the past few years, with the ongoing Run 3 of the LHC and its upcoming High-Luminosity upgrade, the need to study observables that can be both experimentally measured and theoretically predicted with high precision has grown. In particular, on the theory side, improvements of fixed-order perturbative predictions, resummation of logarithmic enhancements, and accurate determination of proton structure have become mandatory. With this thesis, we want to contribute to this effort. We aim to improve the present accuracy in the resummation of the logarithmic enhancements that arise in the coefficient function for partonic scattering, in the high-energy limit. At present, we know how to resum the Leading Logarithmic (LL) contributions to coefficient functions. We aim to extend this resummation to achieve the resummation for the Next-to-Leading Logarithmic (NLL) contributions and this thesis takes a first step in this direction. High-energy (or small-$x$) resummation of LL terms in the coefficient function is based on the so-called $k_t$-factorization theorem, which allows us to separate the coefficient function into two parts. The first one is the so-called off-shell coefficient function, which is similar to the usual coefficient function but is computed with the incoming gluon off-shell. If this coefficient function is computed in a physical gauge, it is free from small-$x$ logarithms. The second is the evolution factor, $\mathcal{U}$, which resums the logarithmic contributions in the coefficient function. To extend this procedure to resum NLL contribution we have to work on these two elements. In this thesis, we take a first step in the direction of this resummation by presenting the light-cone gauge calculation for the off-shell coefficient function for a specific process, the Higgs-induced Deep-Inelastic Scattering (HDIS). Thanks to the work described in this thesis, we have been able to clarify several technical and conceptual aspects of calculations in the light-cone gauge, which because of its complexity, is not commonly used. In particular, we present two prescriptions to regularise the spurious infra-red singularities due to the gauge choice and a general method to compute non-covariant loop integrals. We also discuss in detail the renormalization procedure in this gauge, which is highly nontrivial due to the non-covariant nature of the gauge choice. Our approach and presentation differ from what can be found in the literature because our focus is always on computing off-shell scattering amplitudes.File | Dimensione | Formato | |
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