## VINCIA QCD Antenna Shower Settings

Here, parameters specific to VINCIA's QCD antenna shower are collected. See the main VINCIA antenna shower page for more general parameters that are common to both the QCD and QED showers.

### Main Switches

`flag` Vincia:doII (`default = on`)
Main switch for initial-initial (II) antennae on/off (subject to the `PartonLevel` settings).

`flag` Vincia:doIF (`default = on`)
Main switch for initial-final (IF) antennae on/off (subject to the `PartonLevel` settings). Note: setting this to off will switch off both the initial- and final-state ends of corresponding QCD antennae.

`flag` Vincia:doFF (`default = on`)
Main switch for final-final (FF) antennae on/off (subject to choices made at `PartonLevel`).

`flag` Vincia:doRF (`default = on`)
Main switch for resonance-final (RF) antennae on/off (subject to the `PartonLevel` settings). Note: setting this to off will switch off both the resonance- and final-state ends of corresponding QCD antennae.

`mode` Vincia:nGluonToQuark (`default = 5`; `minimum = 0`; `maximum = 6`)
Number of allowed quark flavours in final-state gluon splittings, g → q qbar, during the shower evolution, phase space permitting. E.g., a change to 4 would exclude g → b bbar but would include the lighter quarks, etc. Note that this parameter does not directly affect the running coupling.

`flag` Vincia:convertGluonToQuark (`default = on`)
Allow incoming gluons to backwards-evolve into (anti)quarks during the initial-state shower evolution.

`flag` Vincia:convertQuarkToGluon (`default = on`)
Allow incoming (anti)quarks to backwards-evolve into (anti)quarks during the initial-state shower evolution.

### The QCD coupling in the Vincia Shower

The strong coupling constant is specified by providing its reference value (interpreted as given at the Z pole in the MSbar scheme) and running properties (loop order, behaviour at top threshold, and any low-scale regularisation/dampening).

Note that VINCIA only uses one global value for the definition of the strong coupling constant. The effective couplings used in shower branchings (renormalisation scheme and scale) are governed by separate parameters which are specified under initial- and final-state showers respectively.

VINCIA implements its own instance of PYTHIA's `AlphaStrong` class for the strong coupling. You can find more documentation of the class in the section on Standard-Model Parameters in the PYTHIA documentation. Here, we list the specific parameters and switches governing its use in VINCIA.

The free parameter of the strong coupling constant is specified by

`parm` Vincia:alphaSvalue (`default = 0.118`; `minimum = 0.06`; `maximum = 2.0`)
The value of αs at the scale mZ, in the MSbar scheme. The default value is chosen to be in agreement with the current world average. The effective value used for showers may be further affected by translation to the CMW scheme (below) and by renormalisation-scale prefactors given for FSR and ISR showers separately.

`mode` Vincia:alphaSorder (`default = 2`; `minimum = 0`; `maximum = 2`)
Order at which αs runs,
`option` 0 : zeroth order, i.e. αs is kept fixed.
`option` 1 : first order, i.e., one-loop running.
`option` 2 : second order, i.e., two-loop running.

Resummation arguments [Cat91] indicate that a set of universal QCD corrections can be absorbed in coherent parton showers by applying the so-called CMW rescaling of the MSbar value of Lambda_QCD, defined by
αs(CMW) = αs(MSbar) * (1 + K * αs(MSbar) / 2π)
with K = CA * (67/18 - π2/6) - 5/9nf. The translation amounts to an NF-dependent rescaling of Lambda_QCD, relative to its MSbar value, by a factor 1.661 for NF=3, 1.618 for NF=4, 1.569 for NF=5, and 1.513 for NF=6. Although the original argument strictly concerned only the eikonal for soft-gluon emissions, the current version of VINCIA only offers the option of switching the rescaling of Lambda_QCD on or off. When on, the rescaling is applied to all branching types, not just gluon emissions.

`flag` Vincia:useCMW (`default = on`)
If set to on, the alphaS value used for shower branchings will be translated from the MSbar value to the CMW ("MC") scheme. If set to off, the MSbar value will be used.

Note 1: If using VINCIA with an externally defined matching scheme, be aware that the CMW rescaling may need be taken into account in the context of matrix-element matching. Note also that this option has only been made available for timelike and spacelike showers, not for hard processes.
Note 2: Tunes using this option need roughly 10% lower values of alphas(mZ) than tunes that do not.

For both one- and two-loop running, the `AlphaStrong` class automatically switches from 3-, to 4-, and then to 5-flavour running as one passes the s, c, and b thresholds, respectively, with matching equations imposed at each flavour threshold to ensure continuous values. By default, a change to 6-flavour running is also included above the t threshold, though this can be disabled using the following parameter:

`mode` Vincia:alphaSnfmax (`default = 6`; `minimum = 5`; `maximum = 6`)
`option` 5 : Use 5-flavour running for all scales above the b flavour threshold (old default).
`option` 6 : Use 6-flavour running above the t threshold (new default).

`parm` Vincia:alphaSmuFreeze (`default = 0.75`; `minimum = 0.0`; `maximum = 10.0`)
The behaviour of the running coupling in the far infrared is regulated by a shift in the effective renormalisation scale, to μeff 2 = μfreeze2 + μR2.

`parm` Vincia:alphaSmax (`default = 2.0`; `minimum = 0.1`; `maximum = 10.0`)
Largest allowed numerical value for alphaS. I.e., the running is forced to plateau at this value.

#### Choice of Renormalisation Scales for Shower Branchings

When `Vincia:alphaSorder` is non-zero, the actual value of alphaS used for shower branchings is governed by the choice of scheme (MSbar or CMW, see the section on AlphaStrong and then by running to the scale kR*Q2, at which the shower evaluates αs, with Q2 the Vincia evolution scale of the branching. The multiplicative scale factor kR is given by

`parm` Vincia:renormMultFacEmitF (`default = 0.66`; `minimum = 0.1`; `maximum = 10.0`)
for gluon emission

and

`parm` Vincia:renormMultFacSplitF (`default = 0.8`; `minimum = 0.1`; `maximum = 10.0`)
for gluon splitting.

For initial-state branchings, the functional form of muR is given by the evolution variable and the scale factor kR is given by

`parm` Vincia:renormMultFacEmitI (`default = 0.66`; `minimum = 0.1`; `maximum = 10.0`)
for gluon emission,

`parm` Vincia:renormMultFacSplitI (`default = 0.5`; `minimum = 0.1`; `maximum = 10.0`)
for gluon splitting (quark in the initial state backwards evolving into a gluon),

`parm` Vincia:renormMultFacConvI (`default = 0.5`; `minimum = 0.1`; `maximum = 10.0`)
for gluon conversion (gluon in the initial state backwards evolving into a (anti)quark)

### Colour Charges

The normalisation of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalisation, all gluon-emission colour factors tend to NC in the large-NC limit while all gluon-splitting colour factors tend to unity. (Thus, e.g., the default normalisation of the qqbar → qgqbar antenna function is 2CF.)

`parm` Vincia:QQEmitII:chargeFactor (`default = 2.66666667`)
Emission of a final-state gluon from an initial-state qqbar pair.

`parm` Vincia:GQEmitII:chargeFactor (`default = 2.83333333`)
Emission of a final-state gluon from an initial-state qg (or gqbar) pair.

`parm` Vincia:GGEmitII:chargeFactor (`default = 3.0`)
Emission of a final-state gluon from an initial-state gg pair.

`parm` Vincia:QXConvII:chargeFactor (`default = 1.0`)
Quark in the initial state backwards evolving into a gluon and emitting an antiquark in the final state.

`parm` Vincia:GXConvII:chargeFactor (`default = 2.66666667`)
Gluon in the initial state backwards evolving into a quark and emitting a quark in the final state (gluon conversion).

`parm` Vincia:QQEmitIF:chargeFactor (`default = 2.66666667`)
Gluon emission of an initial-final qq pair.

`parm` Vincia:GQEmitIF:chargeFactor (`default = 2.83333333`)
Gluon emission off an initial-final gq pair.

`parm` Vincia:QGEmitIF:chargeFactor (`default = 2.83333333`)
Gluon emission of an initial-final qg pair.

`parm` Vincia:GGEmitIF:chargeFactor (`default = 3.0`)
Gluon emission of an initial-final gg pair.

`parm` Vincia:QXConvIF:chargeFactor (`default = 1.0`)
Quark in the initial state evolving backwards into a gluon and emitting an antiquark in the final state.

`parm` Vincia:GXConvIF:chargeFactor (`default = 2.66666667`)
Gluon in the initial state backwards evolving into a quark and emitting a quark into the final state (gluon conversion).

`parm` Vincia:XGSplitIF:chargeFactor (`default = 1.0`)
Gluon splitting in the final state.

`parm` Vincia:QQEmitFF:chargeFactor (`default = 2.66666667`)

`parm` Vincia:QGEmitFF:chargeFactor (`default = 2.85`)

`parm` Vincia:GGEmitFF:chargeFactor (`default = 3.0`)

`parm` Vincia:QGSplitFF:chargeFactor (`default = 1.0`)

`parm` Vincia:GGSplitFF:chargeFactor (`default = 1.0`)

`parm` Vincia:GXSplitFF:chargeFactor (`default = 1.0`)

`parm` Vincia:QQEmitRF:chargeFactor (`default = 2.66666667`)

`parm` Vincia:QGEmitRF:chargeFactor (`default = 2.85`)

`parm` Vincia:XGSplitRF:chargeFactor (`default = 1.0`)
Note: the two permutations g-g → g-q+qbar and g-g → qbar+q-g are explicitly summed over in the code (with appropriate swapping of invariants in the latter case).

### Lower Cutoffs for the QCD evolution

The hadronization cutoff, a.k.a. the infrared regularisation scale, defines the resolution scale at which the perturbative shower evolution is stopped. Thus, perturbative emissions below this scale are treated as fundamentally unresolvable and are in effect 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 scaling does not happen automatically in current hadronization models, such as the string model employed by PYTHIA. Instead, the parameters of the hadronization model are tuned for one specific shower setting at a time and should be retuned if changes are made to the shower cutoff.

`parm` Vincia:cutoffScaleFF (`default = 0.75`; `minimum = 0.1`; `maximum = 10.0`)
This parameter sets the value (in GeV) of the final-state shower cutoff.

`parm` Vincia:cutoffScaleII (`default = 1.25`; `minimum = 0.1`; `maximum = 10.0`)
This parameter sets the value (in GeV) of the shower cutoff for initial-initial antennae.

`parm` Vincia:cutoffScaleIF (`default = 1.5`; `minimum = 0.1`; `maximum = 10.0`)
This parameter sets the value (in GeV) of the shower cutoff for initial-final antennae.

`parm` Vincia:ThresholdMB (`default = 4.8`)
threshold (mass, in GeV) for bottom quark production.

`parm` Vincia:ThresholdMC (`default = 1.5`)
threshold (mass, in GeV) for charm quark production.

### Other QCD Settings

#### Subleading Colour

During the perturbative shower evolution, the first aspect of subleading colour is simply what colour factors are used for the antenna functions. In a strict leading-colour limit, one would use CA for all antennae, thus overestimating the amount of radiation from quarks (note that we use a normalisation convention in which the colour factor for quarks is 2CF, hence the difference is explicitly subleading in colour). A more realistic starting point is to use 2CF for quark-antiquark antennae, CA for gluon-gluon ones, and something inbetween for quark-gluon ones. The following switch determines whether and how subleading-colour corrections are treated in the evolution:

`mode` Vincia:modeSLC (`default = 2`; `minimum = 0`; `maximum = 3`)
`option` 0 : Strict LC evolution. All gluon-emission colour factors are forced equal to CA thus overcounting the radiation from quarks. Note that matrix-element corrections will still generate corrections to the evolution up to the matched number of legs.
`option` 1 : Simple Colour Factors. The `chargeFactor` parameters for each of the antenna functions are used to set the colour factor for each type of gluon-emission antenna; see the section on antenna functions. (Typically, 2CF for qqbar antennae, CA for gg antennae, and the average of 2CF and CA for qg antennae.)
`option` 2 : Interpolating Colour Factors. The colour factor for quark-antiquark antennae is forced equal to 2CF. Gluon-gluon antennae are normalised to CA. The colour factor for QG antennae is 2CF * (1-yij)/(2-yij-yjk) + CA * (1-yjk)/(2-yij-yjk), which is just a simple interpolation between CA in the gluon-collinear limit and 2CF in the quark-collinear limit. More sophisticated choices could also be motivated and may be interesting to explore in future versions.
`option` 3 : Only used for development purposes.

Colour flow is traced using Les-Houches style colour tags, augmented by letting the last digit encode the "colour index", running from 1 to 9, described further in the section below on antenna swing. One ambiguity arises in gluon emission as to which of the daughter antennae should inherit the "parent" colour tag/index, and which should be assigned a new one. This is controlled by the following parameter:

`mode` Vincia:CRinheritMode (`default = 1`; `minimum = -2`; `maximum = 2`)
`option` 0 : Random
`option` 1 : The daughter with the largest invariant mass has a probability 1/(1 + r) to inherit the parent tag, with r < 1 the ratio of the smallest to the largest daughter invariant masses squared.
`option` 2 : The daughter with the largest invariant mass always inherits the parent tag (winner-takes-all extreme variant of option 1).
`option` -1 : (Unphysical, intended for theory-level studies only). Inverted variant of option 1, so that the daughter with the smallest invariant mass preferentially inherits the parent colour tag.
`option` -2 : (Unphysical, intended for theory-level studies only). Inverted variant of option 2, so that the daughter with the smallest invariant mas always inherits the parent colour tag.

### 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.