Christian Schwinn

On-shell recursion relations for all Born QCD amplitudes

We consider on-shell recursion relations for all Born QCD amplitudes. This includes amplitudes with several pairs of quarks and massive quarks. We give a detailed description on how to shift the external particles in spinor space and clarify the allowed helicities of the shifted legs. We proof that the corresponding meromorphic functions vanish at z → ∞. As an application we obtain compact expressions for helicity amplitudes including a pair of massive quarks, one negative helicity gluon and an arbitrary number of positive helicity gluons.

Four-fermion production near the W pair-production threshold

Abstract We perform a dedicated study of the four-fermion production process e − e + → μ − ν ¯ μ u d ¯ X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, Γ W / M W , and the non-relativistic velocity v of the W boson up to next-to-leading order in Γ W / M W ∼ α ew ∼ v 2 . We find that the dominant theoretical uncertainty in M W is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into δ M W ≈ 10 – 15 MeV , and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.

SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks

We use supersymmetric Ward identities to relate multi-gluon helicity amplitudes involving a pair of massive quarks to amplitudes with massive scalars. This allows to use the recent results for scalar amplitudes with an arbitrary number of gluons obtained by on-shell recursion relations to obtain scattering amplitudes involving top quarks.

CSW rules for a massive scalar

Abstract We derive the analog of the Cachazo–Svrcek–Witten (CSW) diagrammatic Feynman rules for four-dimensional Yang–Mills gauge theory coupled to a massive colored scalar. The mass term is shown to give rise to a new tower of vertices in addition to the CSW vertices for massless scalars in non-supersymmetric theories. The rules are derived directly from an action, once through a canonical transformation within light-cone Yang–Mills and once by the construction of a twistor action. The rules are tested against known results in several examples and are used to simplify the proof of on-shell recursion relations for amplitudes with massive scalars.

Deriving CSW rules for massive scalar legs and pure Yang-Mills loops

This article provides two complementary detailed derivations of Cachazo-Svrcek-Witten-style Feynman rules for Yang-Mills gauge theory coupled to a massive coloured scalar as presented in earlier work. These proceed through a direct canonical transformation method on space-time and through a gauge transformation in an action constructed on twistor space. It is shown explicitly that the field transformations are identical in both cases. Some simple tree-level examples of our rules are given and we comment on the application of them to the calculation of the rational part of one-loop pure glue amplitudes. A possible direct quantum completion of pure glue CSW rules based on dimensional regularisation motivated by these results is sketched. Finally, it is shown how to derive CSW rules for effective Higgs-gluon and Higgs-matter couplings proposed in the literature directly from the action. This derivation yields additional towers of vertices which generate a subset of the contributions to effective multi-Higgs scattering amplitudes.

Dominant NNLO corrections to four-fermion production near the W-pair production threshold

Abstract We calculate the parametrically dominant next-to-next-to-leading order corrections to four-fermion production e − e + → μ − ν ¯ μ u d ¯ + X at centre-of-mass energies near the W -pair production threshold employing the method of unstable-particle effective theory. In total the correction is small, leading to a shift of 3 MeV in the W -mass measurement. We also discuss the implementation of realistic cuts and provide a result for the interference of single-Coulomb and soft radiative corrections that can easily be extended to include an arbitrary number of Coulomb photons.

On-shell supersymmetry for massive multiplets

The consequences of on-shell supersymmetry are studied for scattering amplitudes with massive particles in four dimensions. Using the massive version of the spinor helicity formalism the supersymmetry transformations relating products of on-shell states are derived directly from the on-shell supersymmetry algebra for any massive representation. Solutions to the resulting Ward identities can be constructed as functions on the on-shell superspaces that are obtained from the coherent state method. In simple cases it is shown that these superspaces allow one to construct explicitly supersymmetric scattering amplitudes. Supersymmetric on-shell recursion relations for tree-level superamplitudes with massive particles are introduced. As examples, simple supersymmetric amplitudes are constructed in Supersymmetric QCD (SQCD), the Abelian Higgs model, the Coulomb branch of N = 4, SQCD with an eective Higgs-gluon coupling and for massive vector boson currents.

Precision studies of observables in pp → W → lνl and pp → γ , Z → l+l− processes at the LHC.

This report was prepared in the context of the LPCC Electroweak Precision Measurements at the LHC WG (https://lpcc.web.cern.ch/lpcc/index.php?page=electroweak_wg) and summarizes the activity of a subgroup dedicated to the systematic comparison of public Monte Carlo codes, which describe the Drell–Yan processes at hadron colliders, in particular at the CERN Large Hadron Collider (LHC). This work represents an important step towards the definition of an accurate simulation framework necessary for very high-precision measurements of electroweak (EW) observables such as the W boson mass and the weak mixing angle. All the codes considered in this report share at least next-to-leading-order (NLO) accuracy in the prediction of the total cross sections in an expansion either in the strong or in the EW coupling constant. The NLO fixed-order predictions have been scrutinized at the technical level, using exactly the same inputs, setup and perturbative accuracy, in order to quantify the level of agreement of different implementations of the same calculation. A dedicated comparison, again at the technical level, of three codes that reach next-to-next-to-leading-order (NNLO) accuracy in quantum chromodynamics (QCD) for the total cross section has also been performed. These fixed-order results are a well-defined reference that allows a classification of the impact of higher-order sets of radiative corrections. Several examples of higher-order effects due to the strong or the EW interaction are discussed in this common framework. Also the combination of QCD and EW corrections is discussed, together with the ambiguities that affect the final result, due to the choice of a specific combination recipe. All the codes considered in this report have been run by the respective authors, and the results presented here constitute a benchmark that should be always checked/reproduced before any high-precision analysis is conducted based on these codes. In order to simplify these benchmarking procedures, the codes used in this report, together with the relevant input files and running instructions, can be found in a repository at https://twiki.cern.ch/twiki/bin/view/Main/DrellYanComparison.

CSW rules for massive matter legs and glue loops

Cachazo-Svrcek-Witten-type Feynman rules for massive matter scalar legs and pure glue loops are presented, obtained by deriving them directly from the space-time action. We comment on the derivation and some sample applications, in particular to calculating one loop effects in pure Yang-Mills theory. Furthermore, we derive CSW rules for effective Higgs-gluon couplings studied in the literature. In addition, it is shown how twistor techniques for deriving canonical field transformations explored for massless scalars extend to massless fermions.

Unitarity constraints on top quark signatures of Higgsless models

We use conditions for unitarity cancellations to constrain the couplings of the top and bottom quarks to Kaluza-Klein modes in Higgsless models of electroweak symmetry breaking. An example for the mass spectrum of quark resonances in a theory-space model is given and the implications for the collider phenomenology in the top sector are discussed, comparing to signatures of little Higgs and strong electroweak symmetry breaking models.