One-loop weak corrections to three-jet observables at the Z pole

We briefly illustrate the impact of the genuinely weak one-loop virtual terms of the O(αSαEW) factorisable corrections to the three-jet cross section at √ s = MZ . Their importance for the measurement of αS at GigaZ luminosities is emphasised. 1 Three-jets events at leptonic colliders In the case of ee annihilations, the most important QCD quantity to be extracted from multi-jet events is αS. The confrontation of the measured value of the strong coupling constant with that predicted by the theory through the renormalisation group evolution is an important test of the Standard Model (SM) or else an indication of new physics, when its typical mass scale is larger than the collider energy, but which can manifest itself through virtual effects. Not only jet rates, but also jet shape observables, which offer a handle on non-perturbative QCD effects via large power corrections, would be affected. We report here on the calculation of the one-loop weak-interaction corrections to threejet observables in electron-positron annihilations through the order O(αSα EW) generated Work supported in part by the U.K. Particle Physics and Astronomy Research Council (PPARC), by the European Union (EU) under contract HPRN-CT-2000-00149 and by the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) under contract 2001023713 006. Talk given at the ECFA Study of Physics and Detectors for a Linear Collider, Montpellier, France, 13-16 November 2003. via the interference of the graphs in Fig. 1 with the tree-level ones for γ, Z → q̄qg final states, where the external γ, Z current is intended to connect to an incoming ee fermion line. In the figure, the shaded blob represents all the contributions to the gauge boson self-energy and is dependent on the Higgs mass (we have set MH = 115 GeV for the latter). We neglect, however, loops involving the Higgs boson coupling to the fermion lines. The graphs in which the exchanged gauge boson is a W -boson are accompanied by those in which the latter is replaced by its corresponding Goldstone boson. There is then a similar set of diagrams in which the direction of the fermion line is reversed, with the exception of the last graph, as here reversal does not lead to a distinct topology. Corrections along the ee lines are also included in our analysis. In short, we compute the factorisable effects only, i.e., corrections to the initial and final states only. Whereas these should be sufficient to describe adequately the phenomenology of three-jet events at √ s = MZ , at energy scales much larger than the Z-boson mass one expects comparable effects due to the non-factorisable corrections, in which weak gauge-bosons connect via one-loop diagrams electrons and positrons to quarks and antiquarks, whose computation is currently in progress. We will show that such factorisable corrections are of a few percent at √ s = MZ . Hence, while their impact is not dramatic in the context of LEP1 and SLC, where the total error on the measured value of αS is larger, at a future Linear Collider (LC) [1], running at the Z mass peak (e.g., GigaZ), they ought to be taken into account in the experimental fits, as here the uncertainty on the value of the strong coupling constant is expected to be at the 0.1% level or even smaller [2]. The calculation has been performed using helicity amplitudes so that it can be applied to the case of polarised beams, option that is one of the strengths of the LC projects. Besides, another aspect that should be recalled is that weak corrections naturally introduce parity-violating effects in jet observables, detectable through asymmetries in the cross-section, which are often regarded as an indication of physics beyond the SM. Comparison of theoretical predictions involving parity-violation with future LC experimental data is regarded as another powerful tool for confirming or disproving the existence of some beyond the SM scenarios, such as those involving right-handed weak currents and/or new massive gauge bosons.