A. Denner

Electroweak corrections to charged-current e+ e- ---> 4 fermion processes: Technical details and further results

Abstract The complete electroweak O ( α ) corrections have been calculated for the charged-current four-fermion production processes e + e − → ν τ τ + μ − ν ¯ μ , u d ¯ μ − ν ¯ μ , and u d ¯ s c ¯ . Here, technical details of this calculation are presented. These include the algebraic reduction of spinor chains to a few standard structures and the consistent implementation of the finite width of the W boson. To this end, a generalization of the complex-mass scheme to the one-loop level is proposed, and the practical application of this method is described. Finally, the effects of the complete O ( α ) corrections to various differential cross sections of physical interest are discussed and compared to predictions based on the double-pole approximation, revealing that the latter approximation is not sufficient to fully exploit the potential of a future linear collider in an analysis of W-boson pairs at high energies.

Predictions for all processes e+e− → fermions + γ

The complete matrix elements for e+e− → 4 and e+e− → 4fγy are calculated in the Electroweak Standard Model for polarized massless fermions. The matrix elements for all final states are reduced to a few compact generic functions. Monte Carlo generators for e+e− → 4f and e+e− → 4fγ are constructed. We compare different treatments of the finite widths of the electroweak gauge bosons; in particular, we include a scheme with a complex gauge-boson mass that obeys all Ward identities. The detailed discussion of numerical results comprises integrated cross sections as well as photon-energy distributions for all different final states.

Feynman rules for fermion number violating interactions

We present simple algorithmic Feynman rules for fermion-number-violating interactions. They do not involve explicit charge-conjugation matrices and resemble closely the familiar rules for Dirac fermions. We insist on a fermion flow through the graphs along fermion lines and get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions. We only need the familiar Dirac propagator and fewer vertices than in the usual treatment of fermion-number-violating interactions.

Electroweak radiative corrections to e+e−→WW→4 fermions in double-pole approximation — the RacoonWW approach

Abstract We calculate the complete O (α) electroweak radiative corrections to e + e − →WW→4 f in the electroweak Standard Model in the double-pole approximation. We give analytical results for the non-factorizable virtual corrections and express the factorizable virtual corrections in terms of the known corrections to on-shell W-pair production and W decay. The calculation of the bremsstrahlung corrections, i.e., the processes e + e − →4 fγ in lowest order, is based on the full matrix elements. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method and by applying phase-space slicing. The O (α) corrections as well as higher-order initial-state photon radiation are implemented in the Monte Carlo generator RacoonWW . Numerical results of this program are presented for the W-pair-production cross section, angular and W-invariant-mass distributions at LEP2. We also discuss the intrinsic theoretical uncertainty of our approach.We calculate the complete O(alpha) electroweak radiative corrections to e+e- -->WW -->4f in the electroweak Standard Model in the double-pole approximation. We give analytical results for the non-factorizable virtual corrections and express the factorizable virtual corrections in terms of the known corrections to on-shell W-pair production and W decay. The calculation of the bremsstrahlung corrections, i.e. the processes e+e- -->4f+gamma in lowest order, is based on the full matrix elements. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method and by applying phase-space slicing. The O(alpha) corrections as well as higher-order initial-state photon radiation are implemented in the Monte Carlo generator RACOONWW. Numerical results of this program are presented for the W-pair-production cross section, angular and W-invariant-mass distributions at LEP2. We also discuss the intrinsic theoretical uncertainty of our approach.

Complete electroweak O(α) corrections to charged-current e+e−→4 fermion processes

The complete electroweak O(alpha) corrections are calculated for the charged-current four-fermion production processes e+e- -->nu_tau tau+ mu- anti-nu_mu, u anti-d mu- anti-nu_mu, and u anti-d s anti-c. The calculation is performed using complex gauge-boson masses, supplemented by complex couplings to restore gauge invariance. The evaluation of the occurring one-loop tensor integrals, which include 5- and 6-point functions, requires new techniques. Explicit numerical results are presented for total cross sections in the energy range from the W-pair-production threshold region up to a scattering energy of 2TeV. A comparison with the predictions based on thedouble-pole approximation(DPA) provided by the generator RacoonWW reveals corrections beyond DPA of<0.5% in the energy range 170-300GeV, in agreement with previous estimates for the intrinsic DPA uncertainty. The difference to the DPA increases to 1-2% for sqrt{s} = 1-2TeV. At threshold, where the DPA becomes unreliable, the full O(alpha) calculation corrects an improved Born approximation (IBA) by about 1.6%, also consistent with an error estimate of the IBA.

Four-Fermion Production in Electron-Positron Collisions /

This report summarises the results of the four-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the calculation of four-fermion processes in electron-positron collisions at LEP-2 centre-of-mass energies are presented, concentrating on predictions for four main reactions: W-pair production, visible photons in four-fermion events, single-W production and Z-pair production. Based on a comparison of results derived within different approaches, theoretical uncertainties on these predictions are established.

Electroweak one loop contributions to top pair production in hadron colliders

Abstract We give a detailed presentation of the electroweak one-loop contributions to the production mechanisms of top quark pairs, q q → t t and gg → t t , for the energy range of future hadron colliders. The full gauge-invariant set of loop diagrams with Higgs, Z0 and W± bosons is considered including strong Yukawa couplings. The parton cross sections get sizeable modifications up to 40% and are sensitive to the Higgs boson mass and the Yukawa coupling. Results are also given for the observable hadronic cross section pp → t t X , where the large corrections at the parton level are substantially reduced to the order of a few percent. For the electroweak Standard Model the maximum contribution is about 7% for a light Higgs boson with Mη = 60 GeV. For Higgs bosons with Mη > 200 GeV, the electroweak contributions are typically (2–3)%.

Compact Feynman rules for Majorana fermions

We present simple algorithmic Feynman rules for Majorana fermions. Insisting on a fermion flow through the graphs along fermion lines we only need the familiar Dirac propagator and only vertices without explicit charge-conjugation matrices; moreover, we get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions.

High-energy approximation for on-shell W-pair production

Starting from the exact virtual and soft-photonic O(α) corrections to the differential cross section for on-shell W-pair production we derive a high-energy approximation valid for energies much higher than the W-boson mass. This approximation is improved by taking into account extra terms for large top-quark and Higgs-boson masses as well as the exact results for the leading low-energy universal corrections associated with the running of α and the p-parameter. For 90° scattering angle and in those situations where the cross section is large, this approximation reproduces the full virtual and soft-photonic O(α) result to better than ∼ 1% for energies above 500 GeV. In the angular range − 0.9 < cos θ < 0.9 it is better than 1% for energies above 1-3 TeV, depending on the polarization

The Coulomb singularity in off-shell W pair production

Abstract We study the effects of the Coulomb singularity for off-shell W -pair production in the relativistic approach, coming out of the continuum. This involves a careful analysis of the interplay between the Coulomb singularity, the decay width of the W bosons, and their off-shellness. We have observed screening effects related to the finite W width and the off-shellness. In the LEP200 energy range these screening effects and the relativistic effects turn out to be non-negligible.