• precision physics
• pQCD
• LHC
• drell-yan
• collider physics
• quantum chromodynamics

The Standard Model of elementary particle physics (SM) is one of our most successful theory ever conceived. Combining the strong interaction with electromagnetic and weak interactions and including the Higgs mechanism, it has shown remarkable success in describing the vast majority of collider data from high energy experiments, and the discovery of the Higgs boson has brought the last brick for its experimental validation.
Since its formulation, the accuracy with which the SM has been verified is outstanding.
His successes range from the magnetic moment of the electron, which is the most precise measurement in particle physics, to the discovery of every particle predicted. Last but not least, of course, the already mentioned discovery of the Higgs Boson.
Despite these successes, the scientific community is well aware that SM is not a complete theory since it fails to explain many phenomena, such as neutrino oscillations, the origins of matter-antimatter asymmetry, the hierarchy problem and so on.
In this context, in order to discover possible hints of New Physics Beyond Standard Model (BSM), it is essential to keep under control the theoretical predictions of the Standard Model background processes. This task requires the calculation of higher-order radiative corrections in QCD and Electroweak (EW) theory.
In particular, at the CERN Large Hadron Collider (LHC), the most important contributions emerge from QCD corrections. The most classical scattering process in hadron collisions is the dilepton production via the Drell-Yan (DY) mechanism. This process
consists of vector gauge boson (γ=Z,W ±) production followed by leptonic decay. The importance of DY is due to its striking features:
• It has a large cross-section, and the intermediate vector boson decays with a simple and clean experimental signature, given the presence of at least one high pT lepton in the final state. For these reasons, these processes are used as a standard candle for detector calibration and luminosity monitoring at LHC.
• It has been, and continues to be, one of the essential tools for the Standard Model parameter determination. Studying the resonance region of the massive boson, we can extract the W mass and the weak mixing angle sin θW. Besides, it provides a solid test field for the SM predictions, including the transverse momentum distribution, invariant mass measurements, and the angular distributions of dileptons.
• DY massive dilepton production, along with the Deep Inelastic Scattering (DIS), can be used to study the short-distance dynamics of QCD and the partonic substructure of hadrons, such as parton distribution functions (PDFs).
• It can provide valuable clues regarding the BSM physics. The dilepton final states are susceptible to a wide variety of signals. For instance, dimuon invariant mass spectrum at LHC exhibits resonances, where each peak corresponds to the production of a different well-known particle. The same principle can be applied for the production of any neutral state with a large enough invariant mass, and this implies an excellent channel for discoveries of new physics.

Another key element in everything that we have discussed so far is the dependence on the quarks’ masses, which is generally neglected in hard-scattering processes. Although the massless approximation is often justified in channels involving only light quarks (typically quark up, down, and strange), in the context of precision physics, it is crucial to establish these contributions, when having to do with charm and bottom quarks.
In general, those effects are relevant in the region of small momenta of the order of the mass mQ of the heavy quark: in particular, the transverse momenta distribution qT of W=Z bosons is sensitive to the charm and bottom quark masses.
This is the general context in which the thesis takes place, in particular, the main focus of our work is the calculation of bottom quark mass effects in the weak boson emission on Drell-Yan processes at Next-to-Next-to-Leading order (NNLO) in QCD.
The analysis will be concentrated in the region of small transverse momentum, where these contributions are relevant.
Specifically, we will consider the process pp -> W±+X in NNLO in QCD, and we will take into account the bottom quark mass effects in the double-real, real-virtual, and two-loop virtual corrections. By a suitable generalization of the NNLO qT subtraction formalism, we are able to quantify the effects of the finite bottom quark mass for some kinematical distributions which are relevant for the LHC physics program.