A calculation is only as good as the trustworthiness of its uncertainty bands. Although not foolproof, VINCIA attempts to make comprehensive and explicit estimates of the theoretical accuracy of the answers it provides, event by event in phase space. Obviously, VINCIA can only make these estimates for the parts of the calculation that it handles itself - hence the automatic uncertainty estimates are currently limited to the perturbative parts of the calculation.
When switched on, the uncertainty variations are provided as, and can be accessed by the user through, a vector of alternative weights that is provided for each event. If the event is in a phase space region that VINCIA believes to be under good perturbative control (according to the showering and matching criteria specified by the user), the spread in weights will be small, whereas it will be larger for events populating less well controlled phase space regions.
Since the uncertainty estimate is fully differential in phase space, cuts can be imposed post facto without causing any special problems. E.g., if the cuts isolate a poorly controlled region, all the accepted events will have relatively large event weight spreads, and hence the overall relative uncertainty will increase, as expected.
Needless to say, these uncertainties still have to be interpreted with caution, but due to a large amount of flexibility in the VINCIA formalism, VINCIA can perform quite a few variations that are not possible with other generators. We therefore believe that the uncertainties quoted by VINCIA are, at least, reasonably meaningful.
Note also that the "central" set of weights (corresponding to the settings chosen by the user for the current run) is normally unweighted by default in VINCIA. I.e., all the events have identical weights and can be trivially added together statistically. The uncertainty weight sets are computed in such a way that this still holds true on average for each uncertainty variation individually. I.e., although the weights corresponding to uncertainty variation n fluctuate about unity, event to event, their average over many events will still be unity. Formally, this is due to the variations being done in a way that conserves unitarity. Practically, it means that none of the variations change the input total (Born-level) normalization - they only change how it is distributed across phase space. The user should therefore be aware that there can still be an overall "K" factor, not addressed by these uncertainty bands.
The speed of the calculation is not significantly affected by adding uncertainty variations, but the code does run slightly faster without them. We therefore advise to keep them switched off whenever they are not going to be used. See speed below for more on the impact on performance.
The following automatic variations are currently available:
iVar |
|
0 | Current Settings (user definable). |
1 | DEF antennae (VINCIA's default antenna functions) |
2 | DEF antennae with alphaS(pT2 / kAlphaS), where the value of kAlphaS is user-specifiable (see below) |
3 | DEF antennae with alphaS(kAlphaS * pT2), where the value of kAlphaS is user-specifiable (see below) |
4 | MAX antenna set (large finite terms) |
5 | MIN antenna set (small finite terms) |
6 | RESERVED |
7 | RESERVED |
8 | DEF antennae with stronger ordering in pT |
9 | DEF antennae with ordering in mD |
10 | DEF antennae with all color factors for gluon emission = CA |
11 | DEF antennae with all color factors for gluon emission = CF |
Note:These are just the automatic variations you can ask VINCIA to do for you. This in no way restricts the user's own power to do further variations, by adjusting individual parameters in VINCIA. Here, we have merely tried to provide some sensible default variations that an inexperienced user might use to get some idea of the trustworthiness of the answers he or she is getting from VINCIA.
Note 2: these variations only represent variations of the shower parameters. Since VINCIA does not handle the non-perturbative phase of fragmentation itself, uncertainty estimates for parameters related to that part must still be performed in the traditional way.
flag
Vincia:uncertaintyBands
(default = off
)on
VINCIA internally keeps track of
several variations of the shower approximation
and outputs a vector of weights for each event.
parm
Vincia:uncertaintyBandsKAlphaS
(default = 4.0
; minimum = 1.0
; maximum = 16.0
)The first (zero'th) entry in the vector of event weights always corresponds to the settings chosen by the user, and will normally have weights equal to unity (if showering an unweighted set of events), see the page on weights. If showering a weighted set of events, the nominal (user) weights are propagated through VINCIA and can be obtained through the method
vincia.weight();
The uncertainty bands are represented by alternative
sets of weights, where the spread of weights for each indidivual event
gives an estimate of how "sure" VINCIA is about the weight for that
particular event. Regions of phase space where the theoretical
uncertainty is large are thus reflected by large
weight spreads, while regions where the shower approximations work
well have smaller differences.
After showering, the weights corresponding to the uncertainty bands
are accessible via the same method as that used for the central weight
set, by giving a non-zero index to the weight()
method,
vincia.weight(int iVar);
where iVar
is an integer code specifying the particular
variation you want the weight for, and the number of available
variations you can access is given by
vincia.nVariations();
parm
Vincia:uncertaintyBandsMaxDev
(default = 2.0
; minimum = 1.0
; maximum = 10.0
)
Vincia:uncertaintyBandsMaxDev
< P'/P <
Vincia:uncertaintyBandsMaxDev
Vincia:uncertaintyBandsMaxDev
.
parm
Vincia:uncertaintyLimit
(default = 100.0
; minimum = 1.0
; maximum = 100000000.0
)Numerical tests indicate that the additional computational overhead caused by activating the automatic uncertainty evaluation is not very large, generally increasing the runtime for a fully unweighted event sample by less than ten percent, for order of 10 different variations.
Moreover, since the events generated are the same for all the variations, only one event set needs to be passed, e.g., to models for hadronization and/or detector corrections. The bands are correctly propagated through these models by simply keeping track of the different weight sets and applying these at any stage after the shower evolution has finished. Hence substantial overall speed gains compared to a full-fledged traditional uncertainty estimation should be possible.