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 coherence effects to leading logarithmic order, and hence additional constraints, such as angular ordering, are not required.
Choice of functional form of the shower evolution variable (a.k.a. ordering variable) for gluon emissions (see illustrations below).
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 normalization 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 user-definable normalization factor:
NT
specified below.
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
specified below.
The contours below illustrate the progression of each evolution variable (normalized to maximum value unity) over the dipole-antenna phase space for three fixed values of yE = QE2/sIK:
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By default, scales handed to VINCIA from PYTHIA and/or from LHEF files are interpreted as transverse-momentum scales. If VINCIA uses a different normalization for its evolution variables (eg 2pT), the external scales will automatically be converted to VINCIA's internal normalization when used within VINCIA, and the reverse transformation is applied before handing scales back to PYTHIA. Optionally, this automatic conversion can be switched off, using the following flag:
flag
Vincia:normalizeInputPT
(default = on
)parm
Vincia:pTnormalization
(default = 4
; minimum = 1
; maximum = 4
)NT
for the
transverse-momentum variable QT
defined
above. A value of 1 corresponds to the ARIADNE definition. A value of
4 makes the maximal value of the evolution variable (reached when the
two parents are collinear and back-to-back with the emitted parton,
which carries half the total energy) equal to the dipole invariant
mass (as was hardcoded in VINCIA versions prior to 1.029).
parm
Vincia:mDnormalization
(default = 2
; minimum = 1
; maximum = 2
)ND
for the dipole-mass
variable mD
defined above. A value of 1
corresponds to evolution in invariant mass. A value of 2 makes the
maximal value of the evolution variable (reached when the two parents
are collinear and back-to-back with the emitted parton, which carries
half the total energy) equal to the dipole invariant mass
(as was hardcoded in VINCIA versions prior to 1.029).
In addition to the evolution variable, a main choice which decides the ordering of emissions in the shower is whether the evolution is performed as a so-called "global" or "sector" shower. Both options are available in VINCIA, with the default option being "global". In global showers, radiation from different dipole-antennae is allowed 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. The antenna functions used in this case are defined such that their sums reproduce the full QCD singular structure. In sector showers, only allow a single dipole-antenna is allowed to contribute in each phase space point. In this case, additional terms are added to each antenna function such that every single antenna contains the full collinear and soft singularities for the sector it is responsible for.
For global showers, the user has to select what kind of ordering will
be imposed, using the orderingMode
parameter:
mode
Vincia:orderingMode
(default = 2
; minimum = 0
; maximum = 2
)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. 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, defined as
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.
Sector showers are implemented as a non-default option and can be switched on using the flag
flag
Vincia:sectorShower
(default = off
)option
off : No sector ordering is imposed. All antennae are
allowed to contribute freely, independently of overlapping
radiation.
option
on : Only one antenna is allowed to contribute to each
phase space point. Note: when this option is on, a set of additional
terms will automatically be added to VINCIA's
antenna functions, such that the entire collinear singularity of
each gluon is present in each antenna.
When the sector option is on, the following switch determines whether the additional gluon-collinear terms are added to the global antenna functions in order to create proper sector antennae from them,
flag
Vincia:useSectorTerms
(default = on
)on
for normal runs. Setting it to off
will
set the additional gluon-collinear sector antenna term coefficients to
zero.
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.
VINCIA will ignore any externally provided scale information, such as SCALUP. For externally provided multi-parton systems, VINCIA will construct its own unique scales directly from the parton system.
The reasoning behind this is that any externally provided scales are not guaranteed to be compatible with those used by VINCIA, neither in functional form nor in normalization. The exception to this is if the event was generated by VINCIA itself, in which case the correct scales will be reconstructed from the momenta.
Any more complete implementation of external scales should be implemented via PYTHIA's UserHooks interface, using the proper definition of the scale defined by the external program.
For the shower implementation, see the VINCIA Authors' Compendium for relevant definitions, phase-space limits, trial functions, integrals, etc.