Radiative Corrections to W+Jet Production at Hadron Colliders with a Leptonic Decay of the W Boson

The production of W bosons and additional jets at hadron colliders is a topic of great phenomenological interest, because such processes have large cross sections and, owing to the clear decay signature of the W boson, can for instance be used to monitor and calibrate the collider’s luminosity, as well as for a precise determination of the W-boson mass and width. Thus, a profound theoretical understanding of this process class is mandatory. In order to improve the accuracy of the theoretical predictions, this thesis is devoted to the calculation of the electroweak radiative corrections to the production of one W boson with one associated jet at the LHC and the Tevatron within the Standard Model. Since these corrections are at first evaluated on the parton level in a perturbative approach, we work in the parton model, where the hadronic cross section is obtained by folding the partonic contributions with the parton distribution functions that contain the non-perturbative information of the proton structure and have to be determined by experiment. We provide results for a stable W boson that is produced on its mass shell as well as for an intermediate (off-shell) W boson decaying into a charged lepton and a neutrino. For a consistent calculation of the next-to-leading order corrections, we have to take into account the virtual one-loop contributions, as well as the real bremsstrahlung corrections caused by radiation of one additional photon. Within both contributions, mass singularities appear that have to be treated with care within the numerical evaluation. In the calculation with a stable W boson in the final state, we use the method of phase-space slicing in order to exclude such singularities from the numerical phase-space integration and calculate them analytically in the problematic phase-space regions. For the off-shell calculation, however, we use the more sophisticated dipole subtraction technique to subtract the infrared-singular structures on the integrand level to allow for a stable numerical evaluation. Within this thesis, we extend this method to also enable the consistent treatment of non-collinear-safe observables related to photon radiation off muons. Additionally, the calculation of radiative corrections to processes involving an unstable W boson leads to the problem that a finite particle width has to be consistently introduced in the calculation. If this is done carelessly, gauge invariance might be destroyed even at the leading order of the perturbative series. Thus, we work in the complex-mass scheme to account for a proper inclusion of a finite W-boson width in our calculation. This particular scheme respects gauge invariance and can be applied in all phase-space regions. Our results are implemented into a flexible Monte Carlo code that allows for the calculation of total cross sections and differential distributions, where in principle any event-selection criteria that might be of physical interest can be applied. In the numerical analysis we observe large negative electroweak corrections at large transverse momenta that can be attributed to universal Sudakov logarithms. Moreover, relevant deviations in the shape of the transverse-mass distribution of the final-state lepton pair near the resonance are induced that are important with regard to a precise determination of the W mass. Thus, our code can provide crucial information as a tool for the analysis of LHC data. Chapter 1 Motivation and introduction The production of electroweak (EW) W and Z bosons with subsequent leptonic decays is one of the most prominent Standard Model (SM) processes at present and future hadron colliders like the Fermilab Tevatron and the CERN Large Hadron Collider (LHC). The signatures are clean owing to the final-state leptons, and the cross sections are large. In particular, the cross section for W-boson production at the LHC will be about ten times as big as for Z production, corresponding to 200 events per second with a leptonic decay of the W boson, when the collider operates at its design luminosity of LLHC = 10 cm−2/s. Due to the large cross sections and the resulting high statistics even at lower-luminosity runs, the investigation of the charged-current Drell–Yan process pp → W+X → lνl +X (1.0.1) at the LHC will provide the possibility to directly measure the mass (MW) and width (ΓW) of the W boson with the highest accuracy ever. For this purpose, the distributions of the lepton transverse momentum (pT,l) or the transverse mass of the lepton pair (MT,lνl) that are obtained by experiment are compared to the theoretical predictions in a fitting procedure [1, 2], since those leptonic observables exhibit a sensitive dependence on MW and ΓW and are also well-suited for experimental reconstruction. As pointed out in Ref. [2], a precise knowledge of MW and ΓW—which are essential parameters of the SM—is desirable, since a comparison of direct measurements in singleW production at the LHC with indirect measurements from a global fit to EW precision data measured at LEP1/SLD [3], will provide a powerful test of the validity of the SM, i.e. any significant disagreement could be interpreted as a hint to new physics beyond the Standard Model (BSM). Aside, a precise determination of MW and the top-quark mass mt will also allow us to further indirectly constrain the bounds on the mass MH of a SM Higgs boson. The current values for MW and ΓW stated by the Particle Data Group [4] are MW = 80.398± 0.025GeV, ΓW = 2.141± 0.041GeV . (1.0.2) They are obtained combining results from direct measurements at LEP and the Tevatron. At the LHC, the (expected) experimental accuracy is so excellent that one hopes to further improve the precision measurement ofMW to an accuracy of δMW = 15MeV [5], where generally the highest precision for the determination of the W mass can be achieved by fitting 2 1. Motivation and introduction the MT,lνl distribution near the Jacobian peak. In Ref. [1], the ATLAS collaboration even states that for each exploitable leptonic W-boson decay channel (W → eνe, W → μνμ), and for an integrated luminosity of 10 fb−1, an accuracy of δMW = 7MeV on the Wboson mass is aspired in the high-precision mass determination. Additionally, the lineshape of the MT,lνl distribution in the off-shell region will give access to an accurate direct determination of ΓW that might lead to a reduction of the corresponding uncertainty to δΓW = 30MeV after an accumulated luminosity of 10 fb −1 is reached [2]. In addition to its relevance for mass determination, W-boson production can provide important information in the fit of the parton distribution functions (PDFs) for valenceand sea quarks by investigating the W-boson charge asymmetry [2] A(yl) = dσ/dyl − dσ/dyl dσ/dyl + dσ−/dyl , (1.0.3) at the LHC and the Tevatron, where dσ± = dσ(pp/pp → lνl +X) , (1.0.4) and yl denotes the rapidity of the charged lepton. Due to the high production rates, W events may also serve as a luminosity monitor at the LHC, and they will help to understand the detector performance in the early stage of data analysis [6]. Moreover, at high energies, W bosons deliver background to searches for new heavy charged W′ gauge bosons that are predicted in several extensions of the SM [7]. At hadron colliders, the EW gauge bosons are (almost) always produced together with additional QCD radiation. The production cross section of W bosons in association with a hard, visible jet, pp/pp → W+ jet +X → lνl + jet +X, (1.0.5) is still large. Moreover, the intermediate W boson recoils against the jet leading to a new kinematical situation with boosted W bosons. For large pT of the jet the corresponding events contain charged leptons and/or neutrinos with large pT. In fact, in the SM, W+ jet(s) production is the largest source for events with large missing transverse momentum where also a charged lepton is present for triggering. Hence, W+ jet(s) production is not only a SM candle process. It is also an important background for a large class of newphysics searches based on missing transverse momentum. In particular, W + jet(s) production plays a crucial role—besides Z + jet(s) production and tt events—in the one-lepton search mode for R-parity-conserving supersymmetry (SUSY) scenarios at the LHC [8]. Apart from BSM-physics searches, W + 2 jets production also has to be considered as a background process to the possible discovery channel pp → W+H → lνl + bb (1.0.6) for a light SM Higgs boson which is produced via Higgs Strahlung and subsequently decays into a bb pair [9, 10]. To match the prospects and experimental importance of W+jet(s) production at hadron colliders, excellent theoretical predictions are mandatory. The differential cross section for The value of 10 fb will be reached after one year of stable running at a luminosity of L = 10 cm/s, corresponding to about 4·107 W events with a leptonic decay in the exploitable channels.