The matching to first-order matrix-elements is well-defined for massless quarks, and was originally used unchanged for massive ones. A first attempt to include massive matrix elements did not compensate for mass effects in the shower kinematics, and therefore came to exaggerate the suppression of radiation off heavy quarks [Nor01,Bam00]. Now the shower has been modified to solve this issue, and also improved and extended to cover better a host of different reactions [Nor01].
|--||--||(eikonal)||6 - 9|
|11 - 14|
|16 - 19|
|21 - 24|
|26 - 29|
|31 - 34|
|36 - 39|
|41 - 44|
|46 - 49|
|51 - 54|
|56 - 59|
|61 - 64|
|66 - 69|
|71 - 74|
|76 - 79|
|--||--||(eikonal)||81 - 84|
The starting point is the calculation of the processes
, each at leading order, where the ratio
In order to match to the singularity structure of the massive matrix
elements, the evolution variable is changed from to
, i.e. is the propagator of a
massive particle [Nor01]. For the shower history
this gives a differential probability
Top, squarks and gluinos can radiate gluons, as shown in Table for the case of resonance decays. Radiation is included also in a primary production process such as , but then without a perfect match to the respective first-order emission matrix elements, which here also would contain interference with initial-state radiation. Instead a close analogue is found in the Table, with the same final-state colour and spin structure, to ensure that at least the limit of collinear radiation is handled correctly. Furthermore, in this case, the maximum scale of emission is regulated by the standard shower parameters, and not simply set by the decaying resonance mass.
Also subsequent emissions of gluons off the primary particles are corrected to . To this end, a reduced-energy system is constructed, which retains the kinematics of the branching under consideration but omits the gluons already emitted, so that an effective three-body shower state can be mapped to an set of variables. For light quarks this procedure is almost equivalent with the original one of using the simple universal splitting kernels after the first branching. For heavy quarks it offers an improved modelling of mass effects also in the collinear region.
Some related further changes have been introduced, a few minor as default and some more significant ones as non-default options [Nor01]. This includes the description of coherence effects and arguments, in general and more specifically for secondary heavy flavour production by gluon splittings. The problem in the latter area is that data at LEP1 show a larger rate of secondary charm and bottom production than predicted in most shower descriptions [Bam00,Man00], or in analytical studies [Sey95]. This is based on applying the same kind of coherence considerations to branchings as to , which is not fully motivated by theory. In the lack of an unambiguous answer, it is therefore helpful to allow options that can explore the range of uncertainty.
Further issues remain to be addressed, e.g. radiation off particles with non-negligible width, where interference between radiation before and after the decay is not considered. In general, however, the new description of mass effects in the shower should allow an improved description of gluon radiation in many different processes.