The Antenna Shower Model (VINCIA)

  1. Overview
  2. Main Switches
  3. Shower Starting Scales
  4. Further Shower Settings
  5. Merging with VINCIA
  6. Interleaved Resonance Decays
  7. Evolution with Enhanced (Biased) Kernels
  8. VINCIA Tunes
  9. Expert Settings
  10. References

Overview

The cornerstone of VINCIA is a pT-ordered model for QCD + EW/QED showers based on the antenna formalism. Originally developed as a standalone plugin, it has been incorporated into the Pythia 8 source code since Pythia version 8.300.

QCD: VINCIA's QCD antenna functions incorporate both the collinear (DGLAP) and soft (eikonal) limits of QCD matrix elements at leading colour. They hence should exhibit improved colour-coherence effects relative to Pythia's original (DGLAP-based) simple shower model.

QED: VINCIA's default QED antenna-shower module is based on a fully coherent (multipole) treatment of photon radiation, which is interleaved with the QCD evolution. Photon splittings to lepton-antilepton and quark-antiquark pairs are also included.

EW: Optionally, the coherent QED shower can be replaced by a full-fledged electroweak (EW) shower module, which allows for branchings involving Z/W/h bosons as well, with antenna functions capturing the collinear limits of the relevant matrix elements, including ones involving gauge-boson self couplings. This can be used to include weak corrections in electroweak Sudakov factors and to resum multiple weak-boson emissions (and splittings). Note that, since this module is based on collinar approximations, it does not exhibit the full coherence of the pure-QED shower module.

Mass Effects: In all cases, the effects of final-state parton masses (e.g., bottom and top quark masses) are systematically included, and the massive antenna functions have the appropriate quasi-collinear limits.

When VINCIA's option for interleaved resonance decays is selected (see below), resonance decays are interleaved with the rest of the perturbative evolution. This means that each resonance in the hard process (or emitted by the EW shower) is treated as stable until the evolution reaches a pT scale of order the offshellness of that resonance, at which point the resonance is replaced by its decay products and an internal ``resonance shower'' is performed in the decay system, starting from the invariant mass of the decaying resonance and ending at the offshellness scale. The decay+shower system is then merged back into the upstream system and the evolution of the event continues, starting from the offshellness scale. In case of sequential resonance decays, this procedure may be carried out either iteratively or sequentially, depending on the offshellnesses involved.

Interleaved Evolution and MPI: VINCIA's shower evolution is ordered in a measure of transverse momentum and is fully interleaved with Pythia's treatment of multiple parton interactions (MPI). When the Vincia shower model is selected, both the hard interaction and any MPI are showered by Vincia.

Main Switches

mode  Vincia:nFlavZeroMass   (default = 4; minimum = 2; maximum = 6)
Controls the number of flavours that will be treated as massless by VINCIA, ie with massless kinematics and no mass corrections. The remaining flavours will be bookkept with massive kinematics and mass-corrected antenna functions. Note that, even for flavours treated as massless, an elementary phase-space check is still made eg on all g→QQ branchings to ensure m(QQ) >= 2mQ. Likewise, all heavy flavours in the initial state are forced to undergo a conversion into a gluon when the evolution variable reaches their mass threshold (with the threshold determined by the maximum of the PDF threshold and the relevant user-specifiable mass parameter given below).

flag  Vincia:helicityShower   (default = off)
Switch to use helicity-dependent antenna functions (or not). Only meaningful when helicity information is present in the Born-level events.

flag  Vincia:sectorShower   (default = on)
Switch to (de-)activate the sector shower in VINCIA. In this version of VINCIA, the sector shower has become the default, due to its better scaling behaviour in multileg matching and merging, see below.

parm  Vincia:sectorDamp   (default = 1.0; minimum = 0.0; maximum = 1.0)
In the symmetrisation over post-branching gluons that is done to derive the sector antenna functions from the global ones, the branching invariant with swapped gluons is nominally given by yijSym = yik = 1 - yij - yjk. If the swapped gluons are j and k (and straightforwardly generalised if they are i and j) then the collinear yjk→0 limit does not change by adding or subtracting a term of order yjk. Therefore one could equally well use yijSym = 1 - yij (or something inbetween). This is still guaranteed to be positive definite and was indeed the choice in the original sector antenna shower papers. Since the latter definition produces a value for yijSym which is slightly larger than the former, the corresponding 1/yijSym singularities in the antenna function are damped slightly, so that larger values of the sectorDamp parameter produces sector antenna functions which have slightly smaller magnitudes outside the collinear limits. Strictly speaking this choice is an ambiguity that should be varied for uncertainty estimates, in which context we note that we expect it to be almost entirely degenerate with variations of nonsingular terms.

Shower Starting Scales

Similarly to PYTHIA, for processes that include at least one quark, gluon, or photon in the final state, the default choice in VINCIA is to start the shower from the factorisation scale used for the hard process (as given by PYTHIA for internal processes, or defined by the scale value for Les Houches input),while processes that do not include any such partons are allowed to populate the full phase space. This behaviour can be changed by the following option, which is anologous to the SpaceShower:PTmaxMatch option in PYTHIA.

mode  Vincia:pTmaxMatch   (default = 0; minimum = 0; maximum = 2)

option 0 : Showers off processes that include at least one final-state quark, gluon, or photon, are started at the factorisation scale, while processes that do not include any such partons are started at the phase-space maximum.
option 1 : Showers are always started at the factorisation scale.
option 2 : Showers are always started at the phase-space maximum. This option is not recommended for physics runs as it will lead to unphysical double counting in many cases.

When the first branching is limited by the factorisation scale for the hard process, a multiplicative factor can be applied to either increase or decrease the shower starting scale relative to the factorisation scale:

parm  Vincia:pTmaxFudge   (default = 1.0; minimum = 0.1; maximum = 10.0)

parm  Vincia:pTmaxFudgeMPI   (default = 1.0; minimum = 0.1; maximum = 10.0)
Same as above but for MPI systems, affecting the underlying event.

Note that for any (combination of) choices that result in ISR showers not using the factorisation scale as the starting scale, the generated Sudakov factor will effectively produce leftover PDF ratios in the exclusive cross sections produced by the shower.

Further Shower Settings

Merging with VINCIA

VINCIA has its own dedicated approach to merging with higher-multiplicity tree-level matrix elements, called sector merging. Similar in spirit to the CKKW(-L) approaches, it exploits the unique bijective property of VINCIA's sector shower to vastly reduce the complexity of the merging procedure, so that merging especially at high multiplicities becomes more efficient. Settings for VINCIA's sector merging are described here.

Interleaved Resonance Decays

Decays of resonances produced in the hard process can be interleaved with the shower evolution (see also further comments under the equivalent option for Pythia's TimelikeShowers). In VINCIA, this setting is controlled by the following switch:

flag  Vincia:interleaveResDec   (default = on)
When this flag is set to on, decays of hard-process resonances are performed as part of the final-state shower when the event evolution reaches the pT scale defined by VINCIA:resDecScaleChoice below. An internal shower which preserves the invariant mass of the resonance is then performed inside the resonance-decay system (including nested sequential resonance decays) until that system reaches the same overall pT scale as the rest of the event, at which point the resonance-decay system is merged back into the upstream system and the event evolution continues. When this flag is set to off, resonance decays are only performed after the shower off the production process has been completed. All of the subsequent FSR is carried out inside the resonance, with preserved resonance mass.

When decays of hard-process resonances are interleaved with the shower evolution (and for any resonances produced by VINCIA's electroweak shower), the evolution scale at which these decays are performed (including showers and any nested resonance decays at higher scales) is controlled by the following choice:

mode  Vincia:resDecScaleChoice   (default = 1; minimum = 0; maximum = 2)

option 0 : Resonance decays are assigned a fixed scale equal to the on-shell width of the given resonance. (This option is currently not implemented for resonances produced by VINCIA's EW shower.)
option 1 : Resonance decays are assigned a dynamical scale given by |m2 - m02|/m0. This implies, e.g., that the decay of a resonance which has m = m0 ± Γ will be performed at a scale pT ~ sqrt(2) Γ.
option 2 : Resonance decays are assigned a dynamical scale given by sqrt(|m2 - m02|). This implies, e.g., that the decay of a resonance which has m = m0 ± Γ will be performed at a scale pT ~ sqrt(2 Γ m0 ).

Evolution with Enhanced (Biased) Kernels

VINCIA's shower evolution can be biased to populate the multi-jet phase space more efficiently and/or enhance the rate of rare processes such as g→bb and g→cc splittings. It is also possible to inhibit radiation (e.g., to focus on Sudakov regions), by choosing enhancement factors smaller than unity. When these options are used, it is important to note that the event weights will be modified, reflecting that some types of events (e.g., multijet events, or events with gluon splittings to heavy quarks) will be "overrepresented" statistically, and others (events with few jets, or events with no gluon splittings to heavy quarks) underrepresented. Averages and histograms will therefore only be correct if computed using the correct weight for each generated event. A description and proof of the algorithm can be found in [MS16]. Note that care has been taken to ensure that the weights remain positive definite; under normal circumstances, VINCIA's enhancement algorithm should not result in any negative weights.

flag  Vincia:enhanceInHardProcess   (default = on)
This flag controls whether the enhancement factors are applied to shower branchings in the hard-process system.

flag  Vincia:enhanceInResonanceDecays   (default = on)
This flag controls whether the enhancement factors are applied to shower branchings inside resonance-decay systems (like Z/W/H decays) that are treated as factorised from the hard process.

flag  Vincia:enhanceInMPIshowers   (default = off)
This flag controls whether the enhancement factors are applied to shower branchings in MPI systems.

parm  Vincia:enhanceFacAll   (default = 1.0; minimum = 0.01; maximum = 100.0)
This enhancement factor is applied as a multiplicative factor common to all antenna functions, increasing the likelihood of all shower branchings by the same amount. Values greater than unity thus more frequently yields "busy" events, with many shower branchings. Values smaller than unity suppress additional branchings, yielding more Sudakov-like events.

parm  Vincia:enhanceFacBottom   (default = 1.0; minimum = 1.0; maximum = 100.0)
This enhances the probability for all branchings that increase the number of bottom quarks (i.e., FSR g→bb splittings and the corresponding ISR flavour-excitation process). Note: this factor is applied on top of Vincia:biasAll.

parm  Vincia:enhanceFacCharm   (default = 1.0; minimum = 1.0; maximum = 100.0)
Same as Vincia:enhanceFacBottom but for charm quarks. Note: this factor is applied on top of Vincia:biasAll.

parm  Vincia:enhanceCutoff   (default = 10.0; minimum = 0.0; maximum = 1000.0)
Do not apply enhancement factors to branchings below this scale. Intended to be used to focus on enhancements of hard branchings only.

VINCIA Tunes

VINCIA has its own set of dedicated tune presets, which can be specified by the user.

mode  Vincia:Tune   (default = 0; minimum = -1; maximum = 0)

option -1 : None. No VINCIA-specific tune parameter settings will be used during initialisation.
option 0 : Hadronisation and MPI parameters optimised for use with the VINCIA shower model, used as default VINCIA parameters since PYTHIA 8.302.

Note: the requested tune parameters will only be activated when VINCIA is switched on, in order not to interfere with the PYTHIA settings when VINCIA is switched off.

Note 2: as with ordinary Pythia tune parameters, the tuned parameter values will be superseded by any user modifications made in the user's command file or main program. This should allow sufficient flexibility to explore user variations away from the tuned values.

Advice on Tuning

Although there are obviously parameters that it makes more sense to tune than others, there is no explicit restriction imposed on what parameters are allowed to be present in the tune file. This implies some responsibility on the part of the user.

As a guideline, the main parameters that need to be properly tuned are the non-perturbative hadronisation parameters used in PYTHIA's string fragmentation model. Since PYTHIA and VINCIA treat soft radiation somewhat differently, there can be important differences between the two in the soft region that the hadronisation model will not re-absorb automatically and which therefore only a retuning can address.

The strategy used for the default tune of VINCIA is to take the reference value for alphaS from the current world average value in the MSbar scheme, and let the effective shower scheme tuning be done by first translating to the CMW scheme and then fine-tune by modifying the renormalisation-scale prefactors used for shower branchings.

An alternative (but equivalent) strategy that is often used in PYTHIA tunes, is to perceive of the value of the strong coupling itself as a tuning parameter. In this case the interpretation is that extracting alphaS from, e.g., event shapes, can be done equally well using a shower code as with more analytical approaches. The difference is that the alphaS value extracted with the shower code is in an a priori unknown scheme, defined by the shower algorithm. If the shower only includes LO/LL accuracy for the given observable(s), the extraction should be compared with other LO/LL extractions. This typically yields alphaS values ~ 0.13 - 0.14. When explicit NLO corrections are included for the relevant observable(s), values comparable to other NLO extractions should result, around 0.12.

Expert Settings

Importante Note: the parameters in this section are intended for use only by authors or expert users.

Octet Partitioning

Within the antenna formalism, the collinear singularity of two gluons j and k is distributed between two neighboring antennae. One contains the singularity for j becoming soft, one the singularity for k becoming soft. In showers based on so-called global antenna functions (as opposed to sector functions), the two antennae share the collinear singularity, j||k, point by point in phase space, and only after summing over both is the full collinear AP splitting kernel recovered. The parameter below controls the repartition ambiguity and gives the value of "half" the gluon splitting function on its finite end. For sector showers, this parameter has no effect, as the collinear singularities are combined within a single antenna function.

parm  Vincia:octetPartitioning   (default = 0.0; minimum = 0.0; maximum = 1.0)
Gluon-collinear α parameter. Only used for final-final global antennae. Note: only the default value (0) is consistent with the initial-final (and initial-initial) antenna functions in VINCIA. Special values of interest are: α=0, which corresponds to the Gehrmann-Gehrmann-de Ridder-Glover (GGG) partitioning, and α=1, which corresponds to the Gustafson (ARIADNE) partitioning. For the sector shower, the octetPartitioning is forced to α=1, to ensure positivity of the antenna function and as there is no sensible meaning of the parameter anymore.

Verbose Level

mode  Vincia:verbose   (default = 1; minimum = -1; maximum = 3)
Level of detail of information written to standard output on what goes on inside VINCIA.
option -1 : No runtime output.
option 0 : Quiet. Errors and (important) warnings are printed.
option 1 : Normal. All warnings and error messages are printed, but no additional diagnostic output is given. Standard initialisation and summary information is also printed.
option 2 : Report. Enhanced runtime output. As for =1, but additional diagnostic information is printed, especially when/where errors occur, and additional self-consistency checks may be performed. Full initialisation and summary information is printed.
option 3 : Debug. This level is solely intended to assist authors for debugging purposes.

Numerical Checks

flag  Vincia:CheckAntennae   (default = on)
By default, VINCIA checks antenna functions for positivity and absence of dead zones. Switch to control whether to perform antenna self-consistency checks or not.

mode  Vincia:nPointsCheck   (default = 1000; minimum = 0; maximum = 1e6)
Number of random points to check each antenna functions for positivity.

parm  Vincia:deadZoneAvoidance   (default = 0.0001; minimum = 0.0; maximum = 1.0)
During initialisation, warnings are issued if any antenna functions (in dimensionless form, with the Eikonal proportional to 2/y1/y2) become smaller than this number, anywhere in the resolved part of phase space (away from phase-space boundaries). This is to warn against spurious radiation zeroes or large negative finite terms creating "dead zones", or near-dead zones, in the shower. For LL showering and matching up to NLO, there is in principle no problem in taking this parameter to zero if so desired. However, for the NLL and higher-order matching corrections, very small values of this parameter may result in weights greater than unity being generated, since the corrections are multiplicative and large reweighting factors may be needed to "make up" for any near-dead zones at the previous branching step.

Shower Uncertainty Bands

Automated uncertainty bands are not available in this version of the VINCIA code.

References

The main references for the current version of VINCIA are:

Authors and Contributions

The authors of the current version, taking active responsibility for code development and day-to-day maintenance, are

In addition, the following people have made significant individual contributions to the underlying formalism and code development of VINCIA:

About VINCIA

The name VINCIA stands for "VIrtual Numerical Collider with Interleaved Antennae". This reflects its main properties as a numerical model for collider-physics processes based on dipole-antennae and interleaved perturbative evolution. It is also intended to allude to a progression from PYTHIA - a name originating in ancient Greece - to the renaissance era of Leonardo da Vinci. The logo of VINCIA is the "Vitruvian Man", by da Vinci, a choice which also reflects the combination of art and accuracy which is necessary to write a good event generator. Classical antiquity is still indirectly represented, via the namesake of the logo, Vitruvius, a first-century (BC) Roman author, architect, and engineer.