# Project B - Physics with W/Z bosons and Top-Quarks

**S. Dittmaier, B. Heinemann, G. Herten, H. Ita, K. Jakobs, A. Knue, C. Weiser**

The processes of electroweak vector-boson scattering (VBS) and multi-vector-boson production offer good opportunities for indirect searches for new physics beyond the Standard Model (SM) because of their sensitivity to deviations from the SM. The process of electroweak VBS was recently established by both the ATLAS and CMS collaborations. The increasing luminosity of the LHC will allow to perform differential measurements with enhanced granularity and sensitivity. For the interpretation of the results, improved theoretical predictions, e.g. by taking into account electroweak NLO effects, have to accompany the experimental efforts. Investigation of top-quark production and properties represents a different approach to indirect searches for new physics. Because of its large mass - and thus short lifetime - it plays a special role amongst the fundamental fermions, because e.g. its spin state can be accessed. A precise measurement of the top-quark mass allows - together with precision measurements of the W- and Higgs-boson masses - stringent tests of the consistency of the SM. The investigation of the spin structure allows detailed studies of the production process where new physics might contribute. The experimental efforts are supported from the theoretical side through calculations for processes where top-quark pairs are accompanied by hadronic jets. This is also very important for analyses where these processes constitute an important contribution to the background (e.g. ttH).

**B.1 Measurement of absolute and differential cross section for production and scattering of massive electroweak gauge bosons in SM and SMEFT**

The investigation of the scattering of electroweak vector bosons with two jets with large transverse momentum in the forward and backward directions became experimentally accessible with the LHC Run 2. In the SM the cross section at high diboson masses is regularized by quartic gauge couplings and Higgs boson exchange, to prevent unitarity violation. This process is thus ideal to study quartic gauge couplings and to indirectly probe the mechanism of electroweak symmetry breaking. These processes are furthermore sensitive to operators of dimension eight in the context of EFT, which makes these processes particularly interesting. Both the ATLAS and CMS collaboration recently observed VBS processes based on partial datasets of the LHC Run 2. The increasing integrated luminosity will allow more sensitive measurements with increased granularity of kinematic variables. Precision measurements of the *W ^{+}W*

^{-}production process are also of great interest. This is also sensitive to anomalous gauge couplings involving

*W*bosons. It is furthermore an important background source for the

*H→WW*channel and processes of new physics, e.g. the production of chargino pairs, the supersymmetric partners of

*W*bosons. The goal is to achieve an experimental uncertainty of around 3.5%, comparable with the uncertainty of current theoretical predictions. This will contribute to clarify whether significant deviations from the SM exist in this process.

__Thesis topics:__

- Measurement of differential cross sections of electroweak production of two
*W*-bosons of same electric charge in association with jets and EFT interpretations - Measurement of inclusive and differential production cross-sections of W
^{+}W^{-}pairs and EFT interpretations

**B.2 ****Calculation of radiative corrections to the production ****and scattering of electroweak gauge bosons**

__Thesis topics:__

- Field-theoretical techniques for the description of photon and W/Z emission
- Calculation of mixed QCD-EW corrections to gauge-boson pair production at the LHC
- Precision calculations for electroweak vector-boson scattering in theories beyond the SM at the LHC

**B.3 Measurement of top-quark properties and interpretation**

The top quark is by far the heaviest elementary particle in the Standard Model and assumed to play a special role in the mechanism of electroweak symmetry breaking. Top-quark pair are produced in abundance at the Large Hadron Collider, which allows to measure its properties at unprecedented precision.

The measurement of the top-quark mass is a cornerstone of the LHC research programme. Using the full dataset taken by the ATLAS experiment in Run 2 of the LHC allows now to further reduce the systematic uncertainties on the top-quark mass. The reduction of the jet-energy-scale uncertainty and the signal modelling uncertainties is the main focus of the proposed thesis project.

The analysis will be performed in the lepton+jets channel, which has a topology with exactly one charged lepton, four jets (among them two b-jets) and missing transverse energy due to the elusive neutrino. To measure the mass, the top-quark pair event needs to be fully reconstructed. This will be done either with a kinematic likelihood fit or via a deep neural network (DNN). The rejection of events that cannot be correctly reconstructed will also be done using a DNN. The application of these machine-learning techniques will allow to reduce the overall uncertainty.

Additional auxiliary measurements have to be performed to reduce the uncertainties further. One of these is the measurement of the underlying event in tt events, which will allow to define a meaningful colour-reconnection uncertainty.

__Thesis topics:__

- Improved measurement of the top quark mass in the tt→b qq b l ν final state
- Determination of spin correlation in top-quark pair production

**B.4 ****Calculation of scattering amplitudes in NNLO QCD for tt+Jets production at hardron colliders. **

Theory predictions for the associated production of top-pairs and jets are important for measuring top-quark interactions. This process class has been used for the measurement of the top mass. Furthermore, the final state jets allow to probe the kinematic dependence of the coupling and search for indirect new-physics signatures. Finally, the (technically) related signature pp → tt + Photon allows to probe the top-quark charge.

In this research directions we aim for theory predictions for key processes containing top-pairs up to NNLO-QCD corrections and NLO electroweak corrections. Central scattering amplitudes we require are two-loop five-point scattering amplitudes of tops and light partons as well as related one-loop scattering amplitudes in singular phase space regions. The required computations are complex and require a number of components. The main focus will be the application and extension of the numerical unitarity method for the computation of integral coefficients. Initially the master integrals will be obtained via numerical integration using public programs.

The Freiburg groups have already obtained a number of preparatory results for these projects. The group of Stefan Dittmaier was the first to obtain NLO-QCD predictions for the pp → tt+Jets as well as the pp → tt bb signatures. Furthermore with their integral library Collier precision implementation of the one-loop integration is available. The group of Harald Ita could already extend the unitarity approach for in the process pp → Wbb + 3-Jets including quark-mass effects. In particular the recent work on the numerical unitarity method based on exact arithmetics allows for the numerically stable evaluation of integral coefficients. Finally, the group we the first to compute the five-parton two-loop scattering amplitudes recently. The extension to massive particles is certainly an interesting challenge in modern field theory.

__Thesis topics:__

- One-loop amplitudes for Top-pair production in singular phase space with exact arithmetic.
- Two-loop QCD amplitudes for top-pari production in association with jets.