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
)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:
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
)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.
The number of quark flavours allowed in gluon splittings, phase space permitting, is given by
mode
VinciaShower:nGluonToQuark
(default = 5
; minimum = 0
; maximum = 5
)To avoid clutter, further details of the antennae and antenna coefficients implemented in VINCIA are described separately, in
mode
VinciaShower: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, but with a normalization that makes it equal to S_AB
at the upper edge of phase space,
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
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
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
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 | |
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Types 3 and 4: extreme variation | |
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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.
mode
VinciaShower:evolutionMode
(default = 3
; minimum = 0
)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,
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).
flag
VinciaShower:GluonSplittingCorrection
(default = on
)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.
flag
VinciaShower:sectorOrdering
(default = off
)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.
flag
VinciaShower:useCreationScales
(default = on
)parm
VinciaShower:pTmaxFudge
(default = 1.0
)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.
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).
VinciaShower:kineMapType
.
mode
VinciaShower: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.)
parm
Vincia:alphaSvalue
(default = 0.139
)mode
Vincia:alphaSorder
(default = 1
; minimum = 0
; maximum = 1
)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.
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
)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
)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.
parm
Vincia:alphaSmuMin
(default = 0.5
; minimum = 0.0
)parm
Vincia:alphaSMax
(default = 1.0
; minimum = 0.0
)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.
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.
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
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
where again the eikonals must be expressed as dimensionless functions,
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.
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.
mode
Vincia:cutoffType
(default = 1
; minimum = -1
; maximum = 2
)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 ) |
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parm
Vincia:cutoffScale
(default = 1.0
)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.
flag
Vincia:CheckAntennae
(default = on
)