Evolution and Ordering Strategies

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.

Evolution Variable

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:

with the 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

with the normalization factor ND specified below.

Evolution Variable: Phase-Space Contours

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:

Type1 Type2

Evolution Variable: Normalization Factors

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)
Flag to switch conversion from external PT scales to VINCIA's internal normalizations on/off.

parm  Vincia:pTnormalization   (default = 4; minimum = 1; maximum = 4)
Normalization factor 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)
Normalization factor 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).

Ordering Mode

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.

Global Showers

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)
This decides if and how ordering in the evolution variable is imposed on newly created dipole-antennae after a branching.
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

where the hatted QE is the evolution scale evaluated on the pre-branching configuration (for branchings with more than one possible history, QEhat is the smallest of the corresponding evolution scales), and QE is the scale of the next branching. This removes most of the beyond-LL overcounting that would be obtained with option without any ordering at all (option 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

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)
Switch for the additional gluon-collinear terms that should be added in the sector approach. Should be 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.

Use of External Scales

flag  Vincia:useCreationScales   (default = on)
Sets whether to use "creation scale" information from the matrix element as an upper bound on the evolution variable for showering. Not required for VINCIA's internal matching, but can be useful when using VINCIA's showers with alternative matching schemes relying on externally generated matrix-element-level events.

parm  Vincia:pTmaxFudge   (default = 1.0)
Copy of the PYTHIA 8 parameter 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.

Phase-Space Variables, Limits, and Jacobians

For the shower implementation, see the VINCIA Authors' Compendium for relevant definitions, phase-space limits, trial functions, integrals, etc.