VINCIA Shower Parameters
(nb: see the section on Initialization for how to set and change parameters.)

Antenna Sets

The default antenna functions used in VINCIA largely resemble those used by Gehrmann, de-Ridder, and Glover (GGG, see below), but also, e.g., the ones used by ARIADNE and a few more are provided as alternatives. Yet others can be defined by the user.

To use an alternative set of antennae (i.e., non-default), for instance to estimate uncertainties, a convenient way of specifying a collection of non-default parameters is to use

word  VinciaShower:antennaFile   (default = none)
Optional name of a file containing predefined settings for one or more non-default antenna functions. Note that this command file will be read in during construction of the VINCIA plug-in. Any desired further modifications of the antenna functions should therefore only be performed after construction of the plug-in. Some pre-defined antennae shipping with VINCIA are stored in a separate subdirectory called antennae/ (see below). More user-defined antennae can be added and stored in the same directory, if desired. To use them with a program that runs in your main VINCIA directory (default), include the following command in your main program or command file:

VinciaShower:antennaFile = antennae/antennae-GGG.cmnd

(Here we used the "GGG" antennae for illustration.) To use a user-defined antenna set with a program that does not run in your VINCIA main directory, or if the antennae you want to use are not stored in the antennae/ directory, give the full path- and filename instead, as in

Vincia:antennaFile = /Users/skands/vincia/antennae/antennae-GGG.cmnd

Note that the format of the antenna files is the same as that of ordinary PYTHIA 8 command files, hence any combination of VINCIA and PYTHIA 8 commands could in principle be included to define an antenna set, but in general we advise to keep only specific antenna-related parameters in the antenna definition files, to avoid confusions/conflicts between your main command file(s) and the antenna file.

The default antennae have been chosen to be close to the GGG ones and have been verified to give a good average agreement with Z→n matrix elements. The following two examples, included with the VINCIA package in the antennae/ subdirectory, have been defined so as to try to span a reasonable min-max uncertainty range:

Other predefined antenna functions included in the same directory are:

Quark and Lepton Masses

Mass corrections are implemented systematically in VINCIA. The following switches control which quarks and leptons are treated as massive during the event evolution.

flag  VinciaShower:isMassiveS   (default = false)

flag  VinciaShower:isMassiveC   (default = true)

flag  VinciaShower:isMassiveB   (default = true)

flag  VinciaShower:isMassiveTau   (default = true)
tau is treated as massless, its decay width will be put to zero in the MadGraph interface.

Note: new-physics particles will generally be treated as massive if their masses are larger than the lightest quark for which mass corrections are switched on.

Gluon Splitting

The number of quark flavours allowed in gluon splittings, phase space permitting, is given by

mode  VinciaShower:nGluonToQuark   (default = 5; minimum = 0; maximum = 5)
Number of allowed quark flavours in gluon splittings, g → q qbar, during the shower evolution. E.g., a change to 4 would exclude g → b bbar but would include the lighter quarks, etc. Note that quark mass effects are currently not taken into account. Note also that this parameter does not directly affect the running coupling (see the section on alphaS).

Laurent Series Representation

To avoid clutter, further details of the antennae and antenna coefficients implemented in VINCIA are described separately, in

Ordering

These choices govern how the shower fills phase space, and hence how the logarithms generated by it are ordered. This does not affect the LL behaviour, but does affect the tower of higher (subleading) logs generated by the shower and can therefore be signficiant in regions where the leading logs are suppressed or absent. Note that, by construction, the dipole formalism automatically ensures an exact treatment of coherence effects to leading logarithmic order, and hence additional constraints, such as angular ordering, are not required.

Evolution Variable

mode  VinciaShower:evolutionType   (default = 1)
Choice of functional form of the shower ordering variable (a.k.a. evolution variab le), for AB → a r b branchings (see, e.g., illustration of dipole-antenna branching above and/or further illustrations below):
option 1 : Transverse Momentum. This evolution variable is roughly equal to the inverse of the antenna function for gluon emission, and hence is in some sense the most natural evolution variable. We define it as in Ariadne, but with a normalization that makes it equal to S_AB at the upper edge of phase space,

Q_E2 = 4pT2 = 4 s_ar*s_rb/s_AB


option 2 : Daughter Antenna Mass. This mass-like variable represents a fairly moderate variation on the transverse momentum. It will give slightly more priority to soft branchings over collinear branchings, as compared to transverse momentum. We define it as

Q_E2 = 2m_D2 = 2*min(s_ar,s_rb)


option 3 : Energy (of emitted parton, in dipole-antenna CM). This option gives the highest possible prioritization of collinear branchings over soft ones, and is in that sense the asymptotic extreme of type 1 above. We define it as

Q_E2 = (s_ar + s_rb)2/s_AB

Note that this evolution variable does not go to zero on the collinear boundaries of phase space. We therefore include it mostly for theoretical reference and highly discourage using it for physics studies.
option 4 : V, an artificial measure constructed so as to give the highest possible prioritization to soft branchings over collinear ones, and is in that sense an more extreme variant of type 2 above. It is defined as

Q_E2 = s_AB ( (s_ar + s_rb)^(1/2) - |s_ar - s_rb|^(1/2) )

Due to its somewhat contrived nature and more extreme form, this variable is also mostly included for theoretical reference. For normal physics studies, considering types 1 and 2 alone should give a reasonable idea of the uncertainty due to the choice of evolution variable.

The normalizations are chosen such that the maximum value of the evolution variable is equal to the mass of the parent dipole-antenna, Q_max = m_AB = m_arb.

The contours below illustrate the progression of each evolution variable over the dipole-antenna phase space for three fixed values of y_E = Q_E2/s_AB:

Types 1 and 2: moderate variation
Type1 Type2
Types 3 and 4: extreme variation
Type3 Type3

Note that energy-ordering (type 3) is not infrared safe, since contours of finite value of that evolution variable intersect the collinear region along the axes. This would nominally lead to infinitely many collinear branchings being generated during a finite evolution interval, rendering our shower formalism inapplicable. It is therefore not possible to choose energy ordering with a hadronization cutoff in the evolution variable. Instead, energy ordering must be used with a cutoff either in pT or in mass, which is sufficient to regulate the divergence. Note that even with this regularization this ordering should still result in a logarithmically enhanced preponderance of near-collinear branchings.

Ordering Mode

mode  VinciaShower:evolutionMode   (default = 3; minimum = 0)
This decides if and how ordering in the evolution variable is imposed on newly created dipole-antennae after a branching.
option 0 : No Ordering. Not recommended for physics runs. Newly created dipole-antennae are allowed to fill their full phase spaces, regardless of the ordering variable. Since energy and momentum are still conserved, a minimal amount of ordering will still occur, due to the post-branching dipole-antennae being smaller than the pre-branching one. This option could therefore also be called "phase-space ordering". The 2→4 approximation is given by products of nested 2→3 functions, without any further modification. This leads to a large amount of overcounting at the 2→4 level and should give answers similar to standard showers with virtuality-ordering with angular ordering switched off.
option 1 : Strong Ordering. This is identical to ordinary strongly ordered showers. Newly created antennae are restarted at the current evolution scale. Since the ordering condition acts like a step function in phase space, this choice generally implies that the shower may have some dead zones (points that are not reached by any strongly ordered path) starting from 2→4. For sensible evolution variables and maps (i.e., ones that have the appropriate LL singular limits), these dead zones only arise in non-LL-enhanced corners of the full 2→4 space, in which zero may not be such a terrible approximation, so they are not a priori problematic. However, their presence does preclude the use of strongly ordered showers as phase space generators for other purposes (e.g., for matching). The size of these zones depend on the evolution variable and kinematics maps and typically covers a few percent of phase space beyond 2→4 for the standard VINCIA variables (pT and mD).
option 2 : Smooth Ordering with QE-dampening. This option smoothes out the ordinary strong ordering in QE by applying a smooth dampening instead of a sharp cutoff at the ordering scale. Nominally unordered branchings are thus allowed, but with a suppressed probability,

Pimp = 1 / (1 + QE'2/QE2) ,
where QE' is the evolution scale evaluated on the pre-branching configuration (for branchings with more than one possible history, QE' is the smallest of the corresponding evolution scales, and QE is the scale of the next branching. This removes most of the beyond-LL overcounting that would be obtained with option without any ordering at all (option 0) while simultaneously giving a better approximation to 2→4 over all of phase space, with no dead regions. Technically, this option is implemented in the following way: After each branching, all dipole-antennae are restarted at their full phase space, but subsequent branchings are subjected to a veto proportional to the Pimp factor above.
option 3 : Smooth Ordering with pT-dampening. As for option =2 but with pT scales used instead of QE for computing the suppression factor Pimp, regardless of which evolution variable is used. For QE = pT (see evolutionType) this option is obviously identical to =2, but for other evolution types this choice makes the effective antenna functions independent of the evolution variable and gives an extremely good approximation all the way through 2→6, which is the highest order we have checked explicitly (comparing tree-level expansions of VINCIA with Leading-Color matrix elements from MadGraph).

Gluon Splitting Correction

flag  VinciaShower:GluonSplittingCorrection   (default = on)
If two neighbouring dipole-antennae that share the splitting gluon are very unequal in size, then higher-order splitting functions and matrix elements unambiguosly indicate that the total gluon splitting probability is significantly suppressed. This is not taken into account when treating the two antennae as independent radiatiors. As in Ariadne, we include this effect approximately by applying the additional factor

PAri = 2 sN / (sP + sN)
to gluon splittings. sN is the invariant mass of the dipole-antenna sharing the gluon splitting, sP is the invariant mass of the dipole-antenna in which the gluon is splitting. The additional factor reduces to unity when the two invariants are similar, it suppresses splittings in antenna whose neighbour has a very small invariant mass and it slightly enhances splittings in an antenna whose neighbour has a very large invariant mass.
option on : Use the factor PAri. Default since it greatly improves the shower's approximation to matrix emelents.
option off : Don't use the factor PAri. Included mostly for testing purposes.

Sector Ordering

Important note: sector ordering should only be used together with dedicated antenna functions whose collinear singularities have been tailored explicitly to work in this mode (see VinciaAntennae). If used with the default kind of antenna functions, such as the GGG or ARIADNE ones, correct DGLAP evolution will not result.

flag  VinciaShower:sectorOrdering   (default = off)
This decides whether to allow radiation from different dipole-antennae to overlap in each phase space point, such that the total result for n partons is obtained as a sum over all clusterings to (n-1) partons, or whether to only allow one dipole-antenna to contribute in each phase space point.
option off : No sector ordering is imposed. All antennae are allowed to contribute freely, independently of overlapping radiation. Warning: this option should only be used with so-called "global" antenna functions (the default), whose singular terms are such that the collinear singularity of one gluon is obtained by summing two neighbouring antennae over all of phase space.
option on : Only one antenna is allowed to contribute to each phase space point. Warning: this option should only be used with so-called "sector" antenna functions, whose singular terms are such that the collinear singularity of one gluon is represented entirely by the antenna which has the smallest value of pT for the given phase space point.

For the time being, only one option for how to distinguish between sectors has been implemented, as follows. A given trial emission will only be accepted if, after the branching, it has the lowest pT (as defined for Type 1 evolution above) of all possible color-ordered 3→2 clusterings after the branching.

External Scales

flag  VinciaShower:useCreationScales   (default = on)
Sets whether to use "creation scale" information from the matrix element as an upper bound on the evolution variable for showering. Not required for VINCIA's internal matching, but can be useful when using VINCIA's showers with alternative matching schemes relying on externally generated matrix-element-level events.

parm  VinciaShower:pTmaxFudge   (default = 1.0)
Copy of the PYTHIA 8 parameter TimeShower:pTmaxFudge allowing the one used for VINCIA showers to be changed independently of the PYTHIA 8 one. See the PYTHIA 8 documentation for more info.

Recoil Strategy

While the CM momenta of a 2→3 branching are fixed by the generated invariants (and hence by the antenna function), the global orientation of the produced 3-parton system with respect to the rest of the event (or, equivalently, with respect to the original dipole-antenna axis) suffers from an ambiguity outside the LL limits, which can affect the tower of subleading logs generated and can be significant in regions where the leading logs are suppressed or absent.

To illustrate this ambiguity, consider the emissision of a gluon from a qqbar antenna with some finite amount of transverse momentum (meaning transverse to the original dipole-antenna axis, in the CM of the dipole-antenna). The transverse momenta of the qqbar pair after the branching must now add up to an equal, opposite amount, so that total momentum is conserved, i.e., the emission generates a recoil. By an overall rotation of the post-branching 3-parton system, it is possible to align either the q or the qbar with the original axis, such that it becomes the other one that absorbs the entire recoil (the default in showers based on 1→2 branchings such as old-fashioned parton showers and Catani-Seymour showers), or to align both of them slightly off-axis, so that they share the recoil (the default in VINCIA, see illustration below).

Kinematics Map

Note: this setting only applies to massless partons. For massive partons, a generalization of the Kosower map (option 3 below) will be used regardless of the value of VinciaShower:kineMapType. 2->3
			      kinematics

mode  VinciaShower:kineMapType   (default = 3; minimum = 1; maximum = 3)
Selects which method to use for choosing the Euler angle for the global orientation of the post-branching kinematics construction. This setting applies to all massless antennae, irrespective of the branching type.
option 1 : The ARIADNE angle (see illustration). The recoiling mothers share the recoil in proportion to their energy fractions in the CM of the dipole-antenna. Tree-level expansions of the VINCIA shower compared to tree-level matrix elements through third order in alphaS have shown this strategy to give the best overall approximation, followed closely by the KOSOWER map below.
option 2 : LONGITUDINAL. The parton which has the smallest invariant mass together with the radiated parton is taken to be the "radiator". The remaining parton is taken to be the "recoiler". The recoiler remains oriented along the dipole axis in the branching rest frame and recoils longitudinally against the radiator + radiated partons which have equal and opposite transverse momenta (transverse to the original dipole-antenna axis in the dipole-antenna CM). Comparisons to higher-order QCD matrix elements show this to be by far the worst option of the ones so far implemented, hence it could be useful as an extreme case for uncertainty estimates, but should probably not be considered for central tunes. (Note: exploratory attempts at improving the behaviour of this map, e.g., by selecting probabilistically between the radiator and the recoiler according to approximate collinear splitting kernels, only resulted in marginal improvements. Since such variations would introduce additional complications in the VINCIA matching formalism, they have not been retained in the distributed version.)
option 3 : The KOSOWER map. Comparisons to higher-order QCD matrix elements show only very small differences between this and the ARIADNE map above, but since the KOSOWER map is sometimes used in fixed-order contexts, we deem it interesting to include it as a complementary possibility. (Note: the KOSOWER maps in fact represent a whole family of kinematics maps. For experts, the specific choice made here corresponds to using r=sij/(sij+sjk) in the definition of the map.)

The Strong Coupling

Reference Value

The amount of QCD radiation in the shower is determined by

parm  Vincia:alphaSvalue   (default = 0.139)
The alpha_strong value at scale mZ. The default is chosen to obtain a reasonable agreement with LEP event shapes for default shower settings, and is appropriate for a leading-order / leading-log shower (as compared, e.g., to leading-order extractions of alpha_strong at LEP).

Order

mode  Vincia:alphaSorder   (default = 1; minimum = 0; maximum = 1)
Order at which alpha_strong runs,
option 0 : zeroth order, i.e. alpha_strong is kept fixed.
option 1 : first order. This option is recommended for LO matrix elements and LL showers.

Argument of Running Coupling

When Vincia:alphaSorder is non-zero, the actual value is then regulated by running to the scale K*muR, at which the shower evaluates alpha_strong. The functional form of muR is given by Vincia:alphaSmode and the scale factor K is given by Vincia:alphaSscaleFactor.

mode  Vincia:alphaSmode   (default = 3; minimum = 1; maximum = 3)
The functional form of muR is given by
option 1 : The evolution variable (specified by VinciaShower:evolutionType) evaluated at the current branching.
option 2 : The invariant mass of the mother antenna.
option 3 : Transverse momentum, specifically the Type 1 Evolution variable, regardless of what ordering variable is being used in VinciaShower:evolutionType. Note that, since the VINCIA normalization of the transverse-momentum variable corresponds to 2pT, this should normally be used with Vincia:alphaSscaleFactor = 0.5, see below.

parm  Vincia:alphaSscaleFactor   (default = 0.5; minimum = 0.0)
If different from unity, alpha_strong is evaluated at the scale defined by Vincia:alphaSmode times this scale factor, i.e., it gives the value of Kmu in the argument to alphaS(Kmu*muR). Thus, e.g., for transverse momentum, this scale factor should be 0.5, since VINCIA uses 2pT as evolution variable.

Infrared Freezeout Scale

parm  Vincia:alphaSmuMin   (default = 0.5; minimum = 0.0)
Smallest Kmu*muR scale at which alphaS will be evaluated. I.e., the strong coupling is treated as frozen below this scale.

Max Coupling

parm  Vincia:alphaSMax   (default = 1.0; minimum = 0.0)
Largest allowed numerical value for alphaS.

Beyond-LL Matching

Matching to beyond-LL splitting kernels is still at a development stage. There are three main components to such a matching

Next-to-Leading Logarithmic (NLL) Corrections

mode  VinciaShower:NLL   (default = 1; minimum = 0; maximum = 2)

option 0 : Off. Scale variations in alphaS are not compensated at all in the shower evolution.
option 1 : Scale Cancellation Only. Scale variations in alphaS are compensated up to 1st order by matching to the explicit b0-dependent terms in the second-order (NLL) antenna functions.
option 2 : (Reserved for future use.) Full matching to second-order antenna functions.

Next-to-Leading Color (NLC) Corrections

Note: VINCIA uses a special color-factor normalization in which CF=8/3, and hence the difference CA-CF=1/NC2.

In the soft limit, the full radiation pattern from a color-connected chain of partons, qg...gqbar, can be written as a sum of leading-color dipole-antennae spanned between each of the color-connected partons, plus a negative qqbar antenna spanned directly between the endpoint quarks, proportional to CA/NC2. VINCIA contains a few different options for taking this antenna into account at various levels, as follows:

mode  VinciaShower:NLC   (default = 1; minimum = -1; maximum = 2)

option -1 : Strict LC. All gluon emission color factors forced equal to CA. No NLC correction.
option 0 : Ordinary LC. The color factors are taken from the chosen antenna set. I.e., they will typically be CF for qqbar antennae, CA for gg antennae, and something inbetween for qg antennae. No NLC correction.
option 1 : Eikonal NLC. A negative Eikonal suppressed by 1/NC2 is spanned between the two endpoint quarks of each qg...gqbar chain and is absorbed systematically into the radiation off the LC ones. Has been checked to correctly generate the subleading-color 1/ε2 term of the full 1-loop qqbar→qgqbar splitting function, and also improves the agreement with full-color tree-level Z→4,5,6-parton matrix elements relative to option 0.
option 2 : Full NLC. A negative qqbar antenna (Full = Eikonal + single-log terms) suppressed by 1/N2 is spanned between the two endpoint quarks of each qg...gqbar chain and is absorbed systematically into the radiation off the LC ones. Has been checked to correctly generate both the subleading-color 1/ε2 and 1/ε terms of the full 1-loop qqbar→qgqbar splitting function, and also further improves the agreement with full-color tree-level Z→4,5,6-parton matrix elements relative to option 1.

Details on the NLC Correction

Since the subleading-color antenna spanned between the q and qbar is not positive definite, it cannot be treated at the same footing as the leading-color ones. It can, however, be systematically absorbed into the leading-color ones, effectively reducing their color factor from CA towards something closer to CF, with the exact magnitude of the correction depending on the phase space point.

Expressed in dimensionless variables, each LC antenna is modified as follows

aLC( yij , yjk ) → aLC( yij , yjk ) - fj aqq( yij , yjk ) / N2 ,

where N=3 for QCD and the factor fj partitions the full correction among the LC contributions. By default in VINCIA, it is given by

fj = eikonalj / ( Σi eikonali ) .

where again the eikonals must be expressed as dimensionless functions,

eikonalj( yij , yjk ) = 2 ( 1 - yij - yjk ) / ( yij yjk ) .

Practically, the implementation relies on a guess-and-reweight strategy, in which branchings are first generated according to leading-color antennae, but then the resulting configurations are reweighted by vetos, now taking into account the subleading correction which is always negative.

This matching is applied at every branching step (exponentiated) and so is in principle active to all orders. However, since the final state of subleading-color branchings are represented as planar, the approach cannot be used to reach formal 1/NC^4 accuracy.

Hadronization

It is possible to pass the parton systems produced by VINCIA through Pythia's string hadronization model. Normally, this should happen automatically, according to the setting of the Pythia switch HadronLevel:all. The main parameter from the shower side is then the phase-space contour defined by the hadronization cutoff.

The hadronization cutoff, a.k.a. the infrared regularization scale, defines the resolution scale at which the perturbative shower evolution is stopped. Thus, perturbative emissions below this scale are treated as fundmanentally unresolvable and are inclusively summed over.

Important Note: when hadronization is switched on, there is a delicate interplay between the hadronization scale used in the shower and the parameters of the hadronization model. Ideally, the parameters of the hadronization model should scale as a function of the shower cutoff. This, however, is not the case for current hadronization models, such as the string model employed by Pythia and hence by VINCIA as well. Instead, the parameters of the hadronization model are tuned for one specific shower setting at a time. In order to be able to use Pythia's hadronization model together with VINCIA without major retuning efforts, it is therefore essential that VINCIA's cutoff be taken as close as possible to that used by Pythia in the Pythia tuning. What this means in practice is, firstly, that since Pythia's evolution variable is a pT-like variable, the default cutoff in VINCIA is likewise taken to be in a contour of pT. Secondly, there are a few different tunings of Pythia 8 to e+e- data available, each using a different numerical value of the cutoff. It is therefore important to match the value of the hadronization cutoff as well, depending on the PYTHIA tune.

Cutoff Variable

mode  Vincia:cutoffType   (default = 1; minimum = -1; maximum = 2)
This parameter selects the functional form of the infrared shower cutoff (a.k.a. hadronization cutoff), which defines the factorization border between the perturbative and non-perturbative regions. The possible options are:
option -1 : The cutoff is taken in Pythia 8's pTevol variable (times two, in order to use the same normalization as in the rest of Vincia). The cutoff scale is then set by the PYTHIA 8 parameter 2*TimeShower:pTmin. This is intended as a first crude way of using Vincia together with Pythia 8's hadronization model without having to retune the latter. Ultimately, dedicated tunes of the hadronization parameters using VINCIA should be used instead.
option 0 : Automatically set cutoffType equal to VinciaShower:evolutionType (only applies to infrared safe evolution variables)
option 1 : Cutoff in pT (defined as the type 1 evolution variable, see VinciaShower:evolutionType)
option 2 : Cutoff in daughter antenna mass (defined as the type 2 evolution variable, see VinciaShower:evolutionType)

= -1 = 1 = 2
(cutoff at 2*TimeShower:pTmin) (cutoff at Vincia:cutoffScale) (cutoff at Vincia:cutoffScale)
Type-1 Type1 Type2

Cutoff Scale

parm  Vincia:cutoffScale   (default = 1.0)
When Vincia:cutoffType >= 0, this parameter sets the value (in GeV) of the shower cutoff, interpreted according to the functional form selected under Vincia:cutoffType. Note that all evolution/cutoff variables are normalized so that their maximum value is equal to the parent dipole mass. For instance, a type 1 cutoff at Q_I = 1.0 GeV therefore corresponds to a transverse-momentum cutoff at pT = 0.5 GeV. See VinciaShower:evolutionType for further information on the normalization.

Checks and Warnings

Check of antenna functions

By default, Vincia checks antenna functions for positivity and absence of dead zones.

flag  Vincia:CheckAntennae   (default = on)

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