Event Shapes

The measurement of event shape variables has been well-established in e⁺e^- annihilation experiments. An important point in the development of our understanding of QCD is to ensure that the measurement is well-defined theoretically at the required level of precision. In this case variables are chosen which are relatively insensitive to soft gluon emission and collinear parton branching. A determination of $\alpha_S(\mu)$ is therefore possible by comparison with NLO theory plus resummed series or NLLA calculations. At this workshop, impressive results from LEPII were presented which enabled a LEP average $\alpha_S(M_Z) = 0.120 \pm 0.005$ to be extracted [21].

Recent theoretical developments in the understanding of infrared renormalon contributions, which lead to divergences from the perturbative calculations, allow the first steps to be made towards a direct comparison of theory and data without invoking hadronisation models. These power corrections, with a characteristic 1/Q dependence, have been calculated for event shape variables [22] and could also be calculated for differential jet rates.

H1 presented new measurements of the thrust, jet broadening and jet mass in DIS for momentum transfers, 7<Q<100 GeV, in the current region of the Breit frame [23]. The mean values of the event shape data show similar trends to results from e⁺e^- annihilation experiments as a function of Q. In the DIS case, one advantage is that the event axis is determined by the direction of the virtual boson, whereas in e⁺e^- annihilation the axis has to be determined from the final state hadrons using e.g. the thrust axis. The data, shown in Fig. 3, have been fitted to NLO theory plus the calculated power corrections of Dasgupta and Webber. The important conclusion is that the size of the power correction, characterised by the parameter $\bar{\alpha_o}$, is consistent with a single value of $\bar{\alpha_o} = 0.491\pm0.003$ (exp) ^+0.079_-0.042 (theory) for three of the four event shape variables. In the case of jet broadening, the calculation of the power corrections is subject to large uncertainties: hence this particular variable does not satisfy the requirement of being theoretically well-defined and is not included in the global fit. The development of these power corrections is not only intrinsically important, but should also enable more precise extractions of $\alpha_S$ by constraining the hadronisation uncertainties more precisely.

  

Figure: Mean values of event shape variables as a function of Q, from H1. The values are for 1-thrust, calculated using (a) the thrust axis or (b) the photon axis, (c) the jet broadening and (d) the jet mass. The dotted line indicates the NLO calculation. The full line indicates the fit incorporating power corrections.