We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) aà 2 QCD and (ii) a 2 à 3 QCD . Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the Oða 2 Þ terms the I ¼ 0 and I ¼ 2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a 2 lnM 2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.

We present a C++ library for the numerical evaluation of one-loop virtual corrections to multi-jet production in massless QCD. The pure gluon primitive amplitudes are evaluated using NGLUON [1]. A generalized unitarity reduction algorithm is used to construct arbitrary multiplicity fermion-gluon primitive amplitudes. From these basic building blocks the one-loop contribution to the squared matrix element, summed over colour and helicities, is calculated. No approximation in colour is performed. While the primitive amplitudes are given for arbitrary multiplicities we provide the squared matrix elements only for up to 7 external partons allowing the evaluation of the five jet cross section at next-to-leading order accuracy. The library has been recently successfully applied to four jet production at next-to-leading order in QCD [2].

The process pp → µ + ν µ e + ν e jj receives several contributions of different orders in the strong and electroweak coupling constants. Using appropriate event selections, this process is dominated by vector-boson scattering (VBS) and has recently been measured at the LHC. It is thus of prime importance to estimate precisely each contribution. In this article we compute for the first time the full NLO QCD and electroweak corrections to VBS and its irreducible background processes with realistic experimental cuts. We do not rely on approximations but use complete amplitudes involving two different orders at tree level and three different orders at one-loop level. Since we take into account all interferences, at NLO level the corrections to the VBS process and to the QCD-induced irreducible background process contribute at the same orders. Hence the two processes cannot be unambiguously distinguished, and all contributions to the µ + ν µ e + ν e jj final state should be preferably measured together.

For the first time full next-to-leading-order electroweak corrections to off-shell vector-boson scattering are presented. The computation features the complete matrix elements, including all nonresonant and off-shell contributions, to the electroweak process pp → µ + νµe + νejj and is fully differential. We find surprisingly large corrections, reaching −16% for the fiducial cross section, as an intrinsic feature of vector-boson-scattering processes. We elucidate the origin of these large electroweak corrections upon using the double-pole approximation and the effective vector-boson approximation along with leading-logarithmic corrections.

We present a computer library for the numerical evaluation of colour-ordered n-gluon amplitudes at oneloop order in pure Yang-Mills theory. The library uses the recently developed technique of generalised unitarity. Running in double precision the library yields reliable results for up to 14 gluons with only a small fraction of events requiring a re-evaluation using extended floating point arithmetic. We believe that the library presented here provides an important contribution to future LHC phenomenology. The program may also prove useful in cross checking results obtained by other methods. In addition, the code provides a sample implementation which may serve as a starting point for further developments. Program summary Program title: NGluonCatalogue identifier: AEIZ_v1_0 Program summary URL: Nature of problem: Evaluation of next-to-leading order corrections for gluon scattering amplitudes in pure gauge theory. Solution method: Purely numerical approach based on tree amplitudes obtained via Berends-Giele recursion combined with unitarity method. Restrictions: Running in double precision the number of gluons should not exceed 14. Running time: Depending on the number of external gluons between less than a millisecond (4 gluons) up to a 1 s (14 gluons) per phase space point.