The 2→3 (LL) VINCIA antennae have names such as
Vincia:QQEmitFF
(for gluon emission off a final-final qqbar
antenna), Vincia:QGSplitIF
(for gluon splitting to a
quark-antiquark pair inside an initial-final qg antenna).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.
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
)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.
The free parameter of the strong coupling constant is specified by
parm
Vincia:alphaSvalue
(default = 0.118
; minimum = 0.06
; maximum = 2.0
)mode
Vincia:alphaSorder
(default = 2
; minimum = 0
; maximum = 2
)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
flag
Vincia:useCMW
(default = true
)
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.
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
kμ*μR, 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
)and
parm
Vincia:alphaSkMuSplitF
(default = 0.6
; minimum = 0.1
; maximum = 10.0
)
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
kμ*μR, 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
)parm
Vincia:alphaSkMuSplitI
(default = 0.72
; minimum = 0.1
; maximum = 10.0
)parm
Vincia:alphaSkMuConv
(default = 0.72
; minimum = 0.1
; maximum = 10.0
)
and Vincia:alphaSkMuSplitF
for gluon splitting in the final state.
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).
parm
Vincia:alphaSmuFreeze
(default = 0.5
; minimum = 0.0
; maximum = 10.0
)parm
Vincia:alphaSmax
(default = 1.5
; minimum = 0.1
; maximum = 10.0
)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
)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
)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
)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).
mode
Vincia:kineMapType
(default = 3
; minimum = 1
; maximum = 3
)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 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
)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:
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
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:
![]() |
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mode
Vincia:nFlavZeroMassF
(default = 3
; minimum = 0
; maximum = 5
)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
)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
)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
)parm
Vincia:GQemitII:chargeFactor
(default = 2.83333333
)parm
Vincia:GGemitII:chargeFactor
(default = 3.0
)parm
Vincia:QXSplitII:chargeFactor
(default = 1.0
)parm
Vincia:GXConvII:chargeFactor
(default = 2.66666667
)parm
Vincia:QQemitIF:chargeFactor
(default = 2.66666667
)parm
Vincia:GQemitIF:chargeFactor
(default = 2.83333333
)parm
Vincia:QGemitIF:chargeFactor
(default = 2.83333333
)parm
Vincia:GGemitIF:chargeFactor
(default = 3.0
)parm
Vincia:QXSplitIF:chargeFactor
(default = 1.0
)parm
Vincia:GXConvIF:chargeFactor
(default = 2.66666667
)parm
Vincia:XGSplitIF:chargeFactor
(default = 1.0
)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.
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.
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.
![]() |
![]() |
Important Note: All flavours will be treated with massless kinematics. However we apply certain corrections.
mode
Vincia:nFlavZeroMassI
(default = 3
; minimum = 3
; maximum = 5
)
mode
Vincia:massCorrectionLevelI
(default = 1
)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
)parm
Vincia:ThresholdMC
(default = 1.5
)