VINCIA Shower Parameters

  1. Naming Conventions
  2. Helicity Dependence
  3. The Strong Coupling
  4. Final-State Antennae
  5. Initial-State Antennae

Naming/Labeling Conventions

AB->arb

The 2→3 (LL) VINCIA antennae have names such as

The generic name format is thus Vincia:ABxTT, where A and B are the "mothers" and x is emit, split, or conv depending on whether the process is gluon emission, gluon splitting (either in the initial or final state), or a gluon in the initial state backwards-evolving into a quark and emitting a quark into the final state (gluon conversion). TT can be either FF, IF, or FF, depending on whether the antenna in question is spanned between a final-final, initial-final, or initial-initial parton pair. For final-state antennae, the radiating (parent) antenna is always interpreted as spanned between the Les Houches colour tag of A and the anti-colour tag of B, see illustration to the right.

Helicity Dependence

For each antenna function, a full set of helicity-dependent antenna function contributions are implemented. For partons without helicity information, the unpolarised forms (summed over post-branching helicities and averaged over pre-branching ones) are used. The detailed forms of both helicity and helicity-summed/averaged antenna functions are given in the VINCIA Authors' Compendium.

flag  Vincia:helicityShower   (default = on)
Switch to activate the helicity dependent showering (and matrix-element corrections) in VINCIA.

The Strong Coupling

Currently, the only SM parameter that can be configured in VINCIA is the definition of the strong coupling constant, 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). All other parameters are taken from the PYTHIA Couplings database.

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.

Reference Value

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.

Running Order

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.

Effective Renormalisation Scheme

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, applied to all shower branchings.

flag  Vincia:useCMW   (default = true)
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.

Choice of Renormalisation Scales for FSR 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 kμR, at which the shower evaluates αs. μR is the transverse momentum pT A (without the normalisation factor) for gluon emission and mQQ for gluon splitting. The scale factor kμ is given by

parm  Vincia:alphaSkMuF   (default = 0.68; minimum = 0.1; maximum = 10.0)
for gluon emission

and

parm  Vincia:alphaSkMuSplitF   (default = 0.6; minimum = 0.1; maximum = 10.0)
for gluon splitting.

Choice of Renormalisation Scales for ISR 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 kμR, at which the shower evaluates αs. The functional form of μR is given by the evolution variable and the scale factor kμ is given by

parm  Vincia:alphaSkMuI   (default = 0.72; minimum = 0.1; maximum = 10.0)
for gluon emission,

parm  Vincia:alphaSkMuSplitI   (default = 0.72; minimum = 0.1; maximum = 10.0)
for gluon splitting (quark in the initial state backwards evolving into a gluon),

parm  Vincia:alphaSkMuConv   (default = 0.72; minimum = 0.1; maximum = 10.0)
for gluon conversion (gluon in the initial state backwards evolving into a (anti)quark)

and Vincia:alphaSkMuSplitF for gluon splitting in the final state.

Flavour Thresholds

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 treshold 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).

Infrared Freezeout Scale

parm  Vincia:alphaSmuFreeze   (default = 0.5; 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.

Max Coupling

parm  Vincia:alphaSmax   (default = 1.5; minimum = 0.1; maximum = 10.0)
Largest allowed numerical value for alphaS. I.e., the running is forced to plateau at this value.

Final-State Antennae

Within the dipole-antenna formalism, antenna functions are the analogs of the splitting functions used in traditional parton showers. The antenna functions are constructed so as to reproduce the Altarelli-Parisi splitting functions P(z) in collinear limits and the eikonal dipole factor in the soft limit.

We here describe the parameters and switches used to control VINCIA's final-state antenna functions, including their colour factors, the number of flavours allowed in gluon splittings during the shower evolution, their kinematics maps (recoil strategy), and a few more options.

flag  Vincia:FSR   (default = on)
Main switch for final-state radiation on/off.

The number of quark flavours allowed in final-state gluon splittings (in both final-final and initial-final antennae) is given by

mode  Vincia:nGluonToQuarkF   (default = 5; minimum = 0; maximum = 5)
Number of allowed quark flavours in 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.

Colour Charge Factors

The normalisation of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalisation choice, 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: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)
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).

Kinematics and Recoils

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).

2->3
			      kinematics

mode  Vincia: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. (For partons treated as massive, see below, a generalisation of the Kosower map is always used.)
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.)

Evolution Variable for Final State Radition

The choices below 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 (leading-colour) coherence effects to leading logarithmic order, and hence additional constraints, such as angular ordering, are not required.

Note 1: Gluon splittings, g→qq, always use mqqbar as their evolution variable, which are interleaved with the choice made here.

Note 2: The absolute normalisation factors cancel in sequential gluon emissions, but enter in the relative interleaving between gluon emissions and gluon splitting.

mode  Vincia:evolutionType   (default = 1)
Choice of functional form of the shower evolution variable (a.k.a. ordering variable) for gluon emissions (see 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, modulo a normalisation factor:

with the normalisation factor NT=4.
option 2 : Dipole Virtuality. 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

with the normalisation factor ND=2.

The contours below illustrate the progression of each evolution variable (normalized to maximum value unity) over the dipole-antenna phase space for four fixed values of yE = QE2/sIK:

Type1 Type2

Mass Corrections

mode  Vincia:nFlavZeroMassF   (default = 3; minimum = 0; maximum = 5)
Controls the number of flavours that will be treated as strictly massless by VINCIA, ie with massless kinematics and no mass corrections whatsoever. The remaining flavours, up to the b quark, will still be bookkept as having massless kinematics, but a set of minimal approximate mass effects are included (such as thresholds).

Initial-State Antennae

Within the dipole-antenna formalism, antenna functions are the analogs of the splitting functions used in traditional parton showers. The antenna functions are constructed so as to reproduce the Altarelli-Parisi splitting functions P(z) in collinear limits and the eikonal dipole factor in the soft limit.

flag  Vincia:ISR   (default = on)
Main switch for initial-state radiation on/off.

The number of quark flavours allowed in initial-state gluon conversions, phase space permitting, is given by

mode  Vincia:nGluonToQuarkI   (default = 5; minimum = 0; maximum = 5)

Colour Charge Factors

The normalisation of colour factors in VINCIA is chosen such that the coupling factor for all antenna functions is αS/4π. With this normalisation choice, 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.)

For theory tests, individual antenna functions can be switched off by setting the corresponding colour-charge factor to zero.

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:QXSplitII: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:QXSplitIF: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

Kinematics and Recoils for II Antennae

The post-branching momenta are fixed by the following requirements:
1) The direction of the initial state partons is aligned with the beam axis (z-axis).
2) The invariant mass and the rapidity of the final state recoiler are not changed by the branching. This allows a direct construction of the post-branching momenta in the lab frame.

Kinematics and Recoils for IF Antennae

The post-branching momenta are fixed by the following requirements:
1) The direction of the initial state parton is aligned with the beam axis (z-axis).
2) There are no recoils outside of the antenna. This allows a construction of the post-branching momenta in the centre-of-mass frame of the initial-final antenna.

Evolution Variable for Initial State Radiation

Choice of functional form of the shower evolution variable (a.k.a. ordering variable) for initial state radiation (see illustrations below).

Gluon emissions in initial-initial antennae are ordered in transverse momentum. This evolution variable is the physical (lightcone) transverse momentum for massless partons:

Gluon emissions in initial-final antennae are ordered in transverse momentum. This evolution variable is defined as:

Splittings and conversion in initial-initial and initial-final antennae are by default ordered in the invariant mass of the gq, qq, or qqbar pair respectively. However there is the option to switch to the above transverse momentum ordering by switching Vincia:evolveAllInPT to on. Note that with transverse momentum ordering the ordering variable is no longer the inverse of the singularity associated with the branching process. Also the mass corrections are not applied correctly since they rely on ordering in invariant mass.

flag  Vincia:evolveAllInPT   (default = off)

The contours below illustrate the progression of the evolution variable over the dipole-antenna phase space for four fixed values, with sAB=mH^2 for the initial-initial case and xA=0.6 and sAK=25.2 GeV^2 for the initial-final case.

Type1 Type2

Mass Corrections

Important Note: All flavours will be treated with massless kinematics. However we apply certain corrections.

mode  Vincia:nFlavZeroMassI   (default = 3; minimum = 3; maximum = 5)
Controls the number of flavours that will be treated as strictly massless by VINCIA, ie with no mass corrections whatsoever. The remaining flavours, up to the b quark, will still be treated as having massless kinematics, but certain mass effects can be included, according to the switch described below. Top quarks will always be treated as with fully massive kinematics (and hence are so far precluded from appearing in PDFs).

mode  Vincia:massCorrectionLevelI   (default = 1)
Controls the level of mass corrections that will be applied to all but the lightest Vincia:nFlavZeroMassI flavours.
option 0 : No mass effects. Equivalent to using Vincia:nFlavZeroMassI=5.
option 1 : All heavy flavours in the initial state will undergo a conversion into a gluon when the evolution variable goes towards their mass threshold, using the vanishing PDFs. A quark mass is determined by using the maximum of the input value given below and the mass extracted from the PDFs (if possible).

The following mass thresholds are imposed on the evolution for quarks in the initial state:

parm  Vincia:ThresholdMB   (default = 4.8)
for bottom quark production.

parm  Vincia:ThresholdMC   (default = 1.5)
for charm quark production.