## Weak Showers

The emission of W^+- and Z^0 gauge bosons off fermions is intended to be an integrated part of the initial- and final-state radiation frameworks, and is fully interleaved with QCD and QED emissions. It is a new and still not fully explored feature, however, and therefore it is off by default. The weak-emission machinery is described in detail in [Chr14]; here we only bring up some of the most relevant points for using this machinery.

In QCD and QED showers the real and virtual corrections are directly related with each other, which means that the appropriate Sudakov factors can be directly obtained as a by-product of the real-emission evolution. This does not hold for W^+-, owing to the flavour-changing character of emissions, so-called Bloch-Nordsieck violations. These effects are not expected to be large, but they are not properly included, since our evolution framework makes no distinction in this respect between QCD, QED or weak emissions. Another restriction is that there is no simulation of the full gamma^*/Z^0 interference: at low masses the QED shower involves a pure gamma^* component, whereas the weak shower generates a pure Z^0.

The non-negligible W/Z masses have a considerable impact both on the matrix elements and on the phase space for their emission. The shower on its own is not set up to handle those aspects with a particularly good accuracy. Therefore the weak shower emissions are always matched to the matrix element for emission off a f fbar weak dipole, or some other 2 → 3 matrix element that resembles the topology at hand. Even if the match may not be perfect, at least the main features should be caught that way. Notably, the correction procedure is used throughout the shower, not only for the emission closest to the hard 2 → 2 process. In such extended applications, emission rates are normalized to the invariant mass of the dipole at the time of the weak emission, i.e. discounting the energy change by previous QCD/QED emissions.

Also the angular distribution in the subsequent V = W^+-/Z^0 decay is matched to the matrix element expression for f fbar → f fbar V → f fbar f' fbar' (FSR) and f fbar → g^* V → g^* f' fbar' (ISR). Afterwards the f' fbar' system undergoes showers and hadronization just like any W^+-/Z^0 decay products would.

Special for the weak showers is that couplings are different for left- and righthanded fermions. With incoming unpolarized beams this should average out, at least so long as only one weak emission occurs. In the case of several weak emissions off the same fermion the correlation between them will carry a memory of the fermion helicity. Such a memory is retained for the affected dipole end, and is reflected in the `Particle::pol()` property, it being +1 (-1) for fermions considered righthanded (lefthanded), and 0 for the bulk where no choice has been made.

Most events will not contain a W^+-/Z^0 emission at all, which means that dedicated generator studies of weak emissions can become quite inefficient. In a shower framework it is not straightforward to force such emissions to happen without biasing the event sample in some respect. An option is available to enhance the emission rate artificially, but it is then the responsibility of the user to correct the cross section accordingly, and not to pick an enhancement so big that the probability for more than one emission is non-negligible. (It is not enough to assign an event weight 1/e^n where e is the enhancement factor and n is the number of emitted gauge bosons. This still misses to account for the change in phase space for late emissions by the effect of earlier ones, or equivalently for the unwanted change in the Sudakov form factor. See [Lon13a] for a detailed discussion and possible solutions.)

Another enhancement probability is to only allow some specific W^+-/Z^0 decay modes. By default the shower is inclusive, since it should describe all that can happen with unit probability. This also holds even if the W^+- and Z^0 produced in the hard process have been restricted to specific decay channels. The trick that allows this is that two new "aliases" have been produced, a `Zcopy` with identity code 93 and a `Wcopy` with code 94. These copies are used specifically to bookkeep decay channels open for W^+-/Z^0 bosons produced in the shower. For the rest they are invisible, i.e. you will not find these codes in event listings, but only the regular 23 and 24 ones. The identity code duplication allows the selection of specific decay modes for 93 and 94, i.e. for only the gauge bosons produced in the shower. As above it is here up to the user to reweight the event to compensate for the bias introduced, and to watch out for possible complications. In this case there is no kinematics bias, but one would miss out on topologies where a not-selected decay channel could be part of the background to the selected one, notably when more than one gauge boson is produced.

Note that the common theme is that a bias leads to an event-specific weight, since each event is unique. It also means that the cross-section information obtained e.g. by `Pythia::stat()` is misleading, since it has not been corrected for such weights. This is different from biases in a predetermined hard process, where the net reduction in cross section can be calculated once and for all at initialization, and events generated with unit weight thereafter.

The weak shower introduces a possible doublecounting problem. Namely that it is now possible to produce weak bosons in association with jets from two different channels, Drell-Yan weak production with QCD emissions and QCD hard process with a weak emission. A method, built on a classification of each event with the kT jet algorithm, is used to remove the doublecounting. Specifically, consider a tentative final state consisting of a W/Z and two jets. Based on the principle that the shower emission ought to be softer than the hard emission, the emission of a hard W/Z should be vetoed in a QCD event, and that of two hard jets in a Drell-Yan event. The dividing criterion is this whether the first clustering step involves the W/Z or not. It is suggested to turn this method on only if you simulate both Drell-Yan weak production and QCD hard production with a weak shower. Do not turn on the veto algorithm if you only intend to generate one of the two processes.

### Variables

Below are listed the variables related to the weak shower and common to both the initial- and final-state radiation. For variables only related to the initial-state radiation (e.g. to turn the weak shower on for ISR) see Spacelike Showers and for final-state radiation see Timelike Showers.

`parm` WeakShower:enhancement (`default = 1.`; `minimum = 1.`; `maximum = 1000.`)
Enhancement factor for the weak shower. This is used to increase the statistics of weak shower emissions. Remember afterwards to correct for the additional weak emissions (i.e. divide the rate of weak emissions by the same factor).

`flag` WeakShower:singleEmission (`default = off`)
This parameter allows to stop the weak shower after a single emission.
If on, only a single weak emission is allowed.
If off, an unlimited number of weak emissions possible.

`flag` WeakShower:vetoWeakJets (`default = off`)
There are two ways to produce weak bosons in association with jets, namely Drell-Yan weak production with QCD radiation and QCD hard process with weak radiation. In order to avoid double counting between the two production channels, a veto procedure built on the kT jet algorithm is implemented in the evolution starting from a 2 → 2 QCD process, process codes in the range 111 - 129. The veto algorithm finds the first cluster step, and if it does not involve a weak boson the radiation of the weak boson is vetoed when `WeakShower:vetoWeakJets` is on. Note that this flag does not affect other internal or external processes, only the 111 - 129 ones. For the Drell-Yan process the same veto algorithm is used, but this time the event should be vetoed if the first clustering does contain a weak boson, see `WeakShower:vetoQCDjets` below.

`flag` WeakShower:vetoQCDjets (`default = off`)
This flag vetoes some QCD emission for Drell-Yan weak production to avoid doublecounting with weak emission in QCD hard processes. For more information see `WeakShower:vetoWeakJets` above. Note that this flag only affects the process codes 221 and 222, i.e. the main built-in processes for gamma^*/Z^0/W^+- production, and not other internal or external processes.

`parm` WeakShower:vetoWeakDeltaR (`default = 0.6`; `minimum = 0.1`; `maximum = 2.`)
The delta R parameter used in the kT clustering for the veto algorithm used to avoid double counting. Relates to the relative importance given to ISR and FSR emissionbs.

`flag` WeakShower:externalSetup (`default = off`)
This flags tells the shower to use an external setup stored in the info pointer. This is mainly expected to be used in conjunction with the weak merging, and has to be switched on when the weak merging is used.